| Title: | Expiry Estimation Procedures |
|---|---|
| Description: | The Australian Regulatory Guidelines for Prescription Medicines (ARGPM), guidance on "Stability testing for prescription medicines", recommends to predict the shelf life of chemically derived medicines from stability data by taking the worst case situation at batch release into account. Consequently, if a change over time is observed, a release limit needs to be specified. Finding a release limit and the associated shelf life is supported, as well as the standard approach that is recommended by guidance Q1E "Evaluation of stability data" from the International Council for Harmonisation (ICH). |
| Authors: | Pius Dahinden [aut, cre], Tillotts Pharma AG [cph, fnd] |
| Maintainer: | Pius Dahinden <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 0.1.7.9000 |
| Built: | 2025-02-25 08:26:02 UTC |
| Source: | https://github.com/piusdahinden/expirest |
A data set containing the potency stability data (in % of label claim (LC))
of five batches of a drug product obtained over a 24 months period. A total
of independent measurements are available (corresponding to
data shown in Tables IV, VI and VIII in LeBlond et al. (2011)). Data in
Table IV (batches b2, b5 and b7) are compatible with a
common intercept / common slope (cics) model, data in Table VI (batches
b3, b4 and b5) with a different intercept / common slope
(dics) model and data in Table VIII (bathes b4, b5 and
b8) with a different intercept / different slope (dids) model.
data(exp1)data(exp1)
A data frame with 53 observations and 3 variables:
Factor with levels b2, b3, b4, b5,
b7 and b8
Numeric representing the time points of testing from the start (0 months) to the end (24 months) of the study.
Numeric of the measured potency values in %LC
See reference: Example data sets shown in Tables IV, VI and VIII.
LeBlond, D., Griffith, D. and Aubuchon, K. Linear Regression 102: Stability Shelf Life Estimation Using Analysis of Covariance. J Valid Technol (2011) 17(3): 47-68.
str(exp1)str(exp1)
A data set containing the related substance stability data (in % of label
claim (LC)) of three batches of a drug product obtained over a 24 months
period. A total of independent measurements are available
(corresponding to data shown in Table XI in LeBlond et al. (2011)).
data(exp2)data(exp2)
A data frame with 48 observations and 3 variables:
Factor with levels b4, b5 and b8
Numeric representing the time points of testing from the start (0 months) to the end (24 months) of the study.
Numeric of the measured related substance levels in %LC
See reference: Example data sets shown in Table XI.
LeBlond, D., Griffith, D. and Aubuchon, K. Linear Regression 102: Stability Shelf Life Estimation Using Analysis of Covariance. J Valid Technol (2011) 17(3): 47-68.
str(exp2)str(exp2)
A data set containing the moisture stability data (% (w/w)) of three
batches of a drug product obtained over a 24 months period. A total of
independent measurements are available (corresponding to data
shown in Table XIII in LeBlond et al. (2011)).
data(exp3)data(exp3)
A data frame with 33 observations and 3 variables:
Factor with levels b1, b2 and b3
Numeric representing the time points of testing from the start (0 months) to the end (24 months) of the study.
Numeric of the measured moisture levels %(w/w)
See reference: Example data sets shown in Table XIII.
LeBlond, D., Griffith, D. and Aubuchon, K. Linear Regression 102: Stability Shelf Life Estimation Using Analysis of Covariance. J Valid Technol (2011) 17(3): 47-68.
str(exp3)str(exp3)
A data set containing the concentration data (mg/kg) of four batches
obtained over a 24 months period of a drug product. A total of
independent measurements are available (corresponding to the data set
Reliability/Stability.jmp in JMP(R) 12 Reliability and Survival
Methods manual).
data(exp4)data(exp4)
A data frame with 36 observations and 3 variables:
Factor with levels 1_11, 2_12, 3_13 and
4_14.
Numeric representing the time points of testing from the start (0 months) to the end (24 months) of the study.
Numeric of the measured concentrations in .
See reference: Example data set (Stability.jmp) used in chapter Stability Analysis, p. 174-176.
SAS Institute Inc. 2015. JMP(R) 12 Reliability and Survival Methods. Cary, NC: SAS Institute Inc.
str(exp4)str(exp4)
Based on a linear regression model fitted to a stability data set the
function expirest_osle() estimates the shelf life, or retest period,
following the ICH Q1E guideline. The abbreviation “osle” stands for
“ordinary shelf life estimation”.
expirest_osle( data, response_vbl, time_vbl, batch_vbl, sl, sl_sf, srch_range, alpha = 0.05, alpha_pool = 0.25, xform = c("no", "no"), shift = c(0, 0), sf_option = "tight", ivl = "confidence", ivl_type = "one.sided", ivl_side = "lower", ... )expirest_osle( data, response_vbl, time_vbl, batch_vbl, sl, sl_sf, srch_range, alpha = 0.05, alpha_pool = 0.25, xform = c("no", "no"), shift = c(0, 0), sf_option = "tight", ivl = "confidence", ivl_type = "one.sided", ivl_side = "lower", ... )
data |
A data frame with the columns specified by |
response_vbl |
A character string that specifies the response variable
name that must be a column of |
time_vbl |
A character string that specifies the time variable name
that must be a column of |
batch_vbl |
A character string that specifies the column in |
sl |
A numeric value or a numeric vector of length |
sl_sf |
A positive integer or a vector of positive integers that
specifies the number of “significant figures” (sf) of |
srch_range |
A vector of length |
alpha |
A numeric value between 0 and 1 that specifies the significance
level for the calculation of confidence or prediction intervals. The
default is |
alpha_pool |
A numeric value between 0 and 1 that specifies the type I
error rate for the test of the poolability of the batches. The default
is |
xform |
A vector of two character strings that specifies the
transformation of the response and the time variable. The default is
“no” transformation, i.e. |
shift |
A vector of two values which will be added to the variables
|
sf_option |
A character string that specifies if the limits ( |
ivl |
A character string of either |
ivl_type |
A character string that specifies if a “one sided”
or a “two sided” interval should be calculated, i.e. either
|
ivl_side |
A character string that specifies if the specification
limit, given that the limit has only one side, is an “upper” or a
“lower” bound, i.e. it is specified as either |
... |
Additional named or unnamed arguments passed on to
|
According to ICH Q1E guideline, “an appropriate approach to retest period or shelf life estimation is to analyse a quantitative attribute by determining the earliest time at which the 95 percent confidence limit for the mean intersects the proposed acceptance criterion” (in this package, this point is called the “point of intersection” (POI)). Furthermore, it says that “for an attribute known to increase with time, the upper one-sided 95 percent confidence limit should be compared to the acceptance criterion. For an attribute that can either increase or decrease, or whose direction of change is not known, two-sided 95 percent confidence limits should be calculated and compared to the upper and lower acceptance criteria.” The approach can be used to estimate the retest period or shelf life for a single batch or for multiple batches. According to the guideline, “for a drug substance or for a drug product available in a single strength and a single container size and/or fill, the retest period or shelf life is generally estimated based on the stability data from a minimum of three batches.”
Before performing the retest period or shelf life estimation with results from multiple batches, the most suitable model should be determined. It should particularly be verified if data of all test batches are poolable or not. Details on this are described in section “Checking batch poolability” below.
An object of class ‘expirest_osle’ is returned,
containing the following elements:
Data |
Data frame of the original data including new columns with transformed variables, if applicable. |
Parameters |
A list of the parameters with the elements |
Variables |
A list of the variable names, i.e. the original names of
|
Model.Type |
A list of two elements that specifies which model, based
on the ANCOVA analysis, suits best. The first element ( |
Models |
A list of four elements named |
AIC |
A numeric named vector of the Akaike Information Criterion (AIC)
values of the |
BIC |
A numeric named vector of the Bayesian Information Criterion (BIC)
values of each of the |
wc.icpt |
A numeric named vector of the worst case intercepts. The
information about which limit the corresponding confidence interval
crosses is stored in the attribute named |
wc.batch |
A numeric named vector of the batches with the worst case
intercepts. The information about which limit the corresponding confidence
interval crosses is stored in the attribute named |
Limits |
A list of all limits. |
Intercepts |
A list of the intercepts of all models. |
All.POI |
A list of two elements named |
POI |
A numeric named vector of the POI values of the worst case
batches of each model. The information about which limit the corresponding
confidence interval crosses is stored in the attribute named |
According to ICH Q1E guideline, construction of the 95% confidence interval
on the basis of the combined data of all test batches is allowed only if it
has been confirmed by aid of a statistical test whether the regression lines
from the different batches have a common slope and a common intercept. A
significance level of alpha_pool = 0.25 should to be used for both
batch-related terms, and the test of the slopes has to precede the test of
the intercepts. From these tests, three possible models may be appropriate,
i.e.
a common intercept / common slope model (cics),
a different intercept / common slope model (dics) or
a different intercept / different slope model (dids).
The common intercept / different slope model (cids) is of limited practical relevance because the corresponding model is missing an effect. When slopes exhibit significant differences, comparing intercepts becomes inconsequential. Moreover, while initial levels of different batches in a manufacturing process might be relatively well-controlled, it is improbable that these levels are identical. Consequently, if the model probabilities associated with the intercepts and slopes suggest the appropriateness of the cids model, the decision is taken in favour of a dids model. The dids model has individual intercepts and individual slopes, and the calculation of confidence intervals is based on the corresponding individual mean square errors. The different intercept / different slope model where the mean square error is pooled across batches is reported as dids.pmse.
These requirements can be checked by aid of an “ANalysis of
COVAriance” (ANCOVA) including the batch variable as main effect and as
interaction term. The full ANCOVA model
simultaneously tests all the effects, and non-significant effects can be
identified and removed for fitting of the final regression model that is
used for the estimation of the shelf life or retest period.
The significance level (alpha_pool = 0.25, Type I error) is used to
increase the power of the test to detect cases where the data should not be
pooled. Setting alpha_pool = 0.25 decreases the probability of
incorrectly concluding that stability data from multiple batches can be
pooled. On the other hand, though, it increases the probability of using a
single batch to determine expiry when pooling batches would be more
appropriate.
International Council for Harmonisation of Technical Requirements for Registration of Pharmaceuticals for Human (ICH), Harmonised Tripartite Guideline, Evaluation of Stability Data Q1E, step 4, February 2003 (CPMP/ICH/420/02).
expirest_wisle, plot_expirest_wisle,
uniroot, lm,
AIC, BIC.
# Successful estimations # A model with common intercepts / common slopes (cics) res1 <- expirest_osle(data = exp1[exp1$Batch %in% c("b2", "b5", "b7"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") res1$Model.Type res1$POI # Expected results in res1$Model.Type # $type.spec # common.icpt common.slp # 1 1 # # $type.acronym # [1] "cics" # Expected results in res1$POI # cics dics dids.pmse dids # 26.22410 24.80030 23.66724 23.34184 # attr(,"side") # cics dics dids.pmse dids # "lower" "lower" "lower" "lower" # The parameter settings sf_option = "loose" and ivl_side = "lower" (the # default setting of ivl_side) cause the specification limit of 95.0 # (sl_sf = 3, i.e. 3 significant digits) to be reduced by 0.05, i.e. the # actual specification limit is 94.95. # A model with different intercepts / different slopes (dids) res2 <- expirest_osle(data = exp1[exp1$Batch %in% c("b4", "b5", "b8"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") res2$Model.Type res2$POI # Expected results in res2$Model.Type # $type.spec # common.icpt common.slp # 0 0 # # $type.acronym # [1] "dids" # Expected results in res2$POI # cics dics dids.pmse dids # 28.12518 22.47939 15.72348 15.96453 # attr(,"side") # cics dics dids.pmse dids # "lower" "lower" "lower" "lower" # Estimation where it is not know a priori which limit is crossed first, i.e. # letting the estimation be done for both specification limits. res3 <- expirest_osle( data = exp3, response_vbl = "Moisture", time_vbl = "Month", batch_vbl = "Batch", sl = c(1.5, 3.5), sl_sf = c(2, 2), srch_range = c(0, 500), sf_option = "loose", ivl = "confidence", ivl_type = "two.sided", ivl_side = "both") res3$Model.Type res3$POI # Expected results in res3$Model.Type # $type.spec # common.icpt common.slp # 1 1 # # $type.acronym # [1] "cics" # Expected results in res3$POI # cics dics dids.pmse dids # 46.85172 41.84802 22.41808 22.50966 # attr(,"side") # cics dics dids.pmse dids # "upper" "upper" "upper" "lower" # The parameter settings sf_option = "loose" and ivl_side = "both" (the # default setting of ivl_side) cause the specification limits of 1.5 and 3.5 # (sl_sf = 2, i.e. 2 significant digits) to be reduced by 0.05 and increased # by 0.04, respectively, i.e. the actual specification limits are 1.45 and # 3.54, respectively. # Analysis with a single batch res4 <- expirest_osle( data = exp3[exp3$Batch == "b1", ], response_vbl = "Moisture", time_vbl = "Month", batch_vbl = "Batch", sl = c(1.5, 3.5), sl_sf = c(2, 2), srch_range = c(0, 500), sf_option = "tight", ivl = "confidence", ivl_type = "two.sided", ivl_side = "both") # Since only one batch is involved there is no model type. Nevertheless, the # result is reported under the dids model name. res4$Model.Type res4$POI # Expected results in res4$Model.Type # $type.spec # common.icpt common.slp # NA NA # # $type.acronym # [1] "n.a." # Expected results in res4$POI # cics dics dids.pmse dids # NA NA NA 21.42596 # attr(,"side") # cics dics dids.pmse dids # "NA" "NA" "NA" "lower" # Unsuccessful estimations ## Not run: # Intervals are wider than the specification limits (no intersection). res5 <- expirest_osle( data = exp3, response_vbl = "Moisture", time_vbl = "Month", batch_vbl = "Batch", sl = 1.5, sl_sf = 2, srch_range = c(0, 500), sf_option = "tight", ivl = "prediction", ivl_type = "two.sided", ivl_side = "lower") res5$POI # (Expected) results in res5$POI # cics dics dids.pmse dids # NA NA NA NA # attr(,"side") # cics dics dids.pmse dids # "lower" "lower" "lower" "lower" # Estimation may also fail because of an inappropriate 'srch_range' setting. res6 <- expirest_osle(data = exp1[exp1$Batch %in% c("b2", "b5", "b7"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", sl = 95, sl_sf = 3, srch_range = c(0, 5)) res6$POI # (Expected) results in res6$POI # cics dics dids.pmse dids # NA NA NA NA # attr(,"side") # cics dics dids.pmse dids # "lower" "lower" "lower" "lower" ## End(Not run)# Successful estimations # A model with common intercepts / common slopes (cics) res1 <- expirest_osle(data = exp1[exp1$Batch %in% c("b2", "b5", "b7"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") res1$Model.Type res1$POI # Expected results in res1$Model.Type # $type.spec # common.icpt common.slp # 1 1 # # $type.acronym # [1] "cics" # Expected results in res1$POI # cics dics dids.pmse dids # 26.22410 24.80030 23.66724 23.34184 # attr(,"side") # cics dics dids.pmse dids # "lower" "lower" "lower" "lower" # The parameter settings sf_option = "loose" and ivl_side = "lower" (the # default setting of ivl_side) cause the specification limit of 95.0 # (sl_sf = 3, i.e. 3 significant digits) to be reduced by 0.05, i.e. the # actual specification limit is 94.95. # A model with different intercepts / different slopes (dids) res2 <- expirest_osle(data = exp1[exp1$Batch %in% c("b4", "b5", "b8"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") res2$Model.Type res2$POI # Expected results in res2$Model.Type # $type.spec # common.icpt common.slp # 0 0 # # $type.acronym # [1] "dids" # Expected results in res2$POI # cics dics dids.pmse dids # 28.12518 22.47939 15.72348 15.96453 # attr(,"side") # cics dics dids.pmse dids # "lower" "lower" "lower" "lower" # Estimation where it is not know a priori which limit is crossed first, i.e. # letting the estimation be done for both specification limits. res3 <- expirest_osle( data = exp3, response_vbl = "Moisture", time_vbl = "Month", batch_vbl = "Batch", sl = c(1.5, 3.5), sl_sf = c(2, 2), srch_range = c(0, 500), sf_option = "loose", ivl = "confidence", ivl_type = "two.sided", ivl_side = "both") res3$Model.Type res3$POI # Expected results in res3$Model.Type # $type.spec # common.icpt common.slp # 1 1 # # $type.acronym # [1] "cics" # Expected results in res3$POI # cics dics dids.pmse dids # 46.85172 41.84802 22.41808 22.50966 # attr(,"side") # cics dics dids.pmse dids # "upper" "upper" "upper" "lower" # The parameter settings sf_option = "loose" and ivl_side = "both" (the # default setting of ivl_side) cause the specification limits of 1.5 and 3.5 # (sl_sf = 2, i.e. 2 significant digits) to be reduced by 0.05 and increased # by 0.04, respectively, i.e. the actual specification limits are 1.45 and # 3.54, respectively. # Analysis with a single batch res4 <- expirest_osle( data = exp3[exp3$Batch == "b1", ], response_vbl = "Moisture", time_vbl = "Month", batch_vbl = "Batch", sl = c(1.5, 3.5), sl_sf = c(2, 2), srch_range = c(0, 500), sf_option = "tight", ivl = "confidence", ivl_type = "two.sided", ivl_side = "both") # Since only one batch is involved there is no model type. Nevertheless, the # result is reported under the dids model name. res4$Model.Type res4$POI # Expected results in res4$Model.Type # $type.spec # common.icpt common.slp # NA NA # # $type.acronym # [1] "n.a." # Expected results in res4$POI # cics dics dids.pmse dids # NA NA NA 21.42596 # attr(,"side") # cics dics dids.pmse dids # "NA" "NA" "NA" "lower" # Unsuccessful estimations ## Not run: # Intervals are wider than the specification limits (no intersection). res5 <- expirest_osle( data = exp3, response_vbl = "Moisture", time_vbl = "Month", batch_vbl = "Batch", sl = 1.5, sl_sf = 2, srch_range = c(0, 500), sf_option = "tight", ivl = "prediction", ivl_type = "two.sided", ivl_side = "lower") res5$POI # (Expected) results in res5$POI # cics dics dids.pmse dids # NA NA NA NA # attr(,"side") # cics dics dids.pmse dids # "lower" "lower" "lower" "lower" # Estimation may also fail because of an inappropriate 'srch_range' setting. res6 <- expirest_osle(data = exp1[exp1$Batch %in% c("b2", "b5", "b7"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", sl = 95, sl_sf = 3, srch_range = c(0, 5)) res6$POI # (Expected) results in res6$POI # cics dics dids.pmse dids # NA NA NA NA # attr(,"side") # cics dics dids.pmse dids # "lower" "lower" "lower" "lower" ## End(Not run)
Based on a linear regression model fitted to a stability data set the
function expirest_wisle() estimates the shelf life, or retest period,
for the specified release and specification limit following the ARGPM
guidance “Stability testing for prescription medicines”. The
abbreviation “wisle” stands for “what-if shelf life estimation”
(because it estimates the shelf life (“what”) for a given release
limit (“if”)).
expirest_wisle( data, response_vbl, time_vbl, batch_vbl, rl, rl_sf, sl, sl_sf, srch_range, alpha = 0.05, alpha_pool = 0.25, xform = c("no", "no"), shift = c(0, 0), sf_option = "tight", ivl = "confidence", ivl_type = "one.sided", ivl_side = "lower", ... )expirest_wisle( data, response_vbl, time_vbl, batch_vbl, rl, rl_sf, sl, sl_sf, srch_range, alpha = 0.05, alpha_pool = 0.25, xform = c("no", "no"), shift = c(0, 0), sf_option = "tight", ivl = "confidence", ivl_type = "one.sided", ivl_side = "lower", ... )
data |
A data frame with the columns specified by |
response_vbl |
A character string that specifies the response variable
name that must be a column of |
time_vbl |
A character string that specifies the time variable name
that must be a column of |
batch_vbl |
A character string that specifies the column in |
rl |
A numeric value or a numeric vector that specifies the release specification limit(s) for which the corresponding expiry should be estimated. |
rl_sf |
A positive integer or a vector of positive integers that
specifies the number of “significant figures” (sf) of |
sl |
A numeric value or a numeric vector of length |
sl_sf |
A positive integer or a vector of positive integers that
specifies the number of “significant figures” (sf) of |
srch_range |
A vector of length |
alpha |
A numeric value between 0 and 1 that specifies the significance
level for the calculation of confidence or prediction intervals. The
default is |
alpha_pool |
A numeric value between 0 and 1 that specifies the type I
error rate for the test of the poolability of the batches. The default
is |
xform |
A vector of two character strings that specifies the
transformation of the response and the time variable. The default is
“no” transformation, i.e. |
shift |
A vector of two values which will be added to the variables
|
sf_option |
A character string that specifies if the limits ( |
ivl |
A character string of either |
ivl_type |
A character string that specifies if a “one sided”
or a “two sided” interval should be calculated, i.e. either
|
ivl_side |
A character string that specifies if the “upper” or
the “lower” limit is the relevant limit, i.e. either |
... |
Additional named or unnamed arguments passed on to
|
For the shelf life estimation for submissions in Australia the Australian Regulatory Guidelines for Prescription Medicines (ARGPM), i.e. the guidance “Stability testing for prescription medicines”, is binding. In chapter 14.3.1, “Predicting shelf life from stability data”, it is described how the estimation should be done. It recommends to take the worst case situation at batch release into account. The following examples are listed:
For medicine that has a lower Assay release limit of 95 per cent and a lower assay expiry limit of 90 per cent, the maximum decrease in assay allowed over the shelf-life is 5 per cent.
Similarly, for a medicine that has a release limit for an individual impurity of 0.2 per cent and an expiry limit of 0.5 per cent, the maximum increase in the impurity allowed over the shelf life is 0.3 per cent.
For the same medicine, if the actual release assay result is 101 per cent, then the shelf life should be determined at the time the medicine (or confidence interval of the regression line) decreases by 5 per cent and reaches 96 per cent, rather than the expiry limit (90 per cent). This takes into account the possibility of batches being released at the lower release limit (i.e. 95 per cent) and ensures they will comply with the expiry limit throughout the shelf life.
Similarly, if the actual impurity content is 0.1 per cent at batch release, the shelf life should be determined as the time the 95 per cent confidence interval reaches 0.4 per cent (i.e. increases by 0.3 per cent).
Consequently, it is necessary to define
a release limit and
an expiry limit or shelf life limit (usually the specification limit).
If both of these limits were the same the shelf life would be zero, i.e. no
change allowed.
For the estimation of the shelf life or expiry limit it is necessary to find
the point where the upper or lower 95% confidence interval limit of the
linear model fitted to the data (by aid of lm) intersects the
“worst case scenario limit” (WCSL), which is defined by the ARGPM
guidance “Stability testing for prescription medicines” as the
intercept difference between the specification limit and the
release limit, where this differences is added () if the upper limit
is relevant or it is subtracted () if the lower limit is relevant.
In this package, this point is called the “point of intersection” or
“point of interest”, abbreviated POI.
Before performing the retest period or shelf life estimation the most suitable model should be determined. It should particularly be verified if data of all test batches are poolable or not. Details on this are described in section “Checking batch poolability” below.
An object of class ‘expirest_wisle’ is returned,
containing the following elements:
Data |
Data frame of the original data including new columns with transformed variables, if applicable. |
Parameters |
A list of the parameters with the elements |
Variables |
A list of the variable names, i.e. the original names of
|
Model.Type |
A list of two elements that specifies which model, based
on the ANCOVA analysis, suits best. The first element ( |
Models |
A list of four elements named |
AIC |
A numeric named vector of the Akaike Information Criterion (AIC)
values of the |
BIC |
A numeric named vector of the Bayesian Information Criterion (BIC)
values of each of the |
wc.icpt |
A data frame of the worst case intercepts of each of the four fitted models. |
wc.batch |
A list of numeric value(s) of the worst case batch(es) per model type. |
Limits |
A list of all limits. |
POI |
A data frame of the intercepts, the differences between release and shelf life limits, the WCSLs, the expiry and release specification limits, the shelf lives and POI values. |
Structure of the POI data frame:
Intercept.cics |
The intercept of the worst case batch of the cics model. |
Intercept.dics |
The intercept of the worst case batch of the dics model. |
Intercept.dids.pmse |
The intercept of the worst case batch of the dids model with pooled mean square error (pmse). |
Intercept.dids |
The intercept of the worst case batch of the dids model obtained by fitting individual models to the data of each batch. |
Delta.cics |
Absolute difference between the release and and the shelf life specification of the cics model. |
Delta.dics |
Absolute difference between the release and and the shelf life specification of the dics model. |
Delta.dids.pmse |
Absolute difference between the release and and the shelf life specification of the dids model with pooled mean square error (pmse). |
Delta.dids |
Absolute difference between the release and and the shelf life specification of the dids model obtained by fitting individual models to the data of each batch. |
WCSL.cics |
WCSL of the cics model. |
WCSL.dics |
WCSL of the dics model. |
WCSL.dids.pmse |
WCSL of the dids model with pooled mean square error (pmse). |
WCSL.dids |
WCSL of the dids model obtained by fitting individual models to the data of each batch. |
Exp.Spec |
The (expiry) specification, i.e. the specification which is relevant for the determination of the expiry. |
Rel.Spec |
The calculated release specification. |
Shelf.Life.cics |
The estimated shelf life of the cics model. |
Shelf.Life.dics |
The estimated shelf life of the dics model. |
Shelf.Life.dids.pmse |
The estimated shelf life of the dids model with pooled mean square error (pmse). |
Shelf.Life.dids |
The estimated shelf life of the dids model obtained by fitting individual models to the data of each batch. |
POI.Model.cics |
The POI of the cics model. |
POI.Model.dics |
The POI of the dics model. |
POI.Model.dids.pmse |
The POI of the dids model with pooled mean square error (pmse). |
POI.Model.dids |
The POI of the dids model obtained by fitting individual models to the data of each batch. |
According to ICH Q1E guideline, construction of the 95% confidence interval
on the basis of the combined data of all test batches is allowed only if it
has been confirmed by aid of a statistical test whether the regression lines
from the different batches have a common slope and a common intercept. A
significance level of alpha_pool = 0.25 should to be used for both
batch-related terms, and the test of the slopes has to precede the test of
the intercepts. From these tests, three possible models may be appropriate,
i.e.
a common intercept / common slope model (cics),
a different intercept / common slope model (dics) or
a different intercept / different slope model (dids).
The common intercept / different slope model (cids) is of limited practical relevance because the corresponding model is missing an effect. When slopes exhibit significant differences, comparing intercepts becomes inconsequential. Moreover, while initial levels of different batches in a manufacturing process might be relatively well-controlled, it is improbable that these levels are identical. Consequently, if the model probabilities associated with the intercepts and slopes suggest the appropriateness of the cids model, the decision is taken in favour of a dids model. The dids model has individual intercepts and individual slopes, and the calculation of confidence intervals is based on the corresponding individual mean square errors. The different intercept / different slope model where the mean square error is pooled across batches is reported as dids.pmse.
These requirements can be checked by aid of an “ANalysis of
COVAriance” (ANCOVA) including the batch variable as main effect and as
interaction term. The full ANCOVA model
simultaneously tests all the effects, and non-significant effects can be
identified and removed for fitting of the final regression model that is
used for the estimation of the shelf life or retest period.
The significance level (alpha_pool = 0.25, Type I error) is used to
increase the power of the test to detect cases where the data should not be
pooled. Setting alpha_pool = 0.25 decreases the probability of
incorrectly concluding that stability data from multiple batches can be
pooled. On the other hand, though, it increases the probability of using a
single batch to determine expiry when pooling batches would be more
appropriate.
Therapeutic Goods Administration (TGA) of the Department of Health of the Australian Government, Australian Regulatory Guidelines for Prescription Medicines (ARGPM), Stability testing for prescription medicines, Version 1.1, March 2017
International Council for Harmonisation of Technical Requirements for Registration of Pharmaceuticals for Human (ICH), Harmonised Tripartite Guideline, Evaluation of Stability Data Q1E, step 4, February 2003 (CPMP/ICH/420/02).
expirest_osle, plot_expirest_wisle,
uniroot, lm,
AIC, BIC.
# Successful estimations # A model with common intercepts / common slopes (cics) res1 <- expirest_wisle(data = exp1[exp1$Batch %in% c("b2", "b5", "b7"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", rl = 98, rl_sf = 3, sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") res1$Model.Type res1$POI # Expected results in res1$Model.Type # $type.spec # common.icpt common.slp # 1 1 # # $type.acronym # [1] "cics" # (Expected) results in res1$POI # Intercept.cics Intercept.dics Intercept.dids Intercept.dids.pmse Delta.cics # 100.5669 100.3638 100.2491 100.2491 3 # Delta.dics Delta.dids Delta.dids.pmse WCSL.cics WCSL.dics WCSL.dids # 3 3 3 97.56688 97.36375 97.24914 # WCSL.dids.pmse Exp.Spec.Report Exp.Spec Rel.Spec.Report Rel.Spec # 97.24914 95 94.95 98 97.95 # Shelf.Life.cics Shelf.Life.dics Shelf.Life.dids Shelf.Life.dids.pmse # 14.07398 13.23176 13.34561 13.80695 # POI.Model.cics POI.Model.dics POI.Model.dids POI.Model.dids.pmse # 26.2241 24.8003 23.34184 23.66724 # The parameter settings sf_option = "loose" and ivl_side = "lower" (the # default setting of ivl_side) cause the specification limit of 95.0 # (sl_sf = 3, i.e. 3 significant digits) to be reduced by 0.05, i.e. the # actual specification limit is 94.95. Analogously, the release limit of 98.0 # is reduced to 97.95. # A model with different intercepts / different slopes (dids) res2 <- expirest_wisle(data = exp1[exp1$Batch %in% c("b4", "b5", "b8"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", rl = 98, rl_sf = 3, sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") res2$Model.Type res2$POI # Expected results in res2$Model.Type # $type.spec # common.icpt common.slp # 0 0 # # $type.acronym # [1] "dids" # (Expected) results in res2$POI # Intercept.cics Intercept.dics Intercept.dids Intercept.dids.pmse Delta.cics # 101.5498 100.4882 101.2594 101.2594 3 # Delta.dics Delta.dids Delta.dids.pmse WCSL.cics WCSL.dics WCSL.dids # 3 3 3 98.54976 97.48822 98.25938 # WCSL.dids.pmse Exp.Spec.Report Exp.Spec Rel.Spec.Report Rel.Spec # 98.25938 95 94.95 98 97.95 # Shelf.Life.cics Shelf.Life.dics Shelf.Life.dids Shelf.Life.dids.pmse # 13.03332 11.42141 7.619661 7.483223 # POI.Model.cics POI.Model.dics POI.Model.dids POI.Model.dids.pmse # 28.12518 22.47939 15.96453 15.72348 # Analysis with a single batch (i.e. the worst case batch of res2 above) res3 <- expirest_wisle(data = exp1[exp1$Batch == "b8", ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", rl = 98, rl_sf = 3, sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") res3$Model.Type res3$POI # Since only one batch is involved there is no model type. Nevertheless, the # result is reported under the dids model name. # Expected results in res3$Model.Type # $type.spec # common.icpt common.slp # NA NA # # $type.acronym # [1] "n.a." # (Expected) results in res3$POI # Intercept.cics Intercept.dics Intercept.dids Intercept.dids.pmse Delta.cics # NA NA 101.2594 NA NA # Delta.dics Delta.dids Delta.dids.pmse WCSL.cics WCSL.dics WCSL.dids # NA 3 NA NA NA 98.25938 # WCSL.dids.pmse Exp.Spec.Report Exp.Spec Rel.Spec.Report Rel.Spec # NA 95 94.95 98 97.95 # Shelf.Life.cics Shelf.Life.dics Shelf.Life.dids Shelf.Life.dids.pmse # NA NA 7.619661 NA # POI.Model.cics POI.Model.dics POI.Model.dids POI.Model.dids.pmse # NA NA 15.96453 NA # Unsuccessful estimation ## Not run: # The interval does not cross the limit (i.e. not within srch_range). res4 <- expirest_wisle(data = exp1[exp1$Batch %in% c("b2", "b5", "b7"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", rl = 98, rl_sf = 3, sl = 105, sl_sf = 4, srch_range = c(0, 500), sf_option = "loose", ivl_side = "upper") res4$POI # (Expected) results in res3$POI # Intercept.cics Intercept.dics Intercept.dids Intercept.dids.pmse Delta.cics # 100.5669 NA NA NA 3 # Delta.dics Delta.dids Delta.dids.pmse WCSL.cics WCSL.dics WCSL.dids # NA NA NA 107.5669 NA NA # WCSL.dids.pmse Exp.Spec.Report Exp.Spec Rel.Spec.Report Rel.Spec # NA 105 105.04 98 98.04 # Shelf.Life.cics Shelf.Life.dics Shelf.Life.dids Shelf.Life.dids.pmse # NA NA NA NA # POI.Model.cics POI.Model.dics POI.Model.dids POI.Model.dids.pmse # NA NA NA NA # Estimation may also fail because of an inappropriate 'srch_range' setting. res5 <- expirest_wisle(data = exp1[exp1$Batch %in% c("b2", "b5", "b7"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", rl = 98, rl_sf = 3, sl = 95, sl_sf = 3, srch_range = c(0, 5), sf_option = "loose") res5$POI # (Expected) results in res4$POI # Intercept.cics Intercept.dics Intercept.dids Intercept.dids.pmse Delta.cics # 100.5669 NA NA NA 3 # Delta.dics Delta.dids Delta.dids.pmse WCSL.cics WCSL.dics WCSL.dids # NA NA NA 97.56688 NA NA # WCSL.dids.pmse Exp.Spec.Report Exp.Spec Rel.Spec.Report Rel.Spec # NA 95 94.95 98 97.95 # Shelf.Life.cics Shelf.Life.dics Shelf.Life.dids Shelf.Life.dids.pmse # NA NA NA NA # POI.Model.cics POI.Model.dics POI.Model.dids POI.Model.dids.pmse # NA NA NA NA ## End(Not run)# Successful estimations # A model with common intercepts / common slopes (cics) res1 <- expirest_wisle(data = exp1[exp1$Batch %in% c("b2", "b5", "b7"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", rl = 98, rl_sf = 3, sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") res1$Model.Type res1$POI # Expected results in res1$Model.Type # $type.spec # common.icpt common.slp # 1 1 # # $type.acronym # [1] "cics" # (Expected) results in res1$POI # Intercept.cics Intercept.dics Intercept.dids Intercept.dids.pmse Delta.cics # 100.5669 100.3638 100.2491 100.2491 3 # Delta.dics Delta.dids Delta.dids.pmse WCSL.cics WCSL.dics WCSL.dids # 3 3 3 97.56688 97.36375 97.24914 # WCSL.dids.pmse Exp.Spec.Report Exp.Spec Rel.Spec.Report Rel.Spec # 97.24914 95 94.95 98 97.95 # Shelf.Life.cics Shelf.Life.dics Shelf.Life.dids Shelf.Life.dids.pmse # 14.07398 13.23176 13.34561 13.80695 # POI.Model.cics POI.Model.dics POI.Model.dids POI.Model.dids.pmse # 26.2241 24.8003 23.34184 23.66724 # The parameter settings sf_option = "loose" and ivl_side = "lower" (the # default setting of ivl_side) cause the specification limit of 95.0 # (sl_sf = 3, i.e. 3 significant digits) to be reduced by 0.05, i.e. the # actual specification limit is 94.95. Analogously, the release limit of 98.0 # is reduced to 97.95. # A model with different intercepts / different slopes (dids) res2 <- expirest_wisle(data = exp1[exp1$Batch %in% c("b4", "b5", "b8"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", rl = 98, rl_sf = 3, sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") res2$Model.Type res2$POI # Expected results in res2$Model.Type # $type.spec # common.icpt common.slp # 0 0 # # $type.acronym # [1] "dids" # (Expected) results in res2$POI # Intercept.cics Intercept.dics Intercept.dids Intercept.dids.pmse Delta.cics # 101.5498 100.4882 101.2594 101.2594 3 # Delta.dics Delta.dids Delta.dids.pmse WCSL.cics WCSL.dics WCSL.dids # 3 3 3 98.54976 97.48822 98.25938 # WCSL.dids.pmse Exp.Spec.Report Exp.Spec Rel.Spec.Report Rel.Spec # 98.25938 95 94.95 98 97.95 # Shelf.Life.cics Shelf.Life.dics Shelf.Life.dids Shelf.Life.dids.pmse # 13.03332 11.42141 7.619661 7.483223 # POI.Model.cics POI.Model.dics POI.Model.dids POI.Model.dids.pmse # 28.12518 22.47939 15.96453 15.72348 # Analysis with a single batch (i.e. the worst case batch of res2 above) res3 <- expirest_wisle(data = exp1[exp1$Batch == "b8", ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", rl = 98, rl_sf = 3, sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") res3$Model.Type res3$POI # Since only one batch is involved there is no model type. Nevertheless, the # result is reported under the dids model name. # Expected results in res3$Model.Type # $type.spec # common.icpt common.slp # NA NA # # $type.acronym # [1] "n.a." # (Expected) results in res3$POI # Intercept.cics Intercept.dics Intercept.dids Intercept.dids.pmse Delta.cics # NA NA 101.2594 NA NA # Delta.dics Delta.dids Delta.dids.pmse WCSL.cics WCSL.dics WCSL.dids # NA 3 NA NA NA 98.25938 # WCSL.dids.pmse Exp.Spec.Report Exp.Spec Rel.Spec.Report Rel.Spec # NA 95 94.95 98 97.95 # Shelf.Life.cics Shelf.Life.dics Shelf.Life.dids Shelf.Life.dids.pmse # NA NA 7.619661 NA # POI.Model.cics POI.Model.dics POI.Model.dids POI.Model.dids.pmse # NA NA 15.96453 NA # Unsuccessful estimation ## Not run: # The interval does not cross the limit (i.e. not within srch_range). res4 <- expirest_wisle(data = exp1[exp1$Batch %in% c("b2", "b5", "b7"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", rl = 98, rl_sf = 3, sl = 105, sl_sf = 4, srch_range = c(0, 500), sf_option = "loose", ivl_side = "upper") res4$POI # (Expected) results in res3$POI # Intercept.cics Intercept.dics Intercept.dids Intercept.dids.pmse Delta.cics # 100.5669 NA NA NA 3 # Delta.dics Delta.dids Delta.dids.pmse WCSL.cics WCSL.dics WCSL.dids # NA NA NA 107.5669 NA NA # WCSL.dids.pmse Exp.Spec.Report Exp.Spec Rel.Spec.Report Rel.Spec # NA 105 105.04 98 98.04 # Shelf.Life.cics Shelf.Life.dics Shelf.Life.dids Shelf.Life.dids.pmse # NA NA NA NA # POI.Model.cics POI.Model.dics POI.Model.dids POI.Model.dids.pmse # NA NA NA NA # Estimation may also fail because of an inappropriate 'srch_range' setting. res5 <- expirest_wisle(data = exp1[exp1$Batch %in% c("b2", "b5", "b7"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", rl = 98, rl_sf = 3, sl = 95, sl_sf = 3, srch_range = c(0, 5), sf_option = "loose") res5$POI # (Expected) results in res4$POI # Intercept.cics Intercept.dics Intercept.dids Intercept.dids.pmse Delta.cics # 100.5669 NA NA NA 3 # Delta.dics Delta.dids Delta.dids.pmse WCSL.cics WCSL.dics WCSL.dids # NA NA NA 97.56688 NA NA # WCSL.dids.pmse Exp.Spec.Report Exp.Spec Rel.Spec.Report Rel.Spec # NA 95 94.95 98 97.95 # Shelf.Life.cics Shelf.Life.dics Shelf.Life.dids Shelf.Life.dids.pmse # NA NA NA NA # POI.Model.cics POI.Model.dics POI.Model.dids POI.Model.dids.pmse # NA NA NA NA ## End(Not run)
The function plot_expirest_osle() makes a graphical display of the
shelf life estimate done by the expirest_osle() function.
plot_expirest_osle( model, show_grouping = "yes", response_vbl_unit = NULL, x_range = NULL, y_range = NULL, mtbs = "verified", plot_option = "full", ci_app = "line" )plot_expirest_osle( model, show_grouping = "yes", response_vbl_unit = NULL, x_range = NULL, y_range = NULL, mtbs = "verified", plot_option = "full", ci_app = "line" )
model |
An ‘ |
show_grouping |
'r lifecycle::badge("deprecated")'
'show_grouping = \"yes\" or \"no\"' is no longer supported. Use the
|
response_vbl_unit |
A character string that specifies the unit
associated with the response variable. The default is |
x_range |
A numeric vector of the form |
y_range |
A numeric vector of the form |
mtbs |
A character string that specifies the “model to be shown”,
i.e. either |
plot_option |
A character string of either |
ci_app |
A character string of either |
The function plot_expirest_osle() uses the data and the
information about the linear model that was used for the estimation of
the shelf life by aid of the expirest_osle() function. It
plots a graph of the time course of a parameter, a linear regression line
fitted to the data and the associated confidence or prediction interval.
In addition, it shows features of the shelf life estimation.
For plotting, the ggplot() function from the
‘ggplot2’ package is used. The various arguments can be
used to control the appearance of the plot. The ‘ggplot2’
object of the generated plot is contained in the Graph element of
the list that is returned by plot_expirest_osle() and can be
used to modify the appearance of the graph.
An object of class ‘plot_expirest_osle’ is returned
invisibly consisting of the following elements:
Model |
The ‘ |
Expiry |
A data frame of type |
Graph |
A ‘ |
Prediction |
A data frame of the predicted values. |
text |
A data frame of the text elements on the plot. |
hlines |
A data frame of the horizontal line elements on the plot. |
vlines |
A data frame of the vertical line elements on the plot. |
expirest_osle, expirest_wisle,
plot_expirest_wisle.
# Start by making an "ordinary shelf life estimation" (osle). res1 <- expirest_osle(data = exp1[exp1$Batch %in% c("b2", "b5", "b7"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") # Pass the 'expirest_osle' object on to the plot_expirest_osle() function. # This function does not produce any output. It returns a 'plot_expirest_osle' # object that is essentially an 'expirest_osle' object augmented by a 'ggplot' # object. gg1 <- plot_expirest_osle( model = res1, response_vbl_unit = "%", x_range = NULL, y_range = c(93, 105), mtbs = "verified", plot_option = "full", ci_app = "line") ## Not run: gg1 # Since the element gg1$Graph is a 'ggplot' object it can be used for further # manipulation by aid of 'ggplot2' functions. if (requireNamespace("ggplot2")) { library(ggplot2) gg1$Graph + labs(title = "Ordinary Shelf Life Estimation (OSLE)", x = "Time [months]", y = "Potency [% LC]") + scale_x_continuous(limits = c(-1, 31), breaks = seq(0, 30, 6)) } ## End(Not run) # Repeat this for a different intercept / different slope (dids) model. res2 <- expirest_osle(data = exp1[exp1$Batch %in% c("b4", "b5", "b8"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") gg2 <- plot_expirest_osle( model = res2, response_vbl_unit = "%", x_range = c(0, 43), y_range = c(83, 107), mtbs = "verified", plot_option = "full", ci_app = "ribbon") ## Not run: gg2 ## End(Not run) # In case of different intercept / different slope models, individually fit # linear models are shown by default, i.e. with the 'mtbs' parameter set # as "verified". To get the different intercept / different slope model # displayed where the mean square error is pooled across batches, i.e. the # dids.pmse model, the 'mtbs' parameter has to be set accordingly. gg3 <- plot_expirest_osle( model = res2, response_vbl_unit = "%", x_range = c(0, 43), y_range = c(83, 107), mtbs = "dids.pmse", plot_option = "full", ci_app = "ribbon") ## Not run: gg3 ## End(Not run)# Start by making an "ordinary shelf life estimation" (osle). res1 <- expirest_osle(data = exp1[exp1$Batch %in% c("b2", "b5", "b7"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") # Pass the 'expirest_osle' object on to the plot_expirest_osle() function. # This function does not produce any output. It returns a 'plot_expirest_osle' # object that is essentially an 'expirest_osle' object augmented by a 'ggplot' # object. gg1 <- plot_expirest_osle( model = res1, response_vbl_unit = "%", x_range = NULL, y_range = c(93, 105), mtbs = "verified", plot_option = "full", ci_app = "line") ## Not run: gg1 # Since the element gg1$Graph is a 'ggplot' object it can be used for further # manipulation by aid of 'ggplot2' functions. if (requireNamespace("ggplot2")) { library(ggplot2) gg1$Graph + labs(title = "Ordinary Shelf Life Estimation (OSLE)", x = "Time [months]", y = "Potency [% LC]") + scale_x_continuous(limits = c(-1, 31), breaks = seq(0, 30, 6)) } ## End(Not run) # Repeat this for a different intercept / different slope (dids) model. res2 <- expirest_osle(data = exp1[exp1$Batch %in% c("b4", "b5", "b8"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") gg2 <- plot_expirest_osle( model = res2, response_vbl_unit = "%", x_range = c(0, 43), y_range = c(83, 107), mtbs = "verified", plot_option = "full", ci_app = "ribbon") ## Not run: gg2 ## End(Not run) # In case of different intercept / different slope models, individually fit # linear models are shown by default, i.e. with the 'mtbs' parameter set # as "verified". To get the different intercept / different slope model # displayed where the mean square error is pooled across batches, i.e. the # dids.pmse model, the 'mtbs' parameter has to be set accordingly. gg3 <- plot_expirest_osle( model = res2, response_vbl_unit = "%", x_range = c(0, 43), y_range = c(83, 107), mtbs = "dids.pmse", plot_option = "full", ci_app = "ribbon") ## Not run: gg3 ## End(Not run)
The function plot_expirest_wisle() makes a graphical display of the
shelf life estimate done by the expirest_wisle() function.
plot_expirest_wisle( model, rl_index = 1, show_grouping = "yes", response_vbl_unit = NULL, x_range = NULL, y_range = NULL, scenario = "standard", mtbs = "verified", plot_option = "full", ci_app = "line" )plot_expirest_wisle( model, rl_index = 1, show_grouping = "yes", response_vbl_unit = NULL, x_range = NULL, y_range = NULL, scenario = "standard", mtbs = "verified", plot_option = "full", ci_app = "line" )
model |
An ‘ |
rl_index |
A positive integer that specifies which of the release limit
values that have been handed over to |
show_grouping |
'r lifecycle::badge("deprecated")'
'show_grouping = \"yes\" or \"no\"' is no longer supported. Use the
|
response_vbl_unit |
A character string that specifies the unit
associated with the response variable. The default is |
x_range |
A numeric vector of the form |
y_range |
A numeric vector of the form |
scenario |
A character string that specifies if the plot should be
extended (with respect to the |
mtbs |
A character string that specifies the “model to be shown”,
i.e. either |
plot_option |
A character string of either |
ci_app |
A character string of either |
The function plot_expirest_wisle() uses the data and the
information about the linear model that was used for the estimation of
the shelf life by aid of the expirest_wisle() function. It
plots a graph of the time course of a parameter, a linear regression line
fitted to the data and the associated confidence or prediction interval.
In addition, it shows features of the worst case scenario shelf life
estimation.
For plotting, the ggplot() function from the
‘ggplot2’ package is used. The various arguments can be
used to control the appearance of the plot. The ‘ggplot2’
object of the generated plot is contained in the Graph element of
the list that is returned by plot_expirest_wisle() and can be
used to modify the appearance of the graph.
An object of class ‘plot_expirest_wisle’ is returned
invisibly consisting of the following elements:
Model |
The ‘ |
Expiery |
A data frame of type |
Graph |
A ‘ |
Prediction |
A data frame of the predicted values. |
text |
A data frame of the text elements on the plot. |
hlines |
A data frame of the horizontal line elements on the plot. |
vlines |
A data frame of the vertical line elements on the plot. |
segments |
A data frame of segment line elements on the plot. |
arrow |
A data frame of arrow elements on the plot. |
expirest_wisle, expirest_osle,
plot_expirest_osle.
# Start by making a "what-if (approach for) shelf life estimation" (wisle) res1 <- expirest_wisle(data = exp1[exp1$Batch %in% c("b2", "b5", "b7"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", rl = 98, rl_sf = 3, sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") # Pass the 'expirest_wisle' object on to the plot_expirest_wisle() function. # This function does not produce any output. It returns a 'plot_expirest_wisle' # object that is essentially an 'expirest_wisle' object augmented by a 'ggplot' # object. gg1 <- plot_expirest_wisle( model = res1, rl_index = 1, response_vbl_unit = "%", x_range = NULL, y_range = c(93, 105), scenario = "standard", mtbs = "verified", plot_option = "full", ci_app = "line") ## Not run: gg1 # Since the element gg1$Graph is a 'ggplot' object it can be used for further # manipulation by aid of 'ggplot2' functions. if (requireNamespace("ggplot2")) { library(ggplot2) gg1$Graph + labs(title = "What-if Shelf Life Estimation (WISLE)", x = "Time [months]", y = "Potency [% LC]") + scale_x_continuous(limits = c(-5, 31), breaks = seq(0, 30, 6)) } ## End(Not run) # Repeat this for a different intercept / different slope (dids) model. res2 <- expirest_wisle(data = exp1[exp1$Batch %in% c("b4", "b5", "b8"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", rl = 98, rl_sf = 3, sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") gg2 <- plot_expirest_wisle( model = res2, rl_index = 1, response_vbl_unit = "%", x_range = c(0, 26), y_range = c(89, 107), scenario = "standard", mtbs = "verified", plot_option = "full", ci_app = "ribbon") ## Not run: gg2 ## End(Not run) # In case of different intercept / different slope models, individually fit # linear models are shown by default, i.e. with the 'mtbs' parameter set # as "verified". To get the different intercept / different slope model # displayed where the mean square error is pooled across batches, i.e. the # dids.pmse model, the 'mtbs' parameter has to be set accordingly. gg3 <- plot_expirest_wisle( model = res2, rl_index = 1, response_vbl_unit = "%", x_range = c(0, 26), y_range = c(89, 107), scenario = "standard", mtbs = "dids.pmse", plot_option = "full", ci_app = "ribbon") ## Not run: gg3 ## End(Not run)# Start by making a "what-if (approach for) shelf life estimation" (wisle) res1 <- expirest_wisle(data = exp1[exp1$Batch %in% c("b2", "b5", "b7"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", rl = 98, rl_sf = 3, sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") # Pass the 'expirest_wisle' object on to the plot_expirest_wisle() function. # This function does not produce any output. It returns a 'plot_expirest_wisle' # object that is essentially an 'expirest_wisle' object augmented by a 'ggplot' # object. gg1 <- plot_expirest_wisle( model = res1, rl_index = 1, response_vbl_unit = "%", x_range = NULL, y_range = c(93, 105), scenario = "standard", mtbs = "verified", plot_option = "full", ci_app = "line") ## Not run: gg1 # Since the element gg1$Graph is a 'ggplot' object it can be used for further # manipulation by aid of 'ggplot2' functions. if (requireNamespace("ggplot2")) { library(ggplot2) gg1$Graph + labs(title = "What-if Shelf Life Estimation (WISLE)", x = "Time [months]", y = "Potency [% LC]") + scale_x_continuous(limits = c(-5, 31), breaks = seq(0, 30, 6)) } ## End(Not run) # Repeat this for a different intercept / different slope (dids) model. res2 <- expirest_wisle(data = exp1[exp1$Batch %in% c("b4", "b5", "b8"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", rl = 98, rl_sf = 3, sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") gg2 <- plot_expirest_wisle( model = res2, rl_index = 1, response_vbl_unit = "%", x_range = c(0, 26), y_range = c(89, 107), scenario = "standard", mtbs = "verified", plot_option = "full", ci_app = "ribbon") ## Not run: gg2 ## End(Not run) # In case of different intercept / different slope models, individually fit # linear models are shown by default, i.e. with the 'mtbs' parameter set # as "verified". To get the different intercept / different slope model # displayed where the mean square error is pooled across batches, i.e. the # dids.pmse model, the 'mtbs' parameter has to be set accordingly. gg3 <- plot_expirest_wisle( model = res2, rl_index = 1, response_vbl_unit = "%", x_range = c(0, 26), y_range = c(89, 107), scenario = "standard", mtbs = "dids.pmse", plot_option = "full", ci_app = "ribbon") ## Not run: gg3 ## End(Not run)
This is a method for the function plot() for objects of class
‘plot_expirest_osle’.
## S3 method for class 'plot_expirest_osle' plot(x, ...)## S3 method for class 'plot_expirest_osle' plot(x, ...)
x |
An object of class ‘ |
... |
Further arguments passed to or from other methods or arguments
that can be passed down to the |
The element Graph of the ‘plot_expirest_osle’
object that is returned by the function plot_expirest_osle()
is an object of class ‘ggplot’, generated by the function
ggplot() from the ‘ggplot2’ package.
Thus, the corresponding plot method is used for plotting. Arguments
to the ggplot() function can be passed via the
... parameter.
The ‘plot_expirest_osle’ object passed to the x
parameter is returned invisibly.
expirest_osle, plot_expirest_osle,
ggplot(), methods.
# Performing an "ordinary shelf life estimation" (osle) res1 <- expirest_osle(data = exp1[exp1$Batch %in% c("b2", "b5", "b7"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") # The 'expirest_osle' object can be passed on to the plot_expirest_osle() # function. This function does not produce any output but returns a # 'plot_expirest_osle' object. ## Not run: gg1 <- plot_expirest_osle( model = res1, response_vbl_unit = "%", x_range = NULL, y_range = c(93, 105), mtbs = "verified", plot_option = "full", ci_app = "line") gg2 <- plot(gg1) # The plot() function returns the 'plot_expirest_osle' object invisibly. class(gg1) class(gg2) ## End(Not run)# Performing an "ordinary shelf life estimation" (osle) res1 <- expirest_osle(data = exp1[exp1$Batch %in% c("b2", "b5", "b7"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") # The 'expirest_osle' object can be passed on to the plot_expirest_osle() # function. This function does not produce any output but returns a # 'plot_expirest_osle' object. ## Not run: gg1 <- plot_expirest_osle( model = res1, response_vbl_unit = "%", x_range = NULL, y_range = c(93, 105), mtbs = "verified", plot_option = "full", ci_app = "line") gg2 <- plot(gg1) # The plot() function returns the 'plot_expirest_osle' object invisibly. class(gg1) class(gg2) ## End(Not run)
This is a method for the function plot() for objects of class
‘plot_expirest_wisle’.
## S3 method for class 'plot_expirest_wisle' plot(x, ...)## S3 method for class 'plot_expirest_wisle' plot(x, ...)
x |
An object of class ‘ |
... |
Further arguments passed to or from other methods or arguments
that can be passed down to the |
The element Graph of the ‘plot_expirest_wisle’
object that is returned by the function plot_expirest_wisle()
is an object of class ‘ggplot’, generated by the function
ggplot() from the ‘ggplot2’ package.
Thus, the corresponding plot method is used for plotting. Arguments
to the ggplot() function can be passed via the
... parameter.
The ‘plot_expirest_wisle’ object passed to the x
parameter is returned invisibly.
expirest_wisle, plot_expirest_wisle,
ggplot(), methods.
# Performing a "what-if (approach for) shelf life estimation" (wisle) res1 <- expirest_wisle(data = exp1[exp1$Batch %in% c("b2", "b5", "b7"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", rl = 98, rl_sf = 3, sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") # The 'expirest_wisle' object can be passed on to the plot_expirest_wisle() # function. This function does not produce any output but returns a # 'plot_expirest_wisle' object. ## Not run: gg1 <- plot_expirest_wisle( model = res1, rl_index = 1, response_vbl_unit = "%", x_range = NULL, y_range = c(93, 105), scenario = "standard", mtbs = "verified", plot_option = "full", ci_app = "line") gg2 <- plot(gg1) # The plot() function returns the 'plot_expirest_wisle' object invisibly. class(gg1) class(gg2) ## End(Not run)# Performing a "what-if (approach for) shelf life estimation" (wisle) res1 <- expirest_wisle(data = exp1[exp1$Batch %in% c("b2", "b5", "b7"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", rl = 98, rl_sf = 3, sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") # The 'expirest_wisle' object can be passed on to the plot_expirest_wisle() # function. This function does not produce any output but returns a # 'plot_expirest_wisle' object. ## Not run: gg1 <- plot_expirest_wisle( model = res1, rl_index = 1, response_vbl_unit = "%", x_range = NULL, y_range = c(93, 105), scenario = "standard", mtbs = "verified", plot_option = "full", ci_app = "line") gg2 <- plot(gg1) # The plot() function returns the 'plot_expirest_wisle' object invisibly. class(gg1) class(gg2) ## End(Not run)
This is a method for the function print() for objects of class
‘expirest_osle’.
## S3 method for class 'expirest_osle' print(x, ...)## S3 method for class 'expirest_osle' print(x, ...)
x |
An object of class ‘ |
... |
Further arguments passed to or from other methods or arguments
that can be passed down to the |
The function expirest_osle() estimates the shelf
life, or retest period, following the ICH Q1E guideline. By default, batch
poolability is checked as recommended by the guideline at a significance
level of 0.25. Other levels can be used, although not recommended, by
changing the default of the alpha_pool parameter. Three possible
models may be appropriate, i.e.
a common intercept / common slope model (cics),
a different intercept / common slope model (dics) or
a different intercept / different slope model (dids).
The worst case intercept is the intercept of the batch whose confidence
limit is the first crossing the acceptance limit. As in case of the
cics model type all batches have a common intercept and a common
confidence interval, all batches can be regarded as equally worst case. In
case of the dids model type, shelf life estimation is done using the
models obtained from fitting the data of each batch individually.
The ‘expirest_osle’ object passed to the x
parameter is returned invisibly.
expirest_osle, expirest_wisle,
formatC, methods.
# Fit models of different type res1 <- expirest_osle(data = exp1[exp1$Batch %in% c("b2", "b5", "b7"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") res2 <- expirest_osle(data = exp1[exp1$Batch %in% c("b3", "b4", "b5"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") res3 <- expirest_osle(data = exp1[exp1$Batch %in% c("b4", "b5", "b8"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") # The parameter settings sf_option = "loose" and ivl_side = "lower" (the # default setting of ivl_side) cause the specification limit of 95.0 # (sl_sf = 3, i.e. 3 significant digits) to be reduced by 0.05, i.e. the # actual specification limit is 94.95. ## Not run: res1 # Expected output of print(res1) # Summary of shelf life estimation following the ICH Q1E guideline # # The best model accepted at a significance level of 0.25 has # Common intercepts and Common slopes (acronym: cics). # # Worst case intercept: 100.5669 (Potency) # Worst case batch: NA # Estimated shelf life for cics model: 26.2241 (Month) # # Worst case intercepts, POIs and batches of all models # (Including information about the side where the confidence # interval crosses the specification boundary): # Intercept POI Side Batch # cics 100.5669 26.2241 lower NA # dics 100.3638 24.8003 lower b2 # dids.pmse 100.7819 23.66724 lower b5 # dids 100.7819 23.34184 lower b5 res2 # Expected output of print(res2) # Summary of shelf life estimation following the ICH Q1E guideline # # The best model accepted at a significance level of 0.25 has # Different intercepts and Common slopes (acronym: dics). # # Worst case intercept: 100.82 (Potency) # Worst case batch: b5 # Estimated shelf life for dics model: 23.60194 (Month) # # Worst case intercepts, POIs and batches of all models # (Including information about the side where the confidence # interval crosses the specification boundary): # Intercept POI Side Batch # cics 102.0513 29.18093 lower NA # dics 100.82 23.60194 lower b5 # dids.pmse 100.7819 22.49726 lower b5 # dids 102.3841 23.26251 lower b3 res3 # Expected output of print(res3) # Summary of shelf life estimation following the ICH Q1E guideline # # The best model accepted at a significance level of 0.25 has # Different intercepts and Different slopes (acronym: dids). # # Worst case intercept: 101.2594 (Potency) # Worst case batch: b8 # Estimated shelf life for dids model: 15.96453 (Month) # # Worst case intercepts, POIs and batches of all models # (Including information about the side where the confidence # interval crosses the specification boundary): # Intercept POI Side Batch # cics 101.5498 28.12518 lower NA # dics 100.4882 22.47939 lower b8 # dids.pmse 101.2594 15.72348 lower b8 # dids 101.2594 15.96453 lower b8 ## End(Not run)# Fit models of different type res1 <- expirest_osle(data = exp1[exp1$Batch %in% c("b2", "b5", "b7"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") res2 <- expirest_osle(data = exp1[exp1$Batch %in% c("b3", "b4", "b5"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") res3 <- expirest_osle(data = exp1[exp1$Batch %in% c("b4", "b5", "b8"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") # The parameter settings sf_option = "loose" and ivl_side = "lower" (the # default setting of ivl_side) cause the specification limit of 95.0 # (sl_sf = 3, i.e. 3 significant digits) to be reduced by 0.05, i.e. the # actual specification limit is 94.95. ## Not run: res1 # Expected output of print(res1) # Summary of shelf life estimation following the ICH Q1E guideline # # The best model accepted at a significance level of 0.25 has # Common intercepts and Common slopes (acronym: cics). # # Worst case intercept: 100.5669 (Potency) # Worst case batch: NA # Estimated shelf life for cics model: 26.2241 (Month) # # Worst case intercepts, POIs and batches of all models # (Including information about the side where the confidence # interval crosses the specification boundary): # Intercept POI Side Batch # cics 100.5669 26.2241 lower NA # dics 100.3638 24.8003 lower b2 # dids.pmse 100.7819 23.66724 lower b5 # dids 100.7819 23.34184 lower b5 res2 # Expected output of print(res2) # Summary of shelf life estimation following the ICH Q1E guideline # # The best model accepted at a significance level of 0.25 has # Different intercepts and Common slopes (acronym: dics). # # Worst case intercept: 100.82 (Potency) # Worst case batch: b5 # Estimated shelf life for dics model: 23.60194 (Month) # # Worst case intercepts, POIs and batches of all models # (Including information about the side where the confidence # interval crosses the specification boundary): # Intercept POI Side Batch # cics 102.0513 29.18093 lower NA # dics 100.82 23.60194 lower b5 # dids.pmse 100.7819 22.49726 lower b5 # dids 102.3841 23.26251 lower b3 res3 # Expected output of print(res3) # Summary of shelf life estimation following the ICH Q1E guideline # # The best model accepted at a significance level of 0.25 has # Different intercepts and Different slopes (acronym: dids). # # Worst case intercept: 101.2594 (Potency) # Worst case batch: b8 # Estimated shelf life for dids model: 15.96453 (Month) # # Worst case intercepts, POIs and batches of all models # (Including information about the side where the confidence # interval crosses the specification boundary): # Intercept POI Side Batch # cics 101.5498 28.12518 lower NA # dics 100.4882 22.47939 lower b8 # dids.pmse 101.2594 15.72348 lower b8 # dids 101.2594 15.96453 lower b8 ## End(Not run)
This is a method for the function print() for objects of class
‘expirest_wisle’.
## S3 method for class 'expirest_wisle' print(x, ...)## S3 method for class 'expirest_wisle' print(x, ...)
x |
An object of class ‘ |
... |
Further arguments passed to or from other methods or arguments
that can be passed down to the |
The function expirest_wisle() estimates the expiry
for the specified release and specification limit following the ARGPM
guidance “Stability testing for prescription medicines”. By default,
batch poolability is checked as recommended by the ICH Q1E guideline at a
significance level of 0.25. Other levels can be used, although not
recommended, by changing the default of the alpha_pool parameter.
Three possible models may be appropriate, i.e.
a common intercept / common slope model (cics),
a different intercept / common slope model (dics) or
a different intercept / different slope model (dids).
The worst case intercept is the intercept of the batch whose confidence
limit is the first crossing the acceptance limit. As in case of the
cics model type all batches have a common intercept and a common
confidence interval, all batches can be regarded as equally worst case. In
case of the dids model type, shelf life estimation is done using the
models obtained from fitting the data of each batch individually. In
addition to the shelf life estimated according to the ARGPM also the
estimate according to ICH Q1E is shown.
The ‘expirest_wisle’ object passed to the
x parameter is returned invisibly.
expirest_wisle, expirest_osle,
formatC, methods.
# Fit models of different type res1 <- expirest_wisle(data = exp1[exp1$Batch %in% c("b2", "b5", "b7"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", rl = 98, rl_sf = 3, sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") res2 <- expirest_wisle(data = exp1[exp1$Batch %in% c("b3", "b4", "b5"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", rl = 98, rl_sf = 3, sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") res3 <- expirest_wisle(data = exp1[exp1$Batch %in% c("b4", "b5", "b8"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", rl = 98, rl_sf = 3, sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") # The parameter settings sf_option = "loose" and ivl_side = "lower" (the # default setting of ivl_side) cause the specification limit of 95.0 # (sl_sf = 3, i.e. 3 significant digits) to be reduced by 0.05, i.e. the # actual specification limit is 94.95. ## Not run: res1 # Expected output of print(res1) # Summary of shelf life estimation following the ARGPM # guidance "Stability testing for prescription medicines" # # The best model accepted at a significance level of 0.25 has # Common intercepts and Common slopes (acronym: cics). # # Worst case intercept and batch: # RL Batch Intercept # 1 98 NA 100.5669 # # Estimated shelf lives for the cics model: # SL RL wisle osle # 1 95 98 14.07398 26.2241 # # Abbreviations: # ARGPM: Australian Regulatory Guidelines for Prescription Medicines; # ICH: International Council for Harmonisation; # osle: Ordinary shelf life estimation (i.e. following the ICH guidance); # RL: Release Limit; # SL: Specification Limit; # wisle: What-if (approach for) shelf life estimation (see ARGPM guidance). res2 # Expected output of print(res2) # Summary of shelf life estimation following the ARGPM # guidance "Stability testing for prescription medicines" # # The best model accepted at a significance level of 0.25 has # Different intercepts and Common slopes (acronym: dics). # # Worst case intercept and batch: # RL Batch Intercept # 1 98 b5 100.82 # # Estimated shelf lives for the dics model: # SL RL wisle osle # 1 95 98 11.40993 23.60194 # # Abbreviations: # ARGPM: Australian Regulatory Guidelines for Prescription Medicines; # ICH: International Council for Harmonisation; # osle: Ordinary shelf life estimation (i.e. following the ICH guidance); # RL: Release Limit; # SL: Specification Limit; # wisle: What-if (approach for) shelf life estimation (see ARGPM guidance). res3 # Expected output of print(res3) # Summary of shelf life estimation following the ARGPM # guidance "Stability testing for prescription medicines" # # The best model accepted at a significance level of 0.25 has # Different intercepts and Different slopes (acronym: dids). # # Worst case intercept and batch: # RL Batch Intercept # 1 98 b8 101.2594 # # Estimated shelf lives for the dids model (for information, the results of # the model fitted with pooled mean square error (pmse) are also shown: # SL RL wisle wisle (pmse) osle osle (pmse) # 1 95 98 7.619661 7.483223 15.96453 15.72348 # # Abbreviations: # ARGPM: Australian Regulatory Guidelines for Prescription Medicines; # ICH: International Council for Harmonisation; # osle: Ordinary shelf life estimation (i.e. following the ICH guidance); # pmse: Pooled mean square error; # RL: Release Limit; # SL: Specification Limit; # wisle: What-if (approach for) shelf life estimation (see ARGPM guidance). ## End(Not run)# Fit models of different type res1 <- expirest_wisle(data = exp1[exp1$Batch %in% c("b2", "b5", "b7"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", rl = 98, rl_sf = 3, sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") res2 <- expirest_wisle(data = exp1[exp1$Batch %in% c("b3", "b4", "b5"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", rl = 98, rl_sf = 3, sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") res3 <- expirest_wisle(data = exp1[exp1$Batch %in% c("b4", "b5", "b8"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", rl = 98, rl_sf = 3, sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") # The parameter settings sf_option = "loose" and ivl_side = "lower" (the # default setting of ivl_side) cause the specification limit of 95.0 # (sl_sf = 3, i.e. 3 significant digits) to be reduced by 0.05, i.e. the # actual specification limit is 94.95. ## Not run: res1 # Expected output of print(res1) # Summary of shelf life estimation following the ARGPM # guidance "Stability testing for prescription medicines" # # The best model accepted at a significance level of 0.25 has # Common intercepts and Common slopes (acronym: cics). # # Worst case intercept and batch: # RL Batch Intercept # 1 98 NA 100.5669 # # Estimated shelf lives for the cics model: # SL RL wisle osle # 1 95 98 14.07398 26.2241 # # Abbreviations: # ARGPM: Australian Regulatory Guidelines for Prescription Medicines; # ICH: International Council for Harmonisation; # osle: Ordinary shelf life estimation (i.e. following the ICH guidance); # RL: Release Limit; # SL: Specification Limit; # wisle: What-if (approach for) shelf life estimation (see ARGPM guidance). res2 # Expected output of print(res2) # Summary of shelf life estimation following the ARGPM # guidance "Stability testing for prescription medicines" # # The best model accepted at a significance level of 0.25 has # Different intercepts and Common slopes (acronym: dics). # # Worst case intercept and batch: # RL Batch Intercept # 1 98 b5 100.82 # # Estimated shelf lives for the dics model: # SL RL wisle osle # 1 95 98 11.40993 23.60194 # # Abbreviations: # ARGPM: Australian Regulatory Guidelines for Prescription Medicines; # ICH: International Council for Harmonisation; # osle: Ordinary shelf life estimation (i.e. following the ICH guidance); # RL: Release Limit; # SL: Specification Limit; # wisle: What-if (approach for) shelf life estimation (see ARGPM guidance). res3 # Expected output of print(res3) # Summary of shelf life estimation following the ARGPM # guidance "Stability testing for prescription medicines" # # The best model accepted at a significance level of 0.25 has # Different intercepts and Different slopes (acronym: dids). # # Worst case intercept and batch: # RL Batch Intercept # 1 98 b8 101.2594 # # Estimated shelf lives for the dids model (for information, the results of # the model fitted with pooled mean square error (pmse) are also shown: # SL RL wisle wisle (pmse) osle osle (pmse) # 1 95 98 7.619661 7.483223 15.96453 15.72348 # # Abbreviations: # ARGPM: Australian Regulatory Guidelines for Prescription Medicines; # ICH: International Council for Harmonisation; # osle: Ordinary shelf life estimation (i.e. following the ICH guidance); # pmse: Pooled mean square error; # RL: Release Limit; # SL: Specification Limit; # wisle: What-if (approach for) shelf life estimation (see ARGPM guidance). ## End(Not run)
This is a method for the function print() for objects of class
‘plot_expirest_osle’.
## S3 method for class 'plot_expirest_osle' print(x, ...)## S3 method for class 'plot_expirest_osle' print(x, ...)
x |
An object of class ‘ |
... |
Further arguments passed to or from other methods or arguments
that can be passed down to the |
The element Graph of the ‘plot_expirest_osle’
object that is returned by the function plot_expirest_osle()
is an object of class ‘ggplot’, generated by the function
ggplot() from the ‘ggplot2’ package.
Thus, the corresponding plot method is used for plotting. Arguments
to the ggplot() function can be passed via the
... parameter.
The ‘plot_expirest_osle’ object passed to the x
parameter is returned invisibly.
expirest_osle, plot_expirest_osle,
ggplot(), methods.
# Performing an "ordinary shelf life estimation" (osle) res1 <- expirest_osle(data = exp1[exp1$Batch %in% c("b2", "b5", "b7"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") # The 'expirest_osle' object can be passed on to the plot_expirest_osle() # function. This function does not produce any output but returns a # 'plot_expirest_osle' object. ## Not run: gg1 <- plot_expirest_osle( model = res1, response_vbl_unit = "%", x_range = NULL, y_range = c(93, 105), mtbs = "verified", plot_option = "full", ci_app = "line") gg2 <- print(gg1) # The print() function returns the 'plot_expirest_osle' object invisibly. class(gg1) class(gg2) ## End(Not run)# Performing an "ordinary shelf life estimation" (osle) res1 <- expirest_osle(data = exp1[exp1$Batch %in% c("b2", "b5", "b7"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") # The 'expirest_osle' object can be passed on to the plot_expirest_osle() # function. This function does not produce any output but returns a # 'plot_expirest_osle' object. ## Not run: gg1 <- plot_expirest_osle( model = res1, response_vbl_unit = "%", x_range = NULL, y_range = c(93, 105), mtbs = "verified", plot_option = "full", ci_app = "line") gg2 <- print(gg1) # The print() function returns the 'plot_expirest_osle' object invisibly. class(gg1) class(gg2) ## End(Not run)
This is a method for the function print() for objects of class
‘plot_expirest_wisle’.
## S3 method for class 'plot_expirest_wisle' print(x, ...)## S3 method for class 'plot_expirest_wisle' print(x, ...)
x |
An object of class ‘ |
... |
Further arguments passed to or from other methods or arguments
that can be passed down to the |
The element Graph of the ‘plot_expirest_wisle’
object that is returned by the function plot_expirest_wisle()
is an object of class ‘ggplot’, generated by the function
ggplot() from the ‘ggplot2’ package.
Thus, the corresponding plot method is used for plotting. Arguments
to the ggplot() function can be passed via the
... parameter.
The ‘plot_expirest_wisle’ object passed to the x
parameter is returned invisibly.
expirest_wisle, plot_expirest_wisle,
ggplot(), methods.
# Performing a "what-if (approach for) shelf life estimation" (wisle) res1 <- expirest_wisle(data = exp1[exp1$Batch %in% c("b2", "b5", "b7"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", rl = 98, rl_sf = 3, sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") # The 'expirest_wisle' object can be passed on to the plot_expirest_wisle() # function. This function does not produce any output but returns a # 'plot_expirest_wisle' object. ## Not run: gg1 <- plot_expirest_wisle( model = res1, rl_index = 1, response_vbl_unit = "%", x_range = NULL, y_range = c(93, 105), scenario = "standard", mtbs = "verified", plot_option = "full", ci_app = "line") gg2 <- print(gg1) # The print() function returns the 'plot_expirest_wisle' object invisibly. class(gg1) class(gg2) ## End(Not run)# Performing a "what-if (approach for) shelf life estimation" (wisle) res1 <- expirest_wisle(data = exp1[exp1$Batch %in% c("b2", "b5", "b7"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", rl = 98, rl_sf = 3, sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") # The 'expirest_wisle' object can be passed on to the plot_expirest_wisle() # function. This function does not produce any output but returns a # 'plot_expirest_wisle' object. ## Not run: gg1 <- plot_expirest_wisle( model = res1, rl_index = 1, response_vbl_unit = "%", x_range = NULL, y_range = c(93, 105), scenario = "standard", mtbs = "verified", plot_option = "full", ci_app = "line") gg2 <- print(gg1) # The print() function returns the 'plot_expirest_wisle' object invisibly. class(gg1) class(gg2) ## End(Not run)
This is a method for the function summary() for objects of class
‘expirest_osle’.
## S3 method for class 'expirest_osle' summary(object, ...)## S3 method for class 'expirest_osle' summary(object, ...)
object |
An object of class ‘ |
... |
Further arguments passed to or from other methods or arguments
that can be passed down to the |
The function expirest_osle() estimates the shelf
life, or retest period, following the ICH Q1E guideline. By default, batch
poolability is checked as recommended by the guideline at a significance
level of 0.25. Other levels can be used, although not recommended, by
changing the default of the alpha_pool parameter. Three possible
models may be appropriate, i.e.
a common intercept / common slope model (cics),
a different intercept / common slope model (dics) or
a different intercept / different slope model (dids).
The worst case intercept is the intercept of the batch whose confidence
limit is the first crossing the acceptance limit. As in case of the
cics model type all batches have a common intercept and a common
confidence interval, all batches can be regarded as equally worst case. In
case of the dids model type, shelf life estimation is done using the
models obtained from fitting the data of each batch individually.
The ‘expirest_osle’ object passed to the object
parameter is returned invisibly.
expirest_osle, expirest_wisle,
formatC, methods.
# Fit models of different type res1 <- expirest_osle(data = exp1[exp1$Batch %in% c("b2", "b5", "b7"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") res2 <- expirest_osle(data = exp1[exp1$Batch %in% c("b3", "b4", "b5"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") res3 <- expirest_osle(data = exp1[exp1$Batch %in% c("b4", "b5", "b8"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") # The parameter settings sf_option = "loose" and ivl_side = "lower" (the # default setting of ivl_side) cause the specification limit of 95.0 # (sl_sf = 3, i.e. 3 significant digits) to be reduced by 0.05, i.e. the # actual specification limit is 94.95. ## Not run: summary(res1) # Expected output of summary(res1) # Summary of shelf life estimation following the ICH Q1E guideline # # The best model accepted at a significance level of 0.25 has # Common intercepts and Common slopes (acronym: cics). # # Worst case intercept: 100.5669 (Potency) # Worst case batch: NA # Estimated shelf life for cics model: 26.2241 (Month) # # Worst case intercepts, POIs and batches of all models # (Including information about the side where the confidence # interval crosses the specification boundary): # Intercept POI Side Batch # cics 100.5669 26.2241 lower NA # dics 100.3638 24.8003 lower b2 # dids.pmse 100.7819 23.66724 lower b5 # dids 100.7819 23.34184 lower b5 summary(res2) # Expected output of summary(res2) # Summary of shelf life estimation following the ICH Q1E guideline # # The best model accepted at a significance level of 0.25 has # Different intercepts and Common slopes (acronym: dics). # # Worst case intercept: 100.82 (Potency) # Worst case batch: b5 # Estimated shelf life for dics model: 23.60194 (Month) # # Worst case intercepts, POIs and batches of all models # (Including information about the side where the confidence # interval crosses the specification boundary): # Intercept POI Side Batch # cics 102.0513 29.18093 lower NA # dics 100.82 23.60194 lower b5 # dids.pmse 100.7819 22.49726 lower b5 # dids 102.3841 23.26251 lower b3 summary(res3) # Expected output of summary(res3) # Summary of shelf life estimation following the ICH Q1E guideline # # The best model accepted at a significance level of 0.25 has # Different intercepts and Different slopes (acronym: dids). # # Worst case intercept: 101.2594 (Potency) # Worst case batch: b8 # Estimated shelf life for dids model: 15.96453 (Month) # # Worst case intercepts, POIs and batches of all models # (Including information about the side where the confidence # interval crosses the specification boundary): # Intercept POI Side Batch # cics 101.5498 28.12518 lower NA # dics 100.4882 22.47939 lower b8 # dids.pmse 101.2594 15.72348 lower b8 # dids 101.2594 15.96453 lower b8 ## End(Not run)# Fit models of different type res1 <- expirest_osle(data = exp1[exp1$Batch %in% c("b2", "b5", "b7"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") res2 <- expirest_osle(data = exp1[exp1$Batch %in% c("b3", "b4", "b5"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") res3 <- expirest_osle(data = exp1[exp1$Batch %in% c("b4", "b5", "b8"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") # The parameter settings sf_option = "loose" and ivl_side = "lower" (the # default setting of ivl_side) cause the specification limit of 95.0 # (sl_sf = 3, i.e. 3 significant digits) to be reduced by 0.05, i.e. the # actual specification limit is 94.95. ## Not run: summary(res1) # Expected output of summary(res1) # Summary of shelf life estimation following the ICH Q1E guideline # # The best model accepted at a significance level of 0.25 has # Common intercepts and Common slopes (acronym: cics). # # Worst case intercept: 100.5669 (Potency) # Worst case batch: NA # Estimated shelf life for cics model: 26.2241 (Month) # # Worst case intercepts, POIs and batches of all models # (Including information about the side where the confidence # interval crosses the specification boundary): # Intercept POI Side Batch # cics 100.5669 26.2241 lower NA # dics 100.3638 24.8003 lower b2 # dids.pmse 100.7819 23.66724 lower b5 # dids 100.7819 23.34184 lower b5 summary(res2) # Expected output of summary(res2) # Summary of shelf life estimation following the ICH Q1E guideline # # The best model accepted at a significance level of 0.25 has # Different intercepts and Common slopes (acronym: dics). # # Worst case intercept: 100.82 (Potency) # Worst case batch: b5 # Estimated shelf life for dics model: 23.60194 (Month) # # Worst case intercepts, POIs and batches of all models # (Including information about the side where the confidence # interval crosses the specification boundary): # Intercept POI Side Batch # cics 102.0513 29.18093 lower NA # dics 100.82 23.60194 lower b5 # dids.pmse 100.7819 22.49726 lower b5 # dids 102.3841 23.26251 lower b3 summary(res3) # Expected output of summary(res3) # Summary of shelf life estimation following the ICH Q1E guideline # # The best model accepted at a significance level of 0.25 has # Different intercepts and Different slopes (acronym: dids). # # Worst case intercept: 101.2594 (Potency) # Worst case batch: b8 # Estimated shelf life for dids model: 15.96453 (Month) # # Worst case intercepts, POIs and batches of all models # (Including information about the side where the confidence # interval crosses the specification boundary): # Intercept POI Side Batch # cics 101.5498 28.12518 lower NA # dics 100.4882 22.47939 lower b8 # dids.pmse 101.2594 15.72348 lower b8 # dids 101.2594 15.96453 lower b8 ## End(Not run)
This is a method for the function summary() for objects of class
‘expirest_wisle’.
## S3 method for class 'expirest_wisle' summary(object, ...)## S3 method for class 'expirest_wisle' summary(object, ...)
object |
An object of class ‘ |
... |
Further arguments passed to or from other methods or arguments
that can be passed down to the |
The function expirest_wisle() estimates the expiry
for the specified release and specification limit following the ARGPM
guidance “Stability testing for prescription medicines”. By default,
batch poolability is checked as recommended by the ICH Q1E guideline at a
significance level of 0.25. Other levels can be used, although not
recommended, by changing the default of the alpha_pool parameter.
Three possible models may be appropriate, i.e.
a common intercept / common slope model (cics),
a different intercept / common slope model (dics) or
a different intercept / different slope model (dids).
The worst case intercept is the intercept of the batch whose confidence
limit is the first crossing the acceptance limit. As in case of the
cics model type all batches have a common intercept and a common
confidence interval, all batches can be regarded as equally worst case. In
case of the dids model type, shelf life estimation is done using the
models obtained from fitting the data of each batch individually. In
addition to the shelf life estimated according to the ARGPM also the
estimate according to ICH Q1E is shown.
The ‘expirest_wisle’ object passed to the
object parameter is returned invisibly.
expirest_wisle, expirest_osle,
formatC, methods.
# Fit models of different type res1 <- expirest_wisle(data = exp1[exp1$Batch %in% c("b2", "b5", "b7"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", rl = 98, rl_sf = 3, sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") res2 <- expirest_wisle(data = exp1[exp1$Batch %in% c("b3", "b4", "b5"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", rl = 98, rl_sf = 3, sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") res3 <- expirest_wisle(data = exp1[exp1$Batch %in% c("b4", "b5", "b8"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", rl = 98, rl_sf = 3, sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") # The parameter settings sf_option = "loose" and ivl_side = "lower" (the # default setting of ivl_side) cause the specification limit of 95.0 # (sl_sf = 3, i.e. 3 significant digits) to be reduced by 0.05, i.e. the # actual specification limit is 94.95. ## Not run: summary(res1) # Expected output of summary(res1) # Summary of shelf life estimation following the ARGPM # guidance "Stability testing for prescription medicines" # # The best model accepted at a significance level of 0.25 has # Common intercepts and Common slopes (acronym: cics). # # Worst case intercept and batch: # RL Batch Intercept # 1 98 NA 100.5669 # # Estimated shelf lives for the cics model: # SL RL wisle osle # 1 95 98 14.07398 26.2241 # # Abbreviations: # ARGPM: Australian Regulatory Guidelines for Prescription Medicines; # ICH: International Council for Harmonisation; # osle: Ordinary shelf life estimation (i.e. following the ICH guidance); # RL: Release Limit; # SL: Specification Limit; # wisle: What-if (approach for) shelf life estimation (see ARGPM guidance). summary(res2) # Expected output of summary(res2) # Summary of shelf life estimation following the ARGPM # guidance "Stability testing for prescription medicines" # # The best model accepted at a significance level of 0.25 has # Different intercepts and Common slopes (acronym: dics). # # Worst case intercept and batch: # RL Batch Intercept # 1 98 b5 100.82 # # Estimated shelf lives for the dics model: # SL RL wisle osle # 1 95 98 11.40993 23.60194 # # Abbreviations: # ARGPM: Australian Regulatory Guidelines for Prescription Medicines; # ICH: International Council for Harmonisation; # osle: Ordinary shelf life estimation (i.e. following the ICH guidance); # RL: Release Limit; # SL: Specification Limit; # wisle: What-if (approach for) shelf life estimation (see ARGPM guidance). summary(res3) # Expected output of summary(res3) # Summary of shelf life estimation following the ARGPM # guidance "Stability testing for prescription medicines" # # The best model accepted at a significance level of 0.25 has # Different intercepts and Different slopes (acronym: dids). # # Worst case intercept and batch: # RL Batch Intercept # 1 98 b8 101.2594 # # Estimated shelf lives for the dids model (for information, the results of # the model fitted with pooled mean square error (pmse) are also shown: # SL RL wisle wisle (pmse) osle osle (pmse) # 1 95 98 7.619661 7.483223 15.96453 15.72348 # # Abbreviations: # ARGPM: Australian Regulatory Guidelines for Prescription Medicines; # ICH: International Council for Harmonisation; # osle: Ordinary shelf life estimation (i.e. following the ICH guidance); # pmse: Pooled mean square error; # RL: Release Limit; # SL: Specification Limit; # wisle: What-if (approach for) shelf life estimation (see ARGPM guidance). ## End(Not run)# Fit models of different type res1 <- expirest_wisle(data = exp1[exp1$Batch %in% c("b2", "b5", "b7"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", rl = 98, rl_sf = 3, sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") res2 <- expirest_wisle(data = exp1[exp1$Batch %in% c("b3", "b4", "b5"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", rl = 98, rl_sf = 3, sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") res3 <- expirest_wisle(data = exp1[exp1$Batch %in% c("b4", "b5", "b8"), ], response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch", rl = 98, rl_sf = 3, sl = 95, sl_sf = 3, srch_range = c(0, 500), sf_option = "loose") # The parameter settings sf_option = "loose" and ivl_side = "lower" (the # default setting of ivl_side) cause the specification limit of 95.0 # (sl_sf = 3, i.e. 3 significant digits) to be reduced by 0.05, i.e. the # actual specification limit is 94.95. ## Not run: summary(res1) # Expected output of summary(res1) # Summary of shelf life estimation following the ARGPM # guidance "Stability testing for prescription medicines" # # The best model accepted at a significance level of 0.25 has # Common intercepts and Common slopes (acronym: cics). # # Worst case intercept and batch: # RL Batch Intercept # 1 98 NA 100.5669 # # Estimated shelf lives for the cics model: # SL RL wisle osle # 1 95 98 14.07398 26.2241 # # Abbreviations: # ARGPM: Australian Regulatory Guidelines for Prescription Medicines; # ICH: International Council for Harmonisation; # osle: Ordinary shelf life estimation (i.e. following the ICH guidance); # RL: Release Limit; # SL: Specification Limit; # wisle: What-if (approach for) shelf life estimation (see ARGPM guidance). summary(res2) # Expected output of summary(res2) # Summary of shelf life estimation following the ARGPM # guidance "Stability testing for prescription medicines" # # The best model accepted at a significance level of 0.25 has # Different intercepts and Common slopes (acronym: dics). # # Worst case intercept and batch: # RL Batch Intercept # 1 98 b5 100.82 # # Estimated shelf lives for the dics model: # SL RL wisle osle # 1 95 98 11.40993 23.60194 # # Abbreviations: # ARGPM: Australian Regulatory Guidelines for Prescription Medicines; # ICH: International Council for Harmonisation; # osle: Ordinary shelf life estimation (i.e. following the ICH guidance); # RL: Release Limit; # SL: Specification Limit; # wisle: What-if (approach for) shelf life estimation (see ARGPM guidance). summary(res3) # Expected output of summary(res3) # Summary of shelf life estimation following the ARGPM # guidance "Stability testing for prescription medicines" # # The best model accepted at a significance level of 0.25 has # Different intercepts and Different slopes (acronym: dids). # # Worst case intercept and batch: # RL Batch Intercept # 1 98 b8 101.2594 # # Estimated shelf lives for the dids model (for information, the results of # the model fitted with pooled mean square error (pmse) are also shown: # SL RL wisle wisle (pmse) osle osle (pmse) # 1 95 98 7.619661 7.483223 15.96453 15.72348 # # Abbreviations: # ARGPM: Australian Regulatory Guidelines for Prescription Medicines; # ICH: International Council for Harmonisation; # osle: Ordinary shelf life estimation (i.e. following the ICH guidance); # pmse: Pooled mean square error; # RL: Release Limit; # SL: Specification Limit; # wisle: What-if (approach for) shelf life estimation (see ARGPM guidance). ## End(Not run)