The package facilitates shelf life estimation for chemically derived medicines by adhering to established methodologies. It supports both the standard approach as recommended by the International Council for Harmonisation (ICH) in the Q1E Evaluation of Stability Data guideline, as well as the worst-case scenario analysis (what-if analysis) detailed in the Australian Regulatory Guidelines for Prescription Medicines (ARGPM) guidance on stability testing for prescription medicines.
A stable version of expirest can be installed from CRAN:
# install.packages("expirest")The development version is available from GitHub by:
# install.packages("devtools")
devtools::install_github("piusdahinden/expirest")The ICH Q1E guideline outlines methods for estimating the retest period or shelf life of chemically derived medicines. By analyzing the point in time where the 95% confidence limit intersects the acceptance criterion, shelf life estimation can be effectively performed. For attributes that change over time, different approaches are used: one-sided limits for those that increase and two-sided limits for those with uncertain changes. Estimations can be applied to single or multiple batches, often requiring stability data from at least three batches.
Before conducting shelf life estimation with multiple batches, it is crucial to determine the most suitable model and verify if data from all batches are poolable. The guideline recommends statistical tests to assess whether regression lines from different batches share a common intercept and slope. Depending on these tests, three models may be used: common intercept / common slope (cics), different intercept / common slope (dics), and different intercept / different slope (dids). Pooling data only occurs if justified by statistical analysis, using a significance level (Type I error) set at 0.25 to enhance the power of the test to detect cases where the data should not be pooled.
The fourth possible model, i.e. the common intercept/different slope model, is of limited practical relevance because, although initial levels of different batches might be well-controlled, they are unlikely to be identical.
This is a basic example which shows you how to solve a common problem using a data set containing the moisture stability data (% (w/w)) of three batches obtained over a 24 months period of a drug product. A total of n = 33 independent measurements are available (corresponding to data shown in Table XIII in LeBlond et al. (2011).
library(expirest)
# Data frame
str(exp3)
#> 'data.frame': 33 obs. of 3 variables:
#> $ Batch : Factor w/ 3 levels "b1","b2","b3": 1 1 1 1 1 1 1 1 1 1 ...
#> $ Month : num 0 1 2 3 3 6 6 12 12 24 ...
#> $ Moisture: num 2.2 1.7 3.32 2.76 2.43 ...
# Perform what-if shelf life estimation (wisle) and print a summary
res1 <- expirest_wisle(
data = exp3, response_vbl = "Moisture", time_vbl = "Month",
batch_vbl = "Batch", rl = 3.00, rl_sf = 3, sl = c(0.5, 4.5),
sl_sf = c(1, 2), srch_range = c(0, 500), 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 = "upper")
class(res1)
#> [1] "expirest_wisle"
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 3 NA 2.456782
#>
#> Estimated shelf lives for the cics model:
#> SL RL wisle osle
#> 1 4.5 3 72.50545 96.30552
#>
#> 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).
# Prepare graphical representation
ggres1 <- plot_expirest_wisle(
model = res1, rl_index = 1, response_vbl_unit = "% (w/w)",
x_range = NULL, y_range = c(0.2, 5.2), scenario = "standard",
mtbs = "verified", plot_option = "full", ci_app = "ribbon")
class(ggres1)
#> [1] "plot_expirest_wisle"
plot(ggres1)
The model type in Example 1 was common intercept / common slope (cics). The model type in this example is different intercept / different slope (dids). 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 is used. A total of n = 53 independent measurements are available (corresponding to data shown in Tables IV, VI and VIII in LeBlond et al. (2011).
# Data frame
str(exp1)
#> 'data.frame': 53 obs. of 3 variables:
#> $ Batch : Factor w/ 6 levels "b2","b3","b4",..: 1 1 1 1 1 1 1 1 1 1 ...
#> $ Month : num 0 1 3 3 6 6 12 12 24 24 ...
#> $ Potency: num 101 101.3 99.8 99.2 99.5 ...
# Perform what-if shelf life estimation (wisle) and print a summary
res2_1 <- expirest_wisle(
data = exp1[exp1$Batch %in% c("b4", "b5", "b8"), ],
response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch",
rl = c(98.0, 98.5, 99.0), rl_sf = rep(2, 3), sl = 95, sl_sf = 2,
srch_range = c(0, 500), 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")
summary(res2_1)
#>
#> 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 intercepts and batches:
#> RL Batch Intercept
#> 1 98.0 b8 101.2594
#> 2 98.5 b8 101.2594
#> 3 99.0 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 98.0 7.619661 7.483223 15.84487 15.6061
#> 2 95 98.5 8.997036 8.858223 15.84487 15.6061
#> 3 95 99.0 10.303030 11.344407 15.84487 15.6061
#>
#> 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).
# Prepare graphical representation
ggres2_1 <- plot_expirest_wisle(
model = res2_1, rl_index = 2, response_vbl_unit = "%", x_range = NULL,
y_range = c(93, 107), scenario = "standard", mtbs = "verified",
plot_option = "full", ci_app = "ribbon")
class(ggres2_1)
#> [1] "plot_expirest_wisle"
plot(ggres2_1)
Note that if the model type is dids, then by default the results are
plotted that are obtained by fitting individual regression lines to each
batch. To get a plot of the dids model with pooled mean square error
(pmse) instead, use the setting mtbs = "dids.pmse".
# Prepare graphical representation of the dids.pmse model
ggres2_2 <- plot_expirest_wisle(
model = res2_1, rl_index = 2, response_vbl_unit = "%", x_range = NULL,
y_range = c(93, 107), scenario = "standard", mtbs = "dids.pmse",
plot_option = "full", ci_app = "ribbon")
plot(ggres2_2)
The examples above were performed with three batches. The assessment can be performed with any numbers of batches, even with just one batch. If the assessment is performed with a single batch, the results are reported as dids model while the results for all other models are NA. As an example, the following example was performed with batch b4.
# Perform what-if shelf life estimation (wisle) and print a summary
res2_2 <- expirest_wisle(
data = exp1[exp1$Batch == "b4", ],
response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch",
rl = c(98.0, 98.5, 99.0), rl_sf = rep(2, 3), sl = 95, sl_sf = 2,
srch_range = c(0, 500), 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")
summary(res2_2)
#>
#> 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
#> NA intercepts and NA slopes (acronym: n.a.).
#>
#> Worst case intercepts and batches:
#> RL Batch Intercept
#> 1 98.0 b4 104.0706
#> 2 98.5 b4 104.0706
#> 3 99.0 b4 104.0706
#>
#> Estimated shelf lives for the n.a. 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 98.0 13.72633 NA 40.79176 NA
#> 2 95 98.5 16.09778 NA 40.79176 NA
#> 3 95 99.0 18.40465 NA 40.79176 NA
#>
#> 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).
# Prepare graphical representation
ggres2_2 <- plot_expirest_wisle(
model = res2_2, rl_index = 2, response_vbl_unit = "%", x_range = NULL,
y_range = c(93, 107), scenario = "standard", mtbs = "verified",
plot_option = "full", ci_app = "ribbon")
plot(ggres2_2)
The assessments in Example 1 and Example 2 were made with the option
sf_option = "tight". The parameter sf_option affects the shelf life
(sl) and release limits (rl). The setting sf_option = "tight"
means that of the sl and rl limits only the number of significant
digits specified by the parameters rl_sf and sl_sf, respectively,
are taken into account. If sf_option = "loose", then the limits are
widened, i.e. four on the order of the last significant digit + 1 is
added if ivl_side = "upper" or five on the order of the last
significant digit + 1 is subtracted if ivl_side = "lower". For
illustration, the following example reproduces Example 2 with the
option sf_option = "loose".
# Perform what-if shelf life estimation (wisle) and print a summary
res3 <- expirest_wisle(
data = exp1[exp1$Batch %in% c("b4", "b5", "b8"), ],
response_vbl = "Potency", time_vbl = "Month", batch_vbl = "Batch",
rl = c(98.0, 98.5, 99.0), rl_sf = rep(3, 3), sl = 95, sl_sf = 2,
srch_range = c(0, 500), alpha = 0.05, alpha_pool = 0.25,
xform = c("no", "no"), shift = c(0, 0), sf_option = "loose",
ivl = "confidence", ivl_type = "one.sided", ivl_side = "lower")
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 intercepts and batches:
#> RL Batch Intercept
#> 1 98.0 b8 101.2594
#> 2 98.5 b8 101.2594
#> 3 99.0 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 98.0 8.863085 8.724968 17.0387 16.77679
#> 2 95 98.5 10.174754 11.221221 17.0387 16.77679
#> 3 95 99.0 11.440468 11.276686 17.0387 16.77679
#>
#> 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).
# Prepare graphical representation
ggres3 <- plot_expirest_wisle(
model = res3, rl_index = 2, response_vbl_unit = "%", x_range = NULL,
y_range = c(93, 107), scenario = "standard", mtbs = "verified",
plot_option = "full", ci_app = "ribbon")
plot(ggres3)
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.
Pius Dahinden, Tillotts Pharma AG