get_wcs_limit: Determination of the “worst case scenario” (wcs) limit

Description

The function get_wcs_limit() calculates “worst case scenario” (wcs) limit following the ARGPM Guidance “Stability testing for prescription medicines”.

Usage

get_wcs_limit(
  rl,
  sl,
  intercept,
  xform = c("no", "no"),
  shift = c(0, 0),
  ivl_side = "lower"
)

Value

A list with the following elements is returned:

xform: A vector of two character strings specifying the transformation of the response and the time variable.
shift: A vector of two values which has been added to the values of the transformed \(x\) and/or \(y\) variables (specified via the xform parameter).
delta.lim: A numeric value or a numeric vector of the absolute difference(s) between rl and sl, if xform[2] != "no" on the transformed scale.
delta.lim.orig: A numeric value or a numeric vector of the absolute difference(s) between rl and sl on the original scale.
wcs.lim: A numeric value or a numeric vector of the worst case scenario (wcs) limit(s), if xform[2] != "no" on the transformed scale.
wcs.lim.orig: A numeric value or a numeric vector of the worst case scenario (wcs) limit(s) on the original scale.

Arguments

rl: A numeric value specifying the release specification limit(s), on the same scale as sl and intercept.
sl: A numeric value specifying the specification limit, on the same scale as rl and intercept.
intercept: A numeric value representing the intercept of a linear regression model fitted to sample data, on the same scale as rl and sl.
xform: A vector of two character strings specifying the transformation of the response and the time variable. The default is “no” transformation, i.e. c("no", "no"), where the first element specifies the transformation of the \(x\) variable and the second element the transformation of the \(y\) variable. Valid alternatives for \(x\) and/or \(y\) variable transformation are "log" (natural logarithm), "sqrt" (square root) and "sq" (square).
shift: A vector of two values which will be added to the variables \(x\) and/or \(y\) before they are transformed as specified by the xform parameter, where the first element will be added to the \(x\) variable and the second element to the \(y\) variable. The purpose is to prevent an undefined state which could arise when variables with values of \(\leq 0\) are log or square root transformed. The default is c(0, 0).
ivl_side: A character string specifying if the “upper” or the “lower” limit is the relevant limit, i.e. either "upper" or "lower", respectively. The default is "lower".

Details

The function get_wcs_limit() determines the “worst case scenario” (wcs) limit as is proposed by the Australian Regulatory Guidelines for Prescription Medicines (ARGPM) guidance “Stability testing for prescription medicines”. According to this guideline, the shelf life or expiry limit is estimated as the point where the upper or lower limit of the 95% confidence interval of the linear model fitted to the data intersects the wcs limit. The wcs limit is obtained by adding/subtracting the absolute difference of specification limit and release limit to/from the common intercept of the test batches or the intercept of the worst performing batch.

If data have been linearised by transformation, all elements, i.e. rl, sl and intercept must be on the same, i.e. transformed, scale. The results are returned on the transformed scale and on the original scale.

References