ABSTRACT
For simplicity, the following notation is used in this chapter. We let t label denote the established expiration dating period that appears on the container label of a drug product. Also, ttrue is the true shelf life of a particular batch of the drug product. Since ttne is unknown, it is reasonable to assume that kb, will not be granted by the FDA unless ttne !label is statistically justified. According to the FDA guideline, under a fixed effects model, it can be shown that t is label __ actually a confidence lower bound for ttne, and therefore if to is chosen to be
12.2. LINEAR REGRESSION WITH RANDOM COEFFICIENTS Under the assumption that batch is a random variable, stability data can be described by a linear regression model with random coefficients. Consider the following model for a stability study with K batches:
Y,; =X 13, + e,„ j = 1, . . , n„ i = 1, . . , K, (12.2.1) where Y, is the jth assay result (percent of label claim) for the ith batch, X, is a p X 1 vector of the jth value of the regressor for the ith batch and X is its transpose, 13, is a p X 1 vector of random effects for the ith batch, and e,, is the random error in observing Y1. Note that X, 11, is the mean drug characteristic for the ith batch at X, (conditional on 13). The primary assumptions for model (12.2.1) is the same as those for model (10.4.7), which are summarized below. Assumption A
1. 13„ i = 1, . . . , K, are independent and identically distributed (i.i.d.) as N„((3,/p), where 13 is an unknown p X 1 vector and /p is an unknown p X p nonnegative definite matrix.
