The Posterior Probability of Passing a Compendial Standard, Part 1: Uniformity of Dosage Units

Abstract

A compendial standard is a function of data generated by one or more quality testing procedures. Since the data are sampled from an underlying distribution, the probability of passing a compendial test (Pa) can be expressed as a function of the distribution's model parameters. Applying Bayesian methodology to such a function, we show how to compute the posterior distribution of Pa and other quantities of interest. We apply this methodology to the USP<905> compendial standard and illustrate the importance of considering interbatch variance. We show that the operating characteristics of this Bayesian approach depend on the underlying model parameters almost exclusively through the population Pa and use this to develop a simple univariate procedure to determine the number of batches needed for a process qualification. We note some advantages of this Bayesian approach compared to current approaches. To show the simplicity of the approach and encourage its use, example R and WinBUGS code are provided.