Tolerance Intervals Using Dirichlet Processes

TL;DR

This paper introduces a Bayesian nonparametric method using Dirichlet processes to construct tolerance intervals that are robust to distribution assumptions and effective with smaller samples in pharmaceutical quality control.

Contribution

The paper develops a novel Dirichlet process-based approach for tolerance intervals, addressing limitations of parametric and non-parametric methods in pharmaceutical applications.

Findings

Robustness to distributional misspecification

Comparable efficiency to existing methods

Effective with smaller sample sizes

Abstract

In nonclinical pharmaceutical development, tolerance intervals are critical in ensuring product and process quality. They are statistical intervals designed to contain a specified proportion of the population with a given confidence level. Parametric and non-parametric methods have been developed to obtain tolerance intervals. The former work with small samples but can be affected by distribution misspecification. The latter offer larger flexibility but require large sample sizes. As an alternative, we propose Dirichlet process-based Bayesian nonparametric tolerance intervals to overcome the limitations. We develop a computationally efficient tolerance interval construction algorithm based on the analytically tractable quantile process of the Dirichlet process. Simulation studies show that our new approach is very robust to distributional assumptions and performs as efficiently as existing tolerance interval methods. To illustrate how the model works in practice, we apply our method to the tolerance interval estimation for potency data.