Tolerance Intervals Using Dirichlet Processes

2025-12-01

AI Summary

In nonclinical drug development, constructing tolerance intervals faces the challenge of simultaneously addressing small sample sizes, unknown underlying distributions, and statistical robustness. To address this, we propose a Bayesian nonparametric method based on the Dirichlet process (DP). This work is the first to directly leverage the analytical quantile process of the DP for tolerance interval construction—eliminating reliance on parametric distributional assumptions (e.g., normality) while substantially improving estimation efficiency under small samples. The method integrates Bayesian nonparametric modeling with computationally efficient algorithms, accommodating typical pharmaceutical data such as potency measurements. Simulation studies and real-data applications demonstrate that our approach maintains high robustness across skewed, heavy-tailed, and mixture distributions; achieves accuracy comparable to state-of-the-art parametric methods; and delivers superior performance on actual pharmaceutical datasets.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Non-convex Optimization
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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.

Problem

• Develops Bayesian nonparametric tolerance intervals using Dirichlet processes
• Overcomes limitations of small samples and distribution misspecification
• Provides robust tolerance interval estimation for pharmaceutical potency data

Innovation

• Bayesian nonparametric tolerance intervals using Dirichlet processes
• Computationally efficient algorithm based on quantile process
• Robust to distributional assumptions with efficient performance