Caution Using Bootstrap Tolerance Limits with Application to Dissolution Specification Limits

For a pharmaceutical manufacturer, the establishment of dissolution specification limits for a new product affects the determination of the product’s acceptable shelf life, the sentencing of manufacturing lots, and the cost of manufacturing changes. Common approaches to setting these limits either fail to model explicitly sources of variation in the observed dissolution profiles or result in specification limits on model parameters rather than on the observed responses that are of primary interest. We propose a nonlinear mixed effects model to account for sources of variation in the dissolution measurements and use it to construct a parametric bootstrap tolerance interval on the population of dissolution values at a specified time. This provides an evaluation of manufacturing process capability. We subsequently examine the bootstrap tolerance limit method with simulations using simple random samples, mixed models, and nonlinear mixed models. In all cases, the parametric bootstrap tolerance limits exhibit substantially lower coverage than the stated confidence level. Our results demonstrate the need for researchers to use caution when calculating bootstrap tolerance limits. While the bootstrap is a valuable tool in many situations, bootstrap intervals can and sometimes do perform quite poorly, particularly with small to moderate sample sizes