Minimum Area Confidence Set Optimality for Simultaneous Confidence Bands for Percentiles With Applications to Drug Shelf‐Life Estimation

One important property of any drug product is its stability over time. A key objective in drug stability studies is to estimate the shelf-life of a drug, involving a suitable definition of the true shelf-life and the construction of an appropriate estimate of the true shelf-life. Simultaneous confidence bands (SCBs) for percentiles in linear regression are valuable tools for determining the shelf-life in drug stability studies. In this paper, we propose a novel criterion, the Minimum Area Confidence Set (MACS) criterion, for finding the optimal SCB for percentile regression lines. This criterion focuses on the area of the constrained regions for the newly proposed pivotal quantities, which are generated from the confidence set for the unknown parameters of an SCB. We employ the new pivotal quantities to construct exact SCBs over any finite covariate intervals and use the MACS criterion to compare several SCBs of different forms. The optimal SCB under the MACS criterion can be used to construct the interval estimate of the true shelf-life. Furthermore, a new computationally efficient method is proposed for calculating the critical constants of exact SCBs for percentile regression lines. A real data example on drug stability is provided for illustration.