Analysis of nonrandomly censored ordered categorical longitudinal data from analgesic trials

A clinical trial of an analgesic agent compares pain relief scores over time among groups of patients. All subjects experience the same painful procedure, but different subjects are given different randomly assigned doses of active agent or placebo when they first request it. The data are short individual time series of ordered categorical pain relief scores subsequent to dosing. Nonrandom right censoring may be present because patients can elect to remedicate with an active agent if their pain relief is insufficient. The trial is meant to address two questions: (a) Is there proof that the drug relieves pain? If so, (b) What dosage patterns should be investigated further, or recommended for use by a typical patient? Marginal models of human pharmacology are basically empirical models, and although an analysis of a study based on such a model can adequately address the first question, such is not the case for the second question, because this question requires extrapolation to untested dosing patterns. We propose to analyze study data using a hierarchical model so as to address both questions. The analysis uses a semimechanistic subject-specific pain-relief model for the distribution of all (uncensored and censored) observations, conditional on individual random effects, and an empirical model for the censoring outcome, remedication, conditional on observed pain relief and individual random effects. We estimate the parameters of the foregoing (nonlinear mixed effects) model via maximum likelihood, assuming normally distributed random effects. Monte Carlo integration with respect to the random effects is used to compute marginal statistics relevant to the dosing question. Of particular note is that this formulation encourages use of subject matter information in model specification so that the extrapolations required to address the dosing question are credible. An example is given of the application of the analysis to analgesic trial data for the drug ketorolac.