Pharmacodynamic analysis of analgesic clinical trials: nonlinear mixed-effects logistic models

In the development of an analgesic product, placebo-controlled clinical trials in patients with defined pain are used to study the dose-time-response relationship of the drug. In such trials, the response is usually an ordered categorical variable with longitudinal and subject-specific repeated measurements. The primary causal variables are time and analgesic concentration. The response may be informative right-hand censored because remedication with a known analgesic may be given if a patient has inadequate pain relief. Mixed-effects logistic models are used to estimate the probabilities of having certain pain relief or pain severity scores. A jackknife method is proposed to estimate the standard errors of parameter estimates. Posterior estimates of these probabilities, or of the scores themselves, allow the evaluation of efficacy for an analgesic. In this evaluation, therapeutic as well as statistical significance is assessed. Two case studies, one focusing on pain relief and the other on pain severity, are used to demonstrate the approach. The level of baseline pain appears to be a determinant of the pattern of response.