Pharmacodynamic analysis of analgesic clinical trials using empirical methods

Data from analgesic clinical trials have characteristics such as ordered categorical longitudinal responses with repeated measures, delay of effect with respect to analgesic plasma concentration, and right-hand censoring of response due to remedication. In order to determine the concentration-effect relationship of such data, we propose convolving an empirical function for plasma concentration, in the form of broken lines which connect each pair of neighboring observations, with a monoexponential function, to generate "effect site concentration." Effect site concentration and time are used, simultaneously, as independent variables in the fit of the model for the logit of the probability of having a specific pain relief (PR) score at each time point pre-remedication, via maximum likelihood. Using corresponding effect site concentration, the probabilities of having specific PR scores post-remedication are predicted via the concentration-response relationship established. The overall (pre- and post-remedication) predictions and corresponding standard errors for the responses are then estimated. Inference of the PR scoring, using a posterior method, is proposed. An illustration using real data is used to demonstrate these methods.