Yoshitaka Yano, Stuart Beal, Lewis B. Sheiner
University of California; San Francisco; CA 94143; USA
The properties of the posterior predictive check (PPC) for pharmacokinetic and pharmacodynamic model validation is examined. The PPC assigns a value (pPPC) to the probability that a statistic computed on data (and, possibly, model parameters) arising under the analysis model given the real data, is as or more extreme than the value computed on the real data themselves. To test the performance characteristics of the PPC, “real” data are simulated and then analyzed according to an analysis model that may (null hypothesis) or may not (alternative hypothesis) be identical to the real data model. Three analysis models are used: (PK 1) mono-exponential with proportional error, (PK 2), bi-exponential with proportional error, and (PD 1) Emax model (logistic in log X) with additive error under the logit transform. Three null real models are identical to PK 1, PK 2, and PD 1, respectively. Two alternative real models are (PK 2e) bi-exponential with additive error, and (PD 2) sigmoid Emax model with additive error under the logit transform. The simulation/analysis settings (PK 1/PK 1), (PK 2/ /PK 2) and (PD 1/PD 1) evaluate whether the test has appropriate size (a error level under the null), whereas the settings (PK 2/PK 1), (PK 2e/PK 2) and (PD 2/PD 1) evaluate the power of the test (1-b error) under the alternative. For a set of 100 real data sets simulated/analyzed under each model pair according to a stipulated design, the pPPC is computed for a number of statistics, using each of three different approximations to the posterior distribution of the model parameters. We find that in general, (1) The PPC is conservative under the null in the sense that for many statistics, prob(pPPC£ a)<a for small a. For such statistics, this means that useful models will rarely be rejected. (2) Power is not very great, at least for the alternative models we tested, and is especially poor with statistics that are a function of both data and parameters. (3) No clear advantage for one or another method of approximating the posterior distribution of model is found.
Reference: PAGE 9 (2000) Abstr 92 [www.page-meeting.org/?abstract=92]
Poster: oral presentation