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Drug Efficacy Analysis as an Exercise in Dynamic (Indirect-Response) Population PK-PD Modeling

Vladimir Piotrovsky

Advanced PK-PD Modeling & Simulation, Global Clinical Pharmacokinetics and Clinical Pharmacology, Johnson & Johnson Pharmaceutical Research & Development, Beerse, Belgium

Conventional biostatistical analysis of clinical efficacy trials is based on end-points and ignors the longitudinal nature and hierarchical structure of data. It is challenged by the problem of missing data, particularly, dropouts. Usually, changes from baseline are subject to analysis, and this results in a reduced power. An alternative approach is suggested based on dynamic (indirect response) models and mixed effects. It is generic in the sense that the same mathematical formalism with only minor modifications can be applied to a variety of efficacy/safety responses, continuous as well as categorical. The core equation relates the rate of change of a response variable (R; e.g., a symptom intensity score) to the rates of amelioration (vA) and deterioration (vD):

         dR/dt = vA – vD

Disease progression and drug/placebo effect can affect both rates. Onset of action and tolerance are other components of the model. The model may include a pharmacokinetic component, if drug concentration data are available. Alternatively, a dose-response version of the model can be developed.

Two examples will be presented (NONMEM software was used for the analysis). The efficacy of drug A was investigated in a double-blind placebo-controlled Phase III trial with 2 active doses. The response variable was a subjective symptom intensity score which can take any value between 0 (no symptoms) and 10 (highest intensity). This required the model prediction as well as some parameters to be appropriately constrained. There were almost no dropouts in this trial, and also no tolerance was observed. The inference was based on a drug efficacy parameter which was the difference between the overall effect and that produced by placebo. The dose-response model was developed and the significant efficacy of the higher dose was proved.

Four active doses of drug B were compared with placebo in a double-blind placebo-controlled parallel-group Phase III trial. The response variable was a score, which had a wide range, and no constraints for model prediction were needed, however, some parameters had to be constrained. The fraction of dropouts was relatively high and dose-dependent. Also, tolerance was evident in a substantial proportion of patients. Several subgroups were detected and implemented using the mixture modelling technique. The time to last observation (continuous covariate associated with dropouts) was found to affect the overall (placebo+drug) efficacy. The dose-response profile was bell-shaped with the maximum efficacy achieved at the intermediate dose.