Piotrovsky, Vladimir and Van Peer, Achiel
Janssen Research Foundation, Beerse, Belgium
Efficacy/safety trials are usually longitudinal, and the response is measured several times in each patient. We suggest a generic dynamic model for a response variable, R, which is assumed to be a result of a balance between the velocity of increase (Vin) of R and the velocity of its decrease. Vin is assumed to be independent on R while the latter is proportional to R:
dR/dt = Vin – K*R = K*(Ro – R),
where K is a rate constant of the decrease in R, and Ro is an initial value of R at patient inclusion. By definition, Ro=Vin/K. The drug and placebo effect has to be separated from the spontaneous change in R with time which is caused by disease progression, recovery from previous therapy, etc. In the most parsimonious version of the model, it is assumed that a single parameter, S, is responsible for the spontaneous change. It may affect either Vin or K that gives 2 basic models:
dR/dt = Vin – K*S*R = K*(Ro – S*R) (Model 1)
dR/dt = Vin*S – K*R = K*(Ro*S – R) (Model 2)
Placebo may affect Vin or K, too, and this leads to 2 versions of each basic model, totally 4 models. By analogy, the active drug may alter Vin or K, and this results in 4 additional versions. The total number of models is thus 8. As the models are empirical the choice should be based on statistical tests after fitting all possible models to trial data. An additional parameter: the onset of action, was included in the models, and analytical solutions were obtained.
Application of the generic model is illustrated using the results of two double-blinded efficacy trials. A drug was assumed to improve patient conditions which were assessed by a daily symptom severity score ranged from 0 (no symptom) to 10 (highest possible severity). The same symptom was assessed in both trials, but the patients differed with respect to the underlying disease. Two active doses were compared against placebo. An optimal model was selected based on maximum likelihood: model 1 with the drug and placebo affecting K. Dose-response analysis was performed, and the drug was demonstrated to improve patient conditions in a dose-dependent fashion in one of the trials. Controversial results were obtained for another trial.
The proposed generic dynamic model may have a wide range of applications in data analysis and simulations.
Reference: PAGE 10 (2001) Abstr 213 [www.page-meeting.org/?abstract=213]
Poster: poster