Pharmacodynamics of controlled release verapamil in patients with hypertension: an analysis using spline functions

AIMS: To use a nonparametric approach involving longitudinal splines to model the baseline blood pressure profile and investigate the impact of this modelling on the pharmacodynamic analysis for verapamil in patients with angina or hypertension. METHODS: Dose ranging studies were conducted in patients with hypertension and with angina. Subjects received doses of 120, 180, 360 or 540 mg racemic verapamil. Pharmacodynamic data were created by subtracting the (systolic) blood pressure following active drug from the placebo response, either by direct subtraction or after modelling the baseline with a longitudinal spline model fitted to the placebo data by nonlinear mixed effects modelling. An Emax model was then used to describe the relationship between change in blood pressure and (R-)verapamil plasma concentration. RESULTS: The maximum decrease in systolic blood pressure was found to be 57.6 (+/- 26.1) mm and the C50 was 420 (+/- 349) microg/l for the data obtained by direct subtraction of the placebo data. Similar results were obtained when a cubic spline model was used to describe each individual's placebo response. However, the use of a population spline model only allowed a linear pharmacodynamic model to be fitted to the resulting data. Sparse data were created by randomly removing 66% of the data from the placebo and active phases. The population spline model gave very similar parameter estimates for the linear model applied to the sparse data to those obtained from the complete data set. CONCLUSIONS: The use of a longitudinal spline model together with nonlinear mixed effects modelling to account for baseline blood pressure response can be very powerful in a sparse data environment.