Sample Size/Power Calculations for Population Pharmacodynamic Experiments Involving Repeated Count Measurements
Kayode Ogungbenro and Leon Aarons
Centre for Applied Pharmacokinetic Research, School of Pharmacy and Pharmaceutical Sciences, The University of Manchester, Oxford Road, Manchester, M13 9PT, United Kingdom
Objectives: To describe an approach for calculating sample size/power for population pharmacodynamic experiments involving repeated count measurements modelled as a Poisson process based on mixed-effects modelling technique. This work aims to extend the work of Rochon [1] on sample size/power calculations to repeated count measurements based on analysis by a mixed-effects modelling approach using hierarchical models and non-central Wald test.
Methods: The method proposed by Rochon (1) for hypothesis testing between groups under GLM based on analysis by GEE was extended to repeated count measurements under mixed effects modelling using a log link transformation. Expression for the information matrix based on the hypothesis to be tested were derived and used in the procedure for sample size/power calculations. The approach can be used to calculate power/sample size based on a model, parameter estimates and sampling design required to detect the difference in parameter estimates between groups, say placebo and treatment groups. Extensions to account for unequal allocation of subjects and sampling times between and within groups were also described. The approach was applied to a published example [2] based on the quantitative characterisation of the dose-efficacy and dose-side effect relationship of oxybutynin using mixed effects modelling approach. A model that defines the dose-efficacy relationship was developed for placebo and two other formulations: controlled release (XL) and immediate release (IR). Using the experimental design and parameter estimates described, the minimum sample size required to detect the difference between XL and IR dose groups were calculated at power=0.8,0.9 and significance level=0.05,0.01. The sample sizes obtained were also used for simulations in NONMEM and the empirical power of the designs were calculated and compared with the nominal power.
Results: The results obtained showed good agreement between the nominal power and the power of the design obtained from simulations. The results also showed that design factors especially number of sampling times and their placement can affect sample size. Designs obtained by optimising the information matrix required reduced total number of samples compared to the empirical design.
Conclusions: A fast and efficient approach has been described for calculating sample size/power for repeated count measurements in population PD experiments based on analysis by mixed-effects modelling. The method can account for unequal allocation of subjects and sampling times between and within groups. Carefully designed trial will produce efficient study and can help to reduce cost and other resources.
References:
[1] Rochon J. Application of GEE procedures for sample size calculations in repeated measures experiments. Stat. Med., 1998; 17: 1643-1658.
[2] Gupta SK, Sathyan G, Lindemulder EA, Ho PL, Sheiner LB, Aarons L. Quantitative characterization of therapeutic index: application of mixed-effects modeling to evaluate oxybutynin dose-efficacy and dose-side effect relationships. Clinical Pharmacology and Therapeutics, 1999; 65: 672-684.