Considering Over-Dispersion in the Sample Size Calculation for Clinical Trials With Repeated Count Measurements

Abstract

Over-dispersed count variables are frequently encountered in biomedical research. Despite extensive research in analytical methods, addressing over-dispersion in the design of clinical trials has received much less attention. In this study, we propose to directly incorporate over-dispersion into sample size calculation for clinical trials where a count outcome is repeatedly measured on each subject. The proposed method is applicable to the comparison of slopes as well as time-averaged responses. It is easy to compute and flexible enough to account for unbalanced randomization, arbitrary missing patterns, and different correlation structures. We show that sample size requirement is proportional to over-dispersion, which highlights the danger of ignoring over-dispersion in experimental design. Simulation results demonstrate that the proposed sample size calculation methods maintain the nominal levels of power and Type I error over a wide range of scenarios. Application example to an epileptic trial is presented. Supplementary materials for this article are available online.

Keywords:

• Correlated count data
• Experimental Design
• Over-dispersion
• Sample size

Supplementary Materials

In supplementary materials, a simple derivation of Equation (5)(5) $$\begin{array}{c}\widehat{{\beta }_1}=\hspace{0.17em}\text{log}\hspace{0.17em}\left(\frac{\sum _{i=1}^n(1-r_i)\sum _{j=1}^m{\Delta }_{\mathit{ij}}{y}_{\mathit{ij}}}{\sum _{i=1}^n(1-r_i)\sum _{j=1}^m{\Delta }_{\mathit{ij}}{T}_j}\right),\\ \widehat{{\beta }_2}=\hspace{0.17em}\text{log}\hspace{0.17em}\left(\frac{\sum _{i=n}^n{r}_i\sum _{j=1}^m{\Delta }_{\mathit{ij}}{y}_{\mathit{ij}}}{\sum _{i=n1}^n{r}_i\sum _{j=1}^m{\Delta }_{\mathit{ij}}{T}_j}\right)\\ -\hspace{0.17em}\text{log}\hspace{0.17em}\left(\frac{\sum _{i=1}^n(1-r_i)\sum _{j=1}^m{\Delta }_{\mathit{ij}}{y}_{\mathit{ij}}}{\sum _{i=1}^n(1-r_i)\sum _{j=1}^m{\Delta }_{\mathit{ij}}{T}_j}\right).\end{array}$$(5) is provided, a simple description of how to generate correlated count data with over-dispersion is presented and the R code for sample size calculations is provided.