Comparing different ways of calculating sample size for two independent means: A worked example

We discuss different methods of sample size calculation for two independent means, aiming to provide insight into the calculation of sample size at the design stage of a parallel two-arm randomised controlled trial (RCT). We compare different methods for sample size calculation, using published results from a previous RCT. We use variances and correlation coefficients to compare sample sizes using different methods, including 1. The choice of the primary outcome measure: post-intervention score vs. change from baseline score. 2. The choice of statistical methods: t-test without using correlation coefficients vs. analysis of covariance (ANCOVA). We show that the required sample size will depend on whether the outcome measure is the post-intervention score, or the change from baseline score, with or without baseline score included as a covariate. We show that certain assumptions have to be met when using simplified sample size equations, and discuss their implications in sample size calculation when planning an RCT. We strongly recommend publishing the crucial result "mean change (SE, standard error)" in a study paper, because it allows (i) the calculation of the variance of the change score in each arm, and (ii) to pool the variances from both arms. It also enables us to calculate the correlation coefficient in each arm. This subsequently allows us to calculate sample size using change score as the outcome measure. We use simulation to demonstrate how sample sizes by different methods are influenced by the strength of the correlation.