Statistical power in vitamin D randomized control trials investigating biomarkers as continuous outcomes.

It has long been suspected that mean vitamin D level and differences among individuals in the population might deteriorate power in vitamin D randomised controlled trials (RCTs). However, standard statistical planning tools cannot accommodate these considerations. Here, to accommodate the large within-person and between-people heterogeneity in naturally fluctuating 25-hydroxyvitamin D (25OHD) concentration, a simulation based approach was used to investigate the power and sample size requirements in vitamin D supplementation RCTs looking at the proportion of regulatory T cells, %Tregs, as a continuous outcome. A range of sample sizes, mean increases in 25OHD in the intervention arm, and population 25OHD heterogeneity were tested. We found that in a population with a mean 25OHD of 50▒nmol/L and moderate heterogeneity in 25OHD (defined as inter-quartile range IQR = 20), sample size of approximately 1000 participants per arm is required to achieve 80% power if 25OHD increased by 10▒nmol/L in the intervention arm, compared to 250, < 100 and < 50 participants per arm if this increase was 20▒nmol/L, 40▒nmol/L or 60▒nmol/L, respectively. Thus we conclude that the increase in 25OHD in the intervention arm and population heterogeneity impact the power of vitamin D RCTs substantially. Sample size determination through simulation is a powerful approach for non-standard trials, and the work presented can easily be adopted to other intervention-outcome pairs.