Power determination in vitamin D randomised control trials and characterising factors affecting it through a novel simulation-based tool

Abstract

Thousands of observational studies have linked vitamin D deficiency with numerous diseases, but randomised controlled trials (RCTs) often fail to show benefit of supplementation. Population characteristics and trial design have long been suspected to undermine power but were not systematically investigated. We propose a flexible generative model to characterise benefit of vitamin D supplementation at the individual level, and use this to quantify power in RCTs. The model can account for seasonality and population heterogeneity. In a simulated 1-year trial with 1000 participants per arm and assuming a 25-hydroxyvitamin D (25OHD) increase of 20 nmol/L due to the intervention, with baseline 25OHD in the population of 15, 35, 50, 60 and 75 nmol/L, the power to detect intervention effect was 77%, 99%, 95%, 68% and 19%, respectively. The number of participants required per arm to achieve 80% power according to baseline 25OHD of 15-60 nmol/L was 1200, 400, 600 and 1400, respectively. As expected, larger increases in 25OHD due to supplementation improved power in certain scenarios. For a population baseline of 50 nmol/L, with 1500 participants in each arm, there was 100% power to detect a 20 nmol/L 25OHD increase while it was 76% for a 10 nmol/L increase. Population characteristics and trial design, including temporal considerations, have a dramatic impact on power and required sample size in vitamin D RCTs.

Figure 1

25-hydroxyvitamin D (25OHD) status profiles for placebo, fixed-dose supplementation and concentration-controlled intervention schemes. The middle panel on the left compares the fixed-dose scheme with more uptake during deficient periods. Horizontal green dashed lines in the top two panels indicate effective overall mean levels of 25OHD assumed in the model.

Figure 2

Top row left: intensity function for a seasonal infection shown in units of exposures per week. Top row right: generalised logistic curves giving the risk scalings for $l=1$ and $u=1.5,2,3,4$. Bottom row left: example of an individual’s exposures shown in blue, with red centre indicating an infection developed following exposure. Bottom row right: corresponding 25OHD status at exposure, shown as a function of the probability of infection for that status level.

Figure 3

Simulation process for estimating the power of a study.

Figure 4

Power surfaces are shown for intervention that achieves a 25OHD increase of 10 nmol/L (left), 20 nmol/L (centre),and 40 nmol/L (right) versus placebo, against the sample size n and population baseline vitamin D status $\mu$. The top row shows surfaces when relative risk of 2 is assumed between fully insufficient and fully sufficient i.e. $u=2$, and the bottom row shows the same for $u=4$. Here n gives the number of participants in each trial arm.

Figure 5

Six month trials. Top row: power surfaces for “summer trial”, running from May until end of October. Bottom row: “winter trial” running from November through April. All experiments assume relative risk between fully depleted and fully replete of 2, $u=2$. n represents the number of participants in each trial arm.