Sample size re-estimation in cross-over trials: a simulation study investigating the type I error, power and sample size in the AIM HY-INFORM study
Hypertension is the single biggest contributor to the global burden of disease in the UK. It is widely accepted that ethnicity is one factor that is associated with hypertension and which influences the response to existing first-line antihypertensive treatments. In the UK hypertension treatment is stratified by age and self-defined ethnicity (SDE), problems associated with this include a lack of data from UK populations supporting the current SDE stratification and no reference to South Asians – the largest ethnic minority group in the UK. The primary objective of the AIM HY-INFORM study is to determine if the response to existing first-line anti-hypertensive drugs differs by ethnic group for patients on mono- or dual therapies. The work presented here will consider patients on a monotherapy treatment regime. The study design is a 3-period 3-treatment cross-over trial in a multi-ethnic cohort of hypertensives using a linear mixed effects model with subject as a random effect. With the absence of prior estimates of the within-subject SD, one problem with this multilevel design is the calculation of the required sample size to ensure the desired power to detect a single ethnic by treatment interaction. Sample-size re-estimation designs can be used in this context to change the sample size according to accrued information in a statistically robust way. Ahead of trial recruitment, a simulation study was carried out with the main aims of (i) Assessing the properties of the hypothesis tests for the sample size defined in the AIM HY-INFORM study protocol; (ii) Estimating the fixed (single ethnic by treatment interaction) and random (within-subject SD) estimates of interest along with their summary and performance measures; (iii) Simulating an interim analysis after 50 subjects have completed their treatment sequence to re-assess the sample size calculation. Results and performance measures will show that the hypothesis-generating procedure attains a size of 0.05 for 1000 simulations with a protocol sample size of 600 subjects for different within and between-subject SDs. The estimated power is in line with that achieved in the study protocol and an underestimated assumed within-subject SD requires a larger than planned study sample size; providing a means of preserving the power of the study, a distinct advantage over a fixed design.