Reflection on modern methods: calculating a sample size for a repeatability sub-study to correct for measurement error in a single continuous exposure.

Using a continuous exposure variable that is measured with random error in a univariable linear regression model leads to regression dilution bias: the observed association between the exposure and outcome is smaller than it would be if the true value of the exposure could be used. A repeatability sub-study, where a sample of study participants have their data measured again, can be used to correct for this bias. It is important to perform a sample size calculation for such a sub-study, to ensure that correction factors can be estimated with sufficient precision. We describe how a previously published method can be used to calculate the sample size from the anticipated size of the correction factor and its desired precision, and demonstrate this approach using the example of the cross-sectional studies conducted as part of the International Project on Cardiovascular Disease in Russia study. We also provide correction factors calculated from repeat data from the UK Biobank study, which can be used to help plan future repeatability studies