The effect of exposure variance and exposure measurement error on study sample size: implications for the design of...

A small variability of exposure in a population, for example small variance in nutrient intake, limits the power of an epidemiologic study. McKeown-Eyssen and Thomas (J Chron Dis 1985; 38:559-568) have shown that by selecting a population with larger exposure variance vs one with smaller variance, the study sample size can be reduced by a factor equal to the ratio of the smaller to larger variance. The authors show that this benefit may be even greater for exposures measured with error. When there is measurement error, the sample size requirements are greatly increased. However, the proportional reduction in sample size from selecting a population with larger variance may be even greater when there is error than when there is not. Under certain assumptions, the validity of the exposure (correlation coefficient of the mismeasured exposure with the true exposure) is enhanced in the population with larger exposure variance, which provides the additional sample size benefit. Simple equations are presented that demonstrate quantitatively the substantial benefit of selecting a population with larger exposure variance when there is moderate or large measurement error. For example, selecting a population with a 30% greater standard deviation of exposure could reduce sample size requirements by 41% when the exposure is perfectly measured, but when the exposure is poorly measured with a validity coefficient of 0.6, the savings could be 56% if a population with 30% greater standard deviation of exposure could be studied. Applications of these results as well as the limitations of the assumptions are discussed.