Sample Size and Bias Approximations For Continuous Exposures Measured with Error

Abstract: Measurement error is a pervasive challenge across many disciplines, yet its impact on sample size determination and the accuracy and precision of estimators regarding the association between an exposure and an outcome remains understudied in real-world complex scenarios. These include heteroskedastic continuous exposures, error-prone measurements, multiple exposure time points, and the use of calibrated exposure variables. This article develops approximation equations for sample size calculations, estimator accuracy, and standard errors of the estimator in estimating the effect of an exposure on an outcome. For sample size calculations, as an example, we focus on (nested) matched case-control studies with conditional logistic regression. But they could be extended to other settings with sample size equations elsewhere. Our approximation of estimator accuracy is based on linear model approximations that can be applied to logistic regression and linear models. This paper considers non-linear effect estimation using polynomials and addresses non-differential, autocorrelated, and differential additive or multiplicative measurement errors in distributed lag models for heteroskedastic exposures in the absence or presence of exposure validation data. The proposed framework will provide insights into efficient research design and a deeper understanding of measurement error impacts on research.