Sample Size and Bias Approximations For Continuous Exposures Measured with Error

Understanding of sample size and the accuracy and precision of the estimator is very limited when continuous exposure is heteroskedastic, measured with error that may be autocorrelated, or when multiple exposure time points are of interest. Therefore, this article develops approximation equations for sample size, estimates of the estimators, and standard errors, including polynomials for non-linear effect estimation in the absence or presence of autocorrelated measurement error for distributed lags of heteroskedastic exposures. The theory and methods developed here can be used to efficiently design research in various settings when exposure variables are continuous and measured with error.