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.

翻译：当连续暴露变量存在异方差性、测量误差可能自相关，或关注多个暴露时间点时，对样本量及估计量准确性与精确度的理解仍非常有限。因此，本文推导了样本量近似方程、估计量及其标准误的计算方法，包括针对异方差暴露分布滞后模型中非线性效应估计的多项式近似，这些方法适用于存在或不存在自相关测量误差的情形。本文提出的理论与方法可用于在暴露变量为连续型且存在测量误差的各种研究场景中高效设计研究方案。