🤖 AI Summary
Measurement error in heteroscedastic continuous exposures, across multiple time points and calibration settings, substantially biases sample size planning, induces estimation bias, and distorts standard error accuracy in distributed lag models—yet existing methods lack a unified framework to address these challenges. This paper introduces the first analytical approximation framework that jointly accommodates nonlinear exposure–response relationships, diverse measurement error structures (differential vs. nondifferential; additive vs. multiplicative; temporally autocorrelated), and multitemporal calibration with or without validation data. Leveraging error propagation theory and Taylor series expansion, integrated with polynomial effect modeling and heteroscedasticity-robust inference, we derive closed-form expressions for required sample size, bias correction, and standard error adjustment. The proposed method markedly improves estimation accuracy and statistical power, as demonstrated through comprehensive simulations and application to real-world environmental exposure studies.
📝 Abstract
Measurement error is a pervasive challenge across many disciplines, yet its impact on sample size determination and the accuracy and precision of estimators 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. The framework accommodates 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 theory and methods provide practical tools for efficient research design and a deeper understanding of measurement error impacts on research, while seamlessly integrating uncertainty analyses.