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Transportability of Regression Calibration with External Validation Studies for Measurement Error Correction

Zexiang Li, Donna Spiegelman, Molin Wang, Zuoheng Wang, Xin Zhou

TL;DR

This paper investigates the transportability of regression calibration (RC) when correcting measurement error using external validation studies. It derives a necessary and sufficient condition for RC validity: the conditional variance $\mathrm{Var}(\mathbf{x}|\mathbf{W})$ must be the same across the main study and the external validation study, which equivalently reduces to $\mathrm{Var}(\mathbf{Z}|\mathbf{W})$ as a practical indicator. Through simulation studies on continuous and binary outcomes and an illustrative application in the Health Professionals Follow-Up Study, it shows that RC typically reduces bias relative to the naive approach under modest transportability deviations, though larger violations can attenuate the gains. The results provide a principled framework for applying RC with external validation, including a concrete diagnostic via $\mathrm{Var}(\mathbf{Z}|\mathbf{W})$, and offer guidance for alloyed gold standard settings.

Abstract

In nutritional and environmental epidemiology, exposures are impractical to measure accurately, while practical measures for these exposures are often subject to substantial measurement error. Regression calibration is among the most used measurement error correction methods with external validation studies. The use of external studies to assess the measurement error process always carries the risk of introducing estimation bias into the main study analysis. Although the transportability of regression calibration is usually assumed for practical epidemiology studies, it has not been well studied. In this work, under the measurement error process with a mixture of Berkson-like and classical-like errors, we investigate conditions under which the effect estimate from regression calibration with an external validation study is unbiased for the association between exposure and health outcome. We further examine departures from the transportability assumption, under which the regression calibration estimator is itself biased. However, we theoretically prove that, in most cases, it yields lower bias than the naive method. The derived conditions are confirmed through simulation studies and further verified in an example investigating the association between the risk of cardiovascular disease and moderate physical activity in the health professional follow-up study.

Transportability of Regression Calibration with External Validation Studies for Measurement Error Correction

TL;DR

This paper investigates the transportability of regression calibration (RC) when correcting measurement error using external validation studies. It derives a necessary and sufficient condition for RC validity: the conditional variance must be the same across the main study and the external validation study, which equivalently reduces to as a practical indicator. Through simulation studies on continuous and binary outcomes and an illustrative application in the Health Professionals Follow-Up Study, it shows that RC typically reduces bias relative to the naive approach under modest transportability deviations, though larger violations can attenuate the gains. The results provide a principled framework for applying RC with external validation, including a concrete diagnostic via , and offer guidance for alloyed gold standard settings.

Abstract

In nutritional and environmental epidemiology, exposures are impractical to measure accurately, while practical measures for these exposures are often subject to substantial measurement error. Regression calibration is among the most used measurement error correction methods with external validation studies. The use of external studies to assess the measurement error process always carries the risk of introducing estimation bias into the main study analysis. Although the transportability of regression calibration is usually assumed for practical epidemiology studies, it has not been well studied. In this work, under the measurement error process with a mixture of Berkson-like and classical-like errors, we investigate conditions under which the effect estimate from regression calibration with an external validation study is unbiased for the association between exposure and health outcome. We further examine departures from the transportability assumption, under which the regression calibration estimator is itself biased. However, we theoretically prove that, in most cases, it yields lower bias than the naive method. The derived conditions are confirmed through simulation studies and further verified in an example investigating the association between the risk of cardiovascular disease and moderate physical activity in the health professional follow-up study.
Paper Structure (8 sections, 29 equations, 1 figure, 3 tables)

This paper contains 8 sections, 29 equations, 1 figure, 3 tables.

Table of Contents

  1. Introduction
  2. Methods
  3. Review
  4. Measurement Error Mechanism
  5. Validity Condition of RC
  6. Simulation Studies
  7. Illustrative Example
  8. Discussion

Figures (1)

  • Figure 1: Graphs showing the relative bias of the naive estimator (solid), and the relative bias of the RC method (dashes). In the main study, $x_i\sim(a_{0,m}+A_{2,m}W_i,\sigma_m^2), Z_i\sim (c_0 + C_1x_i + C_2W_i,\sigma^2)$. In the external validation study, $x_i\sim(a_{0,v}+A_{2,v}W_i,\sigma_v^2), Z_i\sim (c_0 + C_1x_i + C_2W_i,\sigma^2)$.

Theorems & Definitions (1)

  • proof