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

TL;DR

This paper investigates when regression calibration using external validation studies provides unbiased estimates of exposure effects in epidemiology, analyzing conditions for transportability and bias reduction.

Contribution

It provides theoretical conditions for the transportability of regression calibration with external validation, including bias assessment under departures from assumptions.

Findings

Regression calibration can be biased if transportability assumptions are violated.

Under most conditions, regression calibration yields lower bias than naive methods.

Simulation and real data confirm theoretical bias reduction benefits.

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.