Adjusting for measurement error in the Cox proportional hazards regression model.

Abstract

Background: The Harvard Six Cities Study (Dockery et al.) was the first large-scale cohort study to demonstrate an association between long-term exposure to fine particulate matter less than 2.5 microns in aerodynamic diameter (PM2.5) and mortality in urban centres in the United States. Because of the pivotal role of this study in the establishment of the first U.S. national ambient air quality objective for PM2.5 in 1997 (Greenbaum et al.), the results of this study were subjected to an independent detailed re-analysis to test the robustness of the findings to alternative analytic methods (Krewski et al.), including an assessment of the effect of exposure measurement error on estimates of risk based on the Cox proportional hazards model. It is well-known that random measurement error leads to downward bias in estimates of risk, and overstatement of the precision of such estimates.

Methods: Data from the Harvard Six Cities Study were used to evaluate the potential impact of measurement error on estimates of risk. After introducing a known amount of measurement error into the original data, estimates of risk were calculated using two methods for adjusting for measurement error: regression calibration (RCAL) and simulation extrapolation (SIMEX). With RCAL, the observed value of PM2.5 is replaced by its expected value with respect to the measurement error distribution. SIMEX adjusts for measurement error by adding progressively larger errors to the data and then extrapolating back to the case of no measurement error. Computer simulation was used to evaluate the accuracy and precision of both RCAL and SIMEX, and to assess the robustness of RCAL to mis-specification of the measurement error distribution.

Results and conclusions: When the measurement error distribution was correctly specified, RCAL greatly reduced the downward bias in risk estimates induced by random measurement error, even when the degree of measurement error was relatively large. SIMEX, on the other hand, failed to adequately adjust for the effects of random measurement error in the Cox model, even in the presence of a moderate degree of measurement error. Although RCAL is thus preferable to SIMEX, RCAL was not robust against mis-specification of the measurement error distribution, seriously overestimating (underestimating) risk when the measurement error was overstated (understated).