Metamodels of bias in Cox proportional-hazards and logistic regressions with heteroscedastic measurement error under group-level exposure assessment

In occupational epidemiology, group-based exposure assessment entails estimating the average exposure level in a group of workers and assigning the average to all members of the group. The assigned exposure values can be used in epidemiological analyses and have been shown to produce virtually unbiased relative-risk estimates in many situations. Although the group-based exposure assessment continues to be used widely, it is unclear whether it produces unbiased relative-risk estimates in all circumstance, specifically in Cox proportional-hazards and logistic regressions when between-worker variance is not constant but proportional to the true group mean. This question is important because (i) between-worker variance has been shown to differ among exposure groups in occupational epidemiological studies and (ii) recent theoretical work has suggested that bias may exist in such situations. We conducted computer simulations of occupational epidemiological studies to address this question and analysed simulation results using 'metamodelling'. The results indicate that small-to-negligible bias can be expected to result from heteroscedastic between-worker variance. Cox proportional-hazards models can produce attenuated risk estimates, while logistic regression may result in overestimation of risk gradient. Bias caused by ignoring the heteroscedastic measurement error is unlikely to be large enough to alter the conclusion about the direction of exposure-disease association in occupational epidemiology.