Bayesian Method for Improving Logistic Regression Estimates under Group-Based Exposure Assessment with Additive Measurement Errors

Abstract

The group-based exposure assessment has been widely used in occupational epidemiology. When the sample size used to estimate group means is "large", this leads to negligible attenuation in the estimation of odds ratio. However, the bias is proportional to the between-subject variability and is affected by the difference in true group means. We explore a Bayesian method, which adjusts in a natural way for the extra uncertainty in the outcome model associated with using the predicted values as exposures. We aim to improve the estimate obtained in naïve analysis by exploiting the properties of Berkson type error structure. We consider cases where differences in the proximity of group means and the between-subject variance are both large. The results of the simulations show that our Bayesian measurement error adjustment method that follows group-based exposure assessment improves estimates of odds ratios when the between-subject variance is large and group means are far apart.

A comparison of Bayesian hierarchical modeling with group‐based exposure assessment in occupational epidemiology

“…There is another conclusion from our theoretical calculation, which can be supported by the simulation results mentioned in . Assume that there is the same increment between the adjacent group means.…”

“…Assume that there is the same increment between the adjacent group means. Kim and Burystyn inspected the bias and MSE of the estimated β 1 when β 0 = − 4, β 1 = 0.4, and μ 1 = 0.1 and the increment varies as 0.3,0.5,1, and 1.414 in their simulation studies. They concluded that when the increment between groups is large and the between‐subject variance is relatively small, the group‐based exposure assessment method gives unbiased estimates, whereas it fails to adjust for the measurement errors properly when the increment is small.…”

“…To compare the performance of the fully Bayesian method and the group‐based exposure assessment method, we design the following simulation studies corresponding to some occupational epidemiological settings . We simulate data with 5000 workers, who are categorized into five groups with the true group exposure means, μ g = 1.1, 2.1, 3.1, 4.1, and 5.1.…”

“…Then they postulated an approximate Berkson error model as , where ε gi is normally distributed and . On the basis of this Berkson error model, Kim and Burystyn showed that Bayesian methods can provide less‐biased estimates of the association parameter compared with the group‐based exposure assessment method, when the group means are far apart and there are moderate between‐subject variations. Kim et al further relaxed the requirement on the independence between the group mean exposure and the measurement error, and introduced a quasi‐Berkson measurement error model, which allows for correlation between the group mean and the random error when the group mean is a random effect.…”

Lifetime cumulative exposure to rubber dust, fumes and N-nitrosamines and non-cancer mortality: a 49-year follow-up of UK rubber factory workers

“…Sensitivity analyses were conducted with alternative simulated employment durations based on information on employment durations from another, partly overlapping, cohort of British rubber factory workers6 15 29 and showed that results of the main analyses are robust. Although exposure estimates from JEMs are generated from mean exposure values and therefore do not allow for individual variabilities, errors that arise from them tend to be attenuated Berkson-type errors, which, unlike random errors, generally do not bias exposure–response associations 30–32. Finally, exposure-specific estimates of LCE enabled multipollutant models to explore issues of complex exposure mixtures across the production process.…”