A comparison of two different methods of Bayesian model averaging for assessing the effects of covariate measurement errors

Low-dose radiation risks are generally extrapolated from groups exposed at high levels of dose. Measurement error substantially alters dose-response shape and hence extrapolated risk. Much attention has been paid to methods of dealing with shared errors, common in many datasets, in particular using Bayesian model averaging (BMA) methods. We test two types of BMA model using simulated data. The first we term the quasi-two-dimensional Monte Carlo with BMA (quasi-2DMC + BMA) method, similar to the BMA method proposed by Hoeting et al. but distinct from the 2DMC + BMA method of Kwon et al. The second we term the marginal-quasi-2DMC + BMA method, which uses a more complicated marginal calculation, and may be closer to the 2DMC + BMA method of Kwon et al. Assuming a true linear model of dose response, the coverage probabilities for the linear coefficient are 90–95%, for the quasi-2DMC + BMA method, but lower than this, 52–60%, for the marginal-quasi-2DMC + BMA method. Assuming a true linear-quadratic model the coverage probabilities of both linear/quadratic excess relative risk (ERR) coefficients for quasi-2DMC + BMA are too low, and when shared Berkson error is large (50%) the probabilities do not exceed 5%. By comparison, the coverage probabilities for both linear and quadratic coefficients for the marginal-quasi-2DMC + BMA method are generally too high, about 100%. For the linear model quasi-2DMC + BMA yields good estimates of the ERR coefficient, but for marginal-quasi-2DMC + BMA these are upwardly biased. For the linear-quadratic model both quasi-2DMC + BMA and marginal-quasi-2DMC + BMA methods yield substantially biased estimates. The performance of both quasi-2DMC + BMA and marginal-quasi-2DMC + BMA methods is bad, with bias and poor coverage.