A generalisation of the method of regression calibration and comparison with Bayesian and frequentist model averaging methods
For many cancer sites low-dose risks are not known and must be extrapolated from those observed in groups exposed at much higher levels of dose. Measurement error can substantially alter the dose-response shape and hence the extrapolated risk. Recently, there has been considerable attention paid to methods of dealing with shared errors, which are particularly important in occupational and environmental settings. In this paper we test Bayesian model averaging (BMA) and frequentist model averaging (FMA) methods, the first of these similar to the so-called Bayesian two-dimensional Monte Carlo (2DMC) method, and both fairly recently proposed, against a very newly proposed modification of the regression calibration method, the extended regression calibration (ERC) method. The quasi-2DMC+BMA method performs well when a linear model is assumed, but poorly when a linear-quadratic model is assumed. FMA performs as well as quasi-2DMC+BMA when a linear model is assumed, and generally much better with a linear-quadratic model, although the coverage probability for the quadratic coefficient is uniformly too high. ERC yields coverage probabilities that are too low when shared and unshared Berkson errors are both large (50%), although otherwise it performs well, and coverage is generally better than the quasi-2DMC+BMA or FMA methods, particularly for the linear-quadratic model. The bias of predicted relative risk at a variety of doses is generally smallest for ERC, and largest for quasi-2DMC+BMA and FMA, with standard regression calibration and Monte Carlo maximum likelihood exhibiting bias in predicted relative risk generally somewhat intermediate between ERC and the other two methods. In general ERC performs best in the scenarios presented, and should be the method of choice in situations where there may be substantial shared error, or suspected curvature in the dose response.