A generalisation of the method of regression calibration and comparison with the Bayesian 2-dimensional Monte Carlo method.

For many cancer sites it is necessary to assess risks from low-dose exposures via extrapolation from groups exposed at moderate and high levels of dose. Measurement error can substantially alter the shape of this relationship and hence the derived population risk estimates. Even in studies with direct measurement of low-dose exposures measurement error could be substantial in relation to the size of the dose estimates and thereby distort population risk estimates. Recently, much attention has been devoted to the issue of shared errors, common in many datasets, and particularly important in occupational settings. In this paper we test a Bayesian model averaging method, the so-called Bayesian two-dimensional Monte Carlo (2DMC) method, that has been fairly recently proposed against a very newly proposed modification of the regression calibration method, which is particularly suited to studies in which there is a substantial amount of shared error, and in which there may also be curvature in the true dose response. We also compared both methods against standard regression calibration and Monte Carlo maximum likelihood. The Bayesian 2DMC method performs poorly, with coverage probabilities both for the linear and quadratic dose coefficients that are under 5%, particularly when the magnitudes of classical and Berkson error are both moderate to large (20%-50%). The method also produces substantially biased (by a factor of 10) estimates of both the linear and quadratic coefficients, with the linear coefficient overestimated and the quadratic coefficient underestimated. By comparison the extended regression calibration method 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 Bayesian 2DMC and all other methods. The bias of the predicted relative risk at a variety of doses is generally smallest for extended regression calibration, and largest for the Bayesian 2DMC method (apart from unadjusted regression), with standard regression calibration and Monte Carlo maximum likelihood exhibiting bias in predicted relative risk generally somewhat intermediate between the other two methods.