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For many cancer sites low-dose risks are not known and must be extrapolatedfrom those observed in groups exposed at much higher levels of dose.Measurement error can substantially alter the dose-response shape. Recently,there has been considerable attention paid to methods of dealing with sharederrors, which are common in many datasets. In this paper we test Bayesian modelaveraging (BMA) and frequentist model averaging (FMA) methods, the first ofthese similar to the so-called Bayesian two-dimensional Monte Carlo (2DMC)method, against a newly proposed modification of the regression calibrationmethod. The quasi-2DMC with BMA method performs poorly, with coverageprobabilities both for the linear and quadratic dose coefficients that areunder 5% when the magnitude of shared Berkson error is large (50%). The methodalso produces substantially biased (by a factor of 10) estimates of both linearand quadratic coefficients, with the linear coefficient overestimated and thequadratic coefficient underestimated. FMA performs generally better, althoughthe coverage probability for the quadratic coefficient is uniformly too high.However both linear and quadratic coefficients have upward bias, particularlywhen Berkson error is large. By comparison the extended regression calibrationmethod yields coverage probabilities that are too low when shared and unsharedBerkson errors are both large (50%), although otherwise it performs well, andcoverage is generally better than the quasi-2DMC with BMA or FMA methods. Thebias of the predicted relative risk at a variety of doses is generally smallestfor extended regression calibration, and largest for the quasi-2DMC with BMAand FMA methods, with standard regression calibration and Monte Carlo maximumlikelihood exhibiting bias in predicted relative risk generally somewhatintermediate between the other two methods.

A generalisation of the method of regression calibration and comparison with Bayesian and frequentist model averaging methods