Efficient regression calibration for logistic regression in main study/internal validation study designs with an imperfect reference instrument

An extension to the version of the regression calibration estimator propose d by Rosner et al, for logistic and other generalized linear regression mod els is given for main study/internal validation study designs. This estimat or combines the information about the parameter of interest contained in th e internal validation study with Rosner et al.'s regression calibration est imate, using a generalized inverse-variance weighted average. It is shown t hat the validation study selection model can be ignored as long as this mod el is jointly independent of the outcome and the incompletely observed cova riates, conditional, at most, upon the surrogates and other completely obse rved covariates. In an extensive simulation study designed to follow a comp lex, multivariate setting in nutritional epidemiology, it is shown that wit h validation study sizes of 340 or more, this estimator appears to be asymp totically optimal in the sense that it is nearly unbiased and nearly as eff icient as a properly specified maximum likelihood estimator. A modification to the regression calibration variance estimator which replaces the standa rd uncorrected logistic regression coefficient variance with the sandwich e stimator to account for the possible misspecification of the logistic regre ssion fit to the surrogate covariates in the main study, was also studied i n this same simulation experiment. In this study, the alternative variance formula yielded results virtually identical to the original formula. A vers ion of the proposed estimator is also derived for the case where the refere nce instrument, available only in the validation study, is imperfect but un biased at the individual level and contains error that is uncorrelated with other covariates and with error in the surrogate instrument. Replicate mea sures are obtained in a subset of study participants. In this case it is sh own that the validation study selection model can be ignored when sampling into the validation study depends, at most, only upon perfectly measured co variates. Two data sets, a study of fever in relation to occupational expos ure to antineoplastics among hospital pharmacists and a study of breast can cer incidence in relation to dietary intakes of alcohol and vitamin A, adju sted for total energy intake, from the Nurses' Health Study, were analysed using these new methods. In these data, because the validation studies cont ained less than 200 observations and the events of interest were relatively rare, as is typical, the potential improvements offered by this new estima tor were not apparent. Copyright (C) 2001 John Wiley & Sons, Ltd.