Correcting covariate-dependent measurement error with non-zero mean.

There are many settings in which the distribution of error in a mismeasured covariate varies with the value of another covariate. Take, for example, the case of HIV phylogenetic cluster size, large values of which are an indication of rapid HIV transmission. Researchers wish to find behavioral correlates of HIV phylogenetic cluster size; however, the distribution of its measurement error depends on the correctly measured variable, HIV status, and does not have a mean of zero. Further, it is not feasible to obtain validation data or repeated measurements. We propose an extension of simulation-extrapolation, an estimation technique for bias reduction in the presence of measurement error that does not require validation data and can accommodate errors whose distribution depends on other, error-free covariates. The proposed extension performs well in simulation, typically exhibiting less bias and variability than either regression calibration or multiple imputation for measurement error. We apply the proposed method to data from the province of Quebec in Canada to examine the association between HIV phylogenetic cluster size and the number of reported sex partners.