Abstract
In this paper we study the Buckley-James estimator of accelerated failure time models with auxiliary covariates. Instead of postulating distributional assumptions on the auxiliary covariates, we use a local polynomial approximation method to accommodate them into the Buckley-James estimating equations. The regression parameters are obtained iteratively by minimizing a consecutive distance of the estimates. Asymptotic properties of the proposed estimator are investigated. Simulation studies show that the efficiency gain of using auxiliary information is remarkable when compared to just using the validation sample. The method is applied to the PBC data from the Mayo Clinic trial in primary biliary cirrhosis as an illustration.
Highlights
It is not uncommon to have one or more missing or mismeasured covariates in large cohort epidemiological studies
If the validation sample is relatively small, utilizing the auxiliary information will lead to remarkable efficiency gain, as our simulation results will show
The results show a remarkable efficiency gain over the method which ignores the auxiliary information
Summary
It is not uncommon to have one or more missing or mismeasured covariates in large cohort epidemiological studies. There are always cases in medical studies, where it is difficult to obtain an accurate measurement for all patients due to a procedure being too expensive or invasive. All of the measurements are error prone, while in other cases, a validation subsample, where the measurements are all accurately taken, is made available. The former is a pure measurement error problem. The validation sample could be large enough on its own, so one could choose to ignore all data from subjects that have missing or mismeasured values for any of the covariates, with just a minor efficiency loss. If the validation sample is relatively small, utilizing the auxiliary information will lead to remarkable efficiency gain, as our simulation results will show
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