Fitting Additive-multiplicative Hazard Models For Case-cohort Studies:a Multiple Imputation Approach

In this paper,we consider fitting additive–multiplicative hazard models for case-cohort studies using a multiple imputation approach.In the case-cohort study,the primary exposure variables were measured only in selected cases,but other covariates were typically obtained from the entire cohort.In many potentially large populations,expensive exposures cannot be measured for all individuals.Thus,contact disease association studies are usually based on case-cohort studies,where complete information is obtained only for the individuals sampled.However,there may be a large amount of information available about cheap covariates throughout the whole cohort,and they may be the primary exposed alternative,which is often not be used.We treated the case cohort study plus the rest of the cohort as a full cohort study with missing data.Therefore,we propose to use multiple interpolation to take advantage of the information in the whole cohort when analyzing data getting from substudy.We used complete observational data to fit the model.Using the method of incomplete data which called multiple interpolation,we consider it as a special case design of missing covariates to estimate the regression parameters of the additive-multiplication hazard model.For the interpolation model,we propose an interpolation method based on rejection sampling,and a simple interpolation method that can be naturally applied to the general missing at random situation is also proposed in this paper,and the interpolation effect of rejection sampling method is verified through a large number of simulation studies.In addition,we also use cancer data as an example to demonstrate the process of the proposed interpolation method.