Multiple imputation for estimating hazard ratios and predictive abilities in case-cohort surveys

We performed simulations to validate the MI approach for estimating hazard ratios and the predictive ability of a model or of an additional variable in case-cohort surveys. As an illustration, we analyzed a case-cohort survey from the Three-City study to estimate the predictive ability of D-dimer plasma concentration on coronary heart disease (CHD) and on vascular dementia (VaD) risks.When the imputation model of the phase-2 variable was correctly specified, MI estimates of hazard ratios and predictive abilities were similar to those obtained with full data. When the imputation model was misspecified, MI could provide biased estimates of hazard ratios and predictive abilities. In the Three-City case-cohort study, elevated D-dimer levels increased the risk of VaD (hazard ratio for two consecutive tertiles = 1.69, 95%CI: 1.63-1.74). However, D-dimer levels did not improve the predictive ability of the model.MI is a simple approach for analyzing case-cohort data and provides an easy evaluation of the predictive ability of a model or of an additional variable.Case-cohort surveys produce incomplete data by design. A subcohort is selected by simple or stratified random sampling, all subjects are followed up and the events of interest are recorded. The phase-1 variables are observed for the entire cohort, whilethe phase-2 variables are only known for the case-cohort sample, i.e., subjects belonging to the subcohort and all those presenting the event of interest [1]. Thus, in case-cohort studies, the non-cases who do not belong to the subcohort are incompletely observed by design, enabling cost reduction with a small loss of efficiency.Various approaches have been described to estimate the proportional hazard model in case-cohort surveys: Weighted estimators [2-6] are classically used in these surveys, with analysis restricted to the completely observed subsample, so the information collected for incompletely observed non-cases is ignored and inefficient estimators for the