Multiple imputation analysis of case–cohort studies

Abstract

The usual methods for analyzing case–cohort studies rely on sometimes not fully efficient weighted estimators. Multiple imputation might be a good alternative because it uses all the data available and approximates the maximum partial likelihood estimator. This method is based on the generation of several plausible complete data sets, taking into account uncertainty about missing values. When the imputation model is correctly defined, the multiple imputation estimator is asymptotically unbiased and its variance is correctly estimated. We show that a correct imputation model must be estimated from the fully observed data (cases and controls), using the case status among the explanatory variable. To validate the approach, we analyzed case–cohort studies first with completely simulated data and then with case–cohort data sampled from two real cohorts. The analyses of simulated data showed that, when the imputation model was correct, the multiple imputation estimator was unbiased and efficient. The observed gain in precision ranged from 8 to 37 per cent for phase‐1 variables and from 5 to 19 per cent for the phase‐2 variable. When the imputation model was misspecified, the multiple imputation estimator was still more efficient than the weighted estimators but it was also slightly biased. The analyses of case–cohort data sampled from complete cohorts showed that even when no strong predictor of the phase‐2 variable was available, the multiple imputation was unbiased, as precised as the weighted estimator for the phase‐2 variable and slightly more precise than the weighted estimators for the phase‐1 variables. However, the multiple imputation estimator was found to be biased when, because of interaction terms, some coefficients of the imputation model had to be estimated from small samples. Multiple imputation is an efficient technique for analyzing case–cohort data. Practically, we suggest building the analysis model using only the case–cohort data and weighted estimators. Multiple imputation can eventually be used to reanalyze the data using the selected model in order to improve the precision of the results. Copyright © 2011 John Wiley & Sons, Ltd.

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

“…Breslow et al [9] suggested calibrating or estimating the weights a posteriori, using all the phase-1 information, to improve precision with respect to classical weighted estimators. Marti and Chavance [10] showed that multiple imputation (MI) is a good alternative to classical weighted methods for the analysis of case-cohort data. When the imputation model was correct, the MI approach provided unbiased estimators of the log hazard ratios and correctly estimated the variance of its estimators.…”

Z-estimation and stratified samples: application to survival models

“…To our knowledge, concrete proposals for implementation involve assumptions that may limit applicability, for example, to discrete covariates (Nan 2004), to complete independence (not just conditional on covariates) of survival and censoring times (Scheike and Martinussen 2004) and to situations where all the auxiliary variables are included in the model (Zeng and Lin 2014). Multiple imputation of the “missing data” is another option, but requires correct specification of the imputation model for consistency (Marti and Chavance 2011; Keogh and White 2013). Most of these proposals, furthermore, have been restricted to (stratified) versions of the case-cohort design in which all cases (“deaths”) are sampled at Phase II (Prentice 1986; Borgan et al 2000).…”

Using the Whole Cohort in the Analysis of Case-Control Data

“…One feasible alternative approach is multiple imputation, though the increased efficiency is gained at the price of assuming a correct imputation model. [21]…”