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

Abstract

Case-cohort data analyses often ignore valuable information on cohort members not sampled as cases or controls. The Atherosclerosis Risk in Communities (ARIC) study investigators, for example, typically report data for just the 10%-15% of subjects sampled for substudies of their cohort of 15,972 participants. Remaining subjects contribute to stratified sampling weights only. Analysis methods implemented in the freely available R statistical system (http://cran.r-project.org/) make better use of the data through adjustment of the sampling weights via calibration or estimation. By reanalyzing data from an ARIC study of coronary heart disease and simulations based on data from the National Wilms Tumor Study, the authors demonstrate that such adjustment can dramatically improve the precision of hazard ratios estimated for baseline covariates known for all subjects. Adjustment can also improve precision for partially missing covariates, those known for substudy participants only, when their values may be imputed with reasonable accuracy for the remaining cohort members. Links are provided to software, data sets, and tutorials showing in detail the steps needed to carry out the adjusted analyses. Epidemiologists are encouraged to consider use of these methods to enhance the accuracy of results reported from case-cohort analyses.

Multiple imputation analysis of case–cohort studies

“…The multiple imputation estimator was compared to the standard weighted estimator [6], calibrated weights estimator [3] and re-estimated weights estimator [3]. The mean of the 1,000 log relative risk estimates, corresponding to the 1,000 subcohorts, are given in Table 6.…”

“…Qi et al [10] developed nonparametric methods to estimate selection probabilities and nonparametric kernel-smoothing techniques to estimate conditional expectation in fully augmented weighted estimating functions. Breslow et al [3] suggested calibrating or estimating the weights using all the phase-1 information in order to improve precision: 1) with calibration, the weights are subjected to the constraint that the cohort totals of some auxiliary variables are equal to their weighted sum among all phase-2 subjects. Practically, one builds a prediction model for the phase-2 variable to perform a simple imputation of the predicted values among the controls not belonging to the subcohort, ts the model of interest to the completed data set and uses the in uence function from the model of interest to calibrate.…”

“…The former was strongly predictive of the latter (speci city 98%, sensitivity 74%) and both were available for all the patients. However, like Breslow et al [3], we simulated case cohort studies using central histology as the phase-2 variable. For the NWTS analysis, the Cox model included central histology (phase-2 variable), age as a piecewise linear variable with change point at 1 year, stage III/IV versus I/II, tumor diameter and the interactions local histology*age and stage*diameter.…”

“…For the NWTS analysis, the Cox model included central histology (phase-2 variable), age as a piecewise linear variable with change point at 1 year, stage III/IV versus I/II, tumor diameter and the interactions local histology*age and stage*diameter. Breslow et al [3] de ned 16 strata according to event-free survival, stage (I/II or III/IV), favorable local histology (Yes or No) and age < 1 year (Yes or No). They sampled controls from only three strata, de ned by favorable local histology, and "age < 1 year + stage I/II" (n = 120), "age ≥ 1 + stage I/II" (n = 160) and "age ≥ 1 + stage III/IV" (n = 120), while including all the subjects in the 13 other strata.…”

“…Also, the weighted estimators used to analyze case cohort data are not fully e cient and this could a ect the estimate of the e ect of phase-2 variable(s). Alternatively, Breslow et al [3] suggested optimizing the sampling weights using all the available data. But case cohort studies can also be viewed as a particular example of incomplete data, in which the observation process is controlled by the study organizers.…”