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The case-cohort design obtains complete covariate data only on cases and on arandom sample (the subcohort) of the entire cohort. Subsequent publicationsdescribed the use of stratification and weight calibration to increaseefficiency of estimates of Cox model log relative hazards, and there has beensome work estimating pure risk. Yet there are few examples of these options inthe medical literature, and we could not find programs currently online toanalyze these various options. We therefore present a unified approach and Rsoftware to facilitate such analyses. We used influence functions adapted tothe various design and analysis options together with variance calculationsthat take the two-phase sampling into account. This work clarifies when thewidely used "robust" variance estimate of Barlow is appropriate. Thecorresponding R software, CaseCohortCoxSurvival, facilitates analysis with andwithout stratification and/or weight calibration, for subcohort sampling withor without replacement. We also allow for phase-two data to be missing atrandom for stratified designs. We provide inference not only for log relativehazards in the Cox model, but also for cumulative baseline hazards andcovariate-specific pure risks. We hope these calculations and software willpromote wider use of more efficient and principled design and analysis optionsfor case-cohort studies.

Cox model inference for relative hazard and pure risk from stratified weight-calibrated case-cohort data