  The case-cohort design obtains complete covariate data only on cases and on a
random sample (the subcohort) of the entire cohort. Subsequent publications
described the use of stratification and weight calibration to increase
efficiency of estimates of Cox model log relative hazards, and there has been
some work estimating pure risk. Yet there are few examples of these options in
the medical literature, and we could not find programs currently online to
analyze these various options. We therefore present a unified approach and R
software to facilitate such analyses. We used influence functions adapted to
the various design and analysis options together with variance calculations
that take the two-phase sampling into account. This work clarifies when the
widely used "robust" variance estimate of Barlow is appropriate. The
corresponding R software, CaseCohortCoxSurvival, facilitates analysis with and
without stratification and/or weight calibration, for subcohort sampling with
or without replacement. We also allow for phase-two data to be missing at
random for stratified designs. We provide inference not only for log relative
hazards in the Cox model, but also for cumulative baseline hazards and
covariate-specific pure risks. We hope these calculations and software will
promote wider use of more efficient and principled design and analysis options
for case-cohort studies.
