Case-Cohort Studies

The case-cohort design was proposed by Ross Prentice as an alternative design in epidemiologic follow-up studies that is less expensive than a full-scale cohort study. The case-cohort design involves collecting covariate data only for cases, that is, subjects who experience the event of interest in a cohort, and for members of a relatively small randomly selected subcohort. The subcohort may serve as a comparison group for several different types of disease outcomes.

The case-cohort design can substantially reduce cost and effort of exposure assessment by limiting exposure to a small fraction of the cohort with only a small loss of efficiency compared with a full cohort design. The case-cohort design is most beneficial when the most expensive part of the study is not in ascertaining subjects but in measuring their exposures. If the main cost is in ascertainment, a full cohort analysis might be a more sensible approach to analysis.

The design is particularly suited to settings such as molecular epidemiologic studies, where raw materials for covariate information, for example, biospecimens, can be collected and stored. For the cases, these specimens can then be analyzed after the failure, that is, event of interest, has occurred, to determine what an [Page 132]individual's levels of exposure were at the times before failure. The case-cohort design has been applied in cancer research, cardiovascular disease, and HIV research and has become increasingly popular in genetic epidemiologic studies.

Most methods used to study relative risks in failure time models are based on the Cox proportional hazards model, which assumes a multiplicative form for the model of disease occurrence

where x(t) denotes covariates at time t, λ0(t)standsfor the baseline hazard rate for subjects with x = 0, and rr denotes the relative risk part, with rr(Xi(t), 0) = 1. Under the case-cohort design, most existing relative risk estimators are based on modifications of the full cohort partial likelihood score functions, by weighing the contributions from cases and subcohort members by the inverse of their true or estimated sampling probabilities. In the pseudo-likelihood approach proposed by Ross Prentice, for each failure, a sampled risk set is formed by the case and the controls who are in the subcohort. Subcohort members contribute to the analysis over the entire time on study, but the failures outside the subcohort contribute only at their failure times. The pseudo-likelihood contribution is based on the conditional probability that the case fails given that someone fails among those sampled into the risk set. The pseudo likelihood is then the product of the conditional probabilities over failure times. Letting Yi denote the ‘at-risk’ indicator of the ith subject at the failure time and rr the relative risk part, the pseudo likelihood is given by

This pseudo likelihood differs from the partial likelihood for a full cohort study in that the denominator is summing over subjects at risk in the subcohort rather than subjects at risk in the entire cohort. In addition, as cases are added at the time of event, the risk sets are not nested.

The score of the pseudo likelihood has expected value of 0 at the true value of b, but the inverse information does not estimate the variance of the estimator due to sampling-induced covariances between the score terms. The estimator has an asymptotic normal distribution and several approaches to variance estimation are available. Standard Cox regression software can be used to estimate parameters for case-cohort samples; however, variance computations need to be adapted to accommodate the design, which can be done using the delta beta option available in many statistics software packages.

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