Using the whole cohort in the analysis of countermatched samples

We present a technique for using calibrated weights to incorporate whole-cohort information in the analysis of a countermatched sample. Following Samuelsen's approach for matched case-control sampling, we derive expressions for the marginal sampling probabilities, so that the data can be treated as an unequally-sampled case-cohort design. Pseudolikelihood estimating equations are used to find the estimates. The sampling weights can be calibrated, allowing all whole-cohort variables to be used in estimation; in contrast, the partial likelihood analysis makes use only of a single discrete surrogate for exposure. Using a survey-sampling approach rather than a martingale approach simplifies the theory; in particular, the sampling weights need not be a predictable process. Our simulation results show that pseudolikelihood estimation gives lower efficiency than partial likelihood estimation, but that the gain from calibration of weights can more than compensate for this loss. If there is a good surrogate for exposure, countermatched sampling still outperforms case-cohort and two-phase case-control sampling even when calibrated weights are used. Findings are illustrated with data from the National Wilms' Tumour Study and the Welsh nickel refinery workers study.