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Table 3 Components of the counter-matched (CM) set likelihood calculation for third set illustrated in Fig. 2

From: Study design: Evaluating gene–environment interactions in the etiology of breast cancer – the WECARE study

Possible CM set configuration     
Case Controls pr(case) Case RRT status pr(controls|case) Weighta
9 18, 24 λr(Z 9;β) + 1/12 × 1/7 8/2
18 9, 24 λr(Z 18;β) - 2/(8 × 7) 12
24 9, 18 λr(Z 24;β) + 1/7 × 1/12 8/2
  1. The calculation requires the probability of each of the possible case/control combinations, given that subjects 9,18, and 24 are in the counter-matched set. pr(case) is the probability that the subject is a case based on the proportional hazards model. For instance, for subject 9, λ is the baseline hazard, r(Z 9;β) is the rate ratio based on the covariate value, and is the rate ratio parameter. pr(controls|case) are control selection β probabilities. For example, for subject 18, because she is RRT-, pr(controls = 9,24|case = 18) is the probability of sampling two RRT+ from the 8 in the risk set. aWeights for analysis equal to pr(controls|case) × 12 × (8 × 7/2).