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Table 2 List of pair types and their contribution to stratified partial likelihood

From: On hazard ratio estimators by proportional hazards models in matched-pair cohort studies

Type Number of pairs Observed data in the pair Observed time Y k1 Y k0 L k (β)
1 n 1 Exposed gets event first, followed by unexposed event X k1 < X k0 1 1 \(\frac{{{\text{e}}^{\beta } }}{{1 + {\text{e}}^{\beta } }}\)
2 n 2 Unexposed gets event first, followed by exposed event X k1 > X k0 1 1 \(\frac{1}{{1 + {\text{e}}^{\beta } }}\)
3 n 3 Exposed gets event first, followed by unexposed censored X k1 < X k0 1 0 \(\frac{{{\text{e}}^{\beta } }}{{1 + {\text{e}}^{\beta } }}\)
4 n 4 Unexposed gets event first, followed by exposed censored X k1 > X k0 0 1 \(\frac{1}{{1 + {\text{e}}^{\beta } }}\)
5 n 5 Exposed is censored first, followed by unexposed event X k1 < X k0 0 1 1
6 n 6 Unexposed is censored first, followed by exposed event X k1 > X k0 1 0 1
7 n 7 Exposed is censored first, followed by unexposed censored X k1 < X k0 0 0 1
8 n 8 Unexposed is censored first, followed by exposed censored X k1 > X k0 0 0 1
9 n 9 Exposed and unexposed are censored simultaneously X k1 = X k0 = τ 0 0 1