Model-Based and/or Marginal Analysis for Multiple Event-Time Data?
We will explore the relationship between a marginal proportional hazards formulation for ordered failure times, as proposed by Wei, Lin and Weissfeld (1989) and strongly supported by Therneau (1997), and a conditional formulation advocated by, among others, Clayton (1988), Oakes (1992) and Pepe and Cai (1993). We review the derivation given by Oakes (1992) of a conditional proportional hazards model via an underlying frailty structure. Quite generally, we show that a family of absolutely continuous bivariate survivor functions cannot simultaneously satisfy the proportional hazards model both conditionally and unconditionally. We will explore the efficiency loss in using the marginal approach compared with full likelihood procedures in two simple special cases, and find it to be quite small.
KeywordsFailure Time Marginal Model Failure Time Data Cumulative Hazard Function Asymptotic Relative Efficiency
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