On the Identifiability Crisis in Competing Risks Analysis
本文指出竞争风险分析中基于完全参数模型存在比以往描述更严重的非可识别性问题，即假定的多元分布无法从观测数据中验证，并发现存活一次以上失效的系统也存在类似问题。
Competing risks analysis, based on fully parametric models, suffers from well known non-identifiability in which the assumed multivariate distribution is not verifiable from observed data. It is shown here that the situation is even worse than previously described. Further, systems which survive one or more failures are investigated and an analogous is found. 1. Purpose The theory of competing risks is often based on the distribution of vector T = (T., Tp) of positive random variables. The Tj are notional or latent survival times of an animal or piece of equipment simultaneously exposed to p risks or causes of failure. The essential feature of the basic formulation is that only the time U and cause C of first failure are observable, so U = min(Tj) = Tc. Once failure or death has occurred from an identified cause it cannot occur again later from another cause. Thus the sample consists of bivariate observations on (C, U). Gail (1975) gives an interesting review, and David & Moeschberger (1978) give an extended treatment. Cox (1959) pinpointed difficulty of interpretation. He states (1959, p. 414) that for the bivariate case no data of the present type can be inconsistent with model which has Tl and T2 independent. Tsiatis (1975, theorem 2) proves similar non-identifiability aspect for the general p-variate case and concludes that a realistic treatment of the of competing risks depends on an analysis of biological circumstances more delicate than the model of potential survival times can provide. Peterson (1976) agrees that serious errors can be made in estimating the potential survival functions in the competing risks problem because one can never know from the data whether the Tj are independent or not. Gail (1975, p. 210) says that An inherent difficulty in competing risk analysis is that ... the analysis rests on unverifiable assumptions about the structure of the joint distribution of the Tj.