Epstein L D, Muñoz A
Department of Biostatistics, Johns Hopkins School of Public Health, Baltimore, Maryland 21205, USA.
Stat Med. 1996 Jun 15;15(11):1171-85. doi: 10.1002/(SICI)1097-0258(19960615)15:11<1171::AID-SIM230>3.0.CO;2-8.
In diseases such as acquired immune deficiency syndrome (AIDS), there is great interest in describing the frequency of secondary diagnoses that occur during the course of the disease and their effect on survival. Casting this situation in a more general framework, one distinguishes a terminal event (TE) and an intermediate event (IE) that may or may not occur. In epidemiologic applications the TE is usually death. Earlier studies of IE and TE times have used the latter to censor the IE time for individuals who do not present it. For such cases, we argue that more appropriately the TE removes the individual from the risk set for the IE. With this view, one distinguishes observations of four types, each with a different formula for its likelihood contribution. We propose an approach that uses separate parametric models for the marginal distribution of the survival time D and for the conditional distribution of the time R to the IE given D = d and R < or = D. A central quantity is the probability of presenting the IE given the occurrence of the TE at time d. This function of d can reveal important connections between the two events. We suggest a model derived from Weibull distributions where the parameters control the shape of this function. One can obtain inferences about other probabilities of interest such as the proportion of individuals who present the IE, P(R < or = D), the marginal distribution of R among the IE cases, P(R > r [symbol: see text] R < or = D) and the residual survival after the IE occurs, P(D - R > v [symbol: see text] R < or = D, R = r). We apply the model to the analysis of time to secondary Kaposi's sarcoma (KS) diagnosis and time to death in a large cohort study of homosexual men infected with the human immunodeficiency virus type 1 (HIV) and who had an initial non-KS AIDS diagnosis.
在诸如获得性免疫缺陷综合征（艾滋病）等疾病中，人们对描述疾病过程中发生的二次诊断频率及其对生存的影响非常感兴趣。将这种情况置于更一般的框架中，区分一个可能发生或不发生的终末事件（TE）和一个中间事件（IE）。在流行病学应用中，TE通常是死亡。早期关于IE和TE时间的研究使用后者对未出现IE的个体的IE时间进行截尾。对于此类情况，我们认为更合适的是TE将个体从IE的风险集中移除。基于这种观点，区分了四种类型的观察结果，每种类型的似然贡献公式不同。我们提出一种方法，该方法对生存时间D的边际分布以及给定D = d且R≤D时到IE的时间R的条件分布使用单独的参数模型。一个核心量是在时间d发生TE的情况下出现IE的概率。d的这个函数可以揭示两个事件之间的重要联系。我们建议一个源自威布尔分布的模型，其中参数控制这个函数的形状。可以获得关于其他感兴趣概率的推断，例如出现IE的个体比例P(R≤D)；IE病例中R的边际分布P(R > r | R≤D)；以及IE发生后的剩余生存时间P(D - R > v | R≤D, R = r)。我们将该模型应用于一项对感染1型人类免疫缺陷病毒（HIV）且最初诊断为非卡波西肉瘤（KS）型艾滋病的同性恋男性的大型队列研究中，分析二次KS诊断时间和死亡时间。
