Do We Really Want a Marginal Model for Correlated Survival Data?

• Main Author: 洪慧茹
• Other Authors: 胡賦強
• Format: Others
• Language: zh-TW
• Published: 1997
• Online Access: http://ndltd.ncl.edu.tw/handle/18225036353534949560

碩士 === 國立臺灣大學 === 流行病學研究所 === 85 === Correlated survival data may come in various forms: (1) multivariate survival data we measure the times to several different events on each subject, e.g. times to the recovery from a disease and to the occurrence of an unwanted side-effect (in a randomized clinical trial): (2) repeated survival data - we measure the time to one recurrent event, i.e. the event can occur more than once over time, on each subject; (3) clustered survival data - we measure the time to an event on subjects from clusters, e.g. pup litters, pairs of eves, multiple blood samples (from a patient), twins, patient families, hospitals (in a multicenter trial), or cluster randomization units. Also, we may come across combinations of these three types of correlated survival data. Although each type of correlated survival data has its special features, the common feature in them is that a vector of correlated survival times is measured independently on each subject (e.g. pair of eyes) or cluster (e.g. twins). We are interested in modeling the marginal distribution (e.g. hazard function) of each element in the random vector of the survival times to a set of covariates. The currently popular approaches are either using a frailty model or a marginal model, depending on the scientific questions to be answered, as reviewed in Liang, Self, Bandeen-Roche, and Zeger (1996). Having clustered survival data in mind as our target, we consider a "local" approach for developing marginal models - that is, we deal with the correlation problem at each death time separately. We first examine the impact of the correlated observations in the risk set at each death time. Then, we make necessary modifications at each death time on usual marginal survival models, e.g. Cox's proportional hazards models, for independent survival data in order to keep the original martingale structure for those marginal models. Yet, by doing so, we find that there rarely exist practically useful marginal models for clustered survival data due to the fact that the "true" covariate effect on the survival response can not be obtained in such marginal models, which is confounded by the correlation within the clusters. The size of the confounding bias on the covariates in the marginal model depends on the strength of the correlation between the correlated survival times, which will be shown in our simulation study. Hence, we propose a new class of semi-conditional models, in which a time-dependent covariate is added into the usual marginal Cox's proportional hazards models to indicate whether the other cluster members have already had the event for each subject in the risk set at each death time, for analyzing clustered survival data. In addition, the partial regression coefficient of this time-dependent covariate can be thought as a global measure of dependence between correlated survival times and would have an odds ratio-like interpretation; and thus, it can also be used for testing the independence between the potentially correlated survival times, adjusting for the effects of other covariates, for uncensored or censored survival data.