Partly Conditional Survival Models for Longitudinal Data

University of Washington Seattle, Seattle, Washington, United States
Biometrics (Impact Factor: 1.57). 07/2005; 61(2):379-91. DOI: 10.1111/j.1541-0420.2005.00323.x
Source: PubMed


It is common in longitudinal studies to collect information on the time until a key clinical event, such as death, and to measure markers of patient health at multiple follow-up times. One approach to the joint analysis of survival and repeated measures data adopts a time-varying covariate regression model for the event time hazard. Using this standard approach, the instantaneous risk of death at time t is specified as a possibly semi-parametric function of covariate information that has accrued through time t. In this manuscript, we decouple the time scale for modeling the hazard from the time scale for accrual of available longitudinal covariate information. Specifically, we propose a class of models that condition on the covariate information through time s and then specifies the conditional hazard for times t, where t > s. Our approach parallels the "partly conditional" models proposed by Pepe and Couper (1997, Journal of the American Statistical Association 92, 991-998) for pure repeated measures applications. Estimation is based on the use of estimating equations applied to clusters of data formed through the creation of derived survival times that measure the time from measurement of covariates to the end of follow-up. Patient follow-up may be terminated either by the occurrence of the event or by censoring. The proposed methods allow a flexible characterization of the association between a longitudinal covariate process and a survival time, and facilitate the direct prediction of survival probabilities in the time-varying covariate setting.

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    ABSTRACT: While the development of failure time models with longitudinal covariates for prediction purposes is an area of active research, assessment of their predictive accuracy has been treated with less interest. An appropriate assessment measure should be model independent, i.e. robust against misspecification, and treat the chronological order of events correctly so as not to introduce time dependent bias. We propose the expected quadratic loss as suitable measure and show that it can be decomposed into two parts, one of which constitutes the contribution of subjects still at risk at the time point of prediction. This latter part, which we call conditional prediction error, is most relevant in applications, while a view on the overall measure allows an insight into the global behavior of different predictions. Properties of the proposed measure such as its robustness against misspecification are discussed on a population level and similarities and differences to related suggestions in the literature are highlighted. Consistent estimators for the conditional prediction error in different censoring situations based on the inverse probability of censoring weighting (IPCW) technique are developed. An extension of the measure for competing risk data is proposed together with consistent estimators. A simulation study investigates the behavior of the estimators for finite sample sizes and selected joint distributions of covariate process and event time. In two real data examples, one of which is a competing risk dataset, the suggested estimators are applied to compare different prognostic models to each other.
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    No preview · Article · Jun 2007 · Biometrics
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