Partly conditional survival models for longitudinal data
ABSTRACT 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. Die Entwicklung von prädiktiven Modellen in der Ereignisanalyse, die zeitabhängige Kovariablen berücksichtigen, ist Gegenstand aktiver Forschung, jedoch wurde der Bewertung der prädiktiven Güte dieser Modelle bislang eher weniger Aufmerksamkeit geschenkt. Eine angemessene Bewertung sollte modellunabhängig, also robust gegenüber Misspezifierung, sein und die chronologische Reihenfolge der Ereignisse korrekt berücksichtigen. Diese Arbeit untersucht den erwarteten quadratischen Verlust einer Prädiktion als Bewertungsmass und zeigt, dass dieser die erwünschten Eigenschaften besitzt. Weitere Eigenschaften, Unterschiede und Parallelen des erwarteten quadratischen Verlustes zu verwandten Vorschlägen in der Literatur werden auf Populationsebene diskutiert. Konsistente Schätzer für verschiedene Zensierungsmechanismen und für Situationen, in denen mehr als einen Ausfallgrund möglich ist, werden vorgestellt, die auf der IPCW (inverse probability of censoring weighting) Methode basieren. Eine Simulationsstudie untersucht das Verhalten der vorgeschlagenen Schätzer bei realistische Stichprobengrössen. Abschliessend wird die Methodik in zwei Datensätzen angewendet, um verschiedene prognostische Modelle miteinander zu vergleichen.
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ABSTRACT: This article advocates the landmarking approach that dynamically adjusts predictive models for survival data during the follow up. This updating is achieved by directly fitting models for the individuals still at risk at the landmark point. Using this approach, simple proportional hazards models are able to catch the development over time for models with time-varying effects of covariates or data with time-dependent covariates (biomarkers). To smooth the effect of the landmarking, sequences of models are considered with parametric effects of the landmark time point and fitted by maximizing appropriate pseudo log-likelihoods that extend the partial log-likelihood to cover the landmarking approach. Copyright 2007 Board of the Foundation of the Scandinavian Journal of Statistics..Scandinavian Journal of Statistics 03/2007; 34(1):70-85. DOI:10.1111/j.1467-9469.2006.00529.x · 1.06 Impact Factor
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ABSTRACT: In this article we focus on appropriate statistical methods for characterizing the prognostic value of a longitudinal clinical marker. Frequently it is possible to obtain repeated measurements. If the measurement has the ability to signify a pending change in the clinical status of a patient then the marker has the potential to guide key medical decisions. Heagerty, Lumley, and Pepe (2000, Biometrics 56, 337-344) proposed characterizing the diagnostic accuracy of a marker measured at baseline by calculating receiver operating characteristic curves for cumulative disease or death incidence by time t. They considered disease status as a function of time, D(t) = 1(T<or=t), for a clinical event time T. In this article we aim to address the question of how well Y(s), a diagnostic marker measured at time s(s>or= 0, after the baseline time) can discriminate between people who become diseased and those who do not in a subsequent time interval [s, t]. We assume the disease status is derived from an observed event time T and thus interest is in individuals who transition from disease free to diseased. We seek methods that also allow the inclusion of prognostic covariates that permit patient-specific decision guidelines when forecasting a future change in health status. Our proposal is to use flexible semiparametric models to characterize the bivariate distribution of the event time and marker values at an arbitrary time s. We illustrate the new methods by analyzing a well-known data set from HIV research, the Multicenter AIDS Cohort Study data.Biometrics 06/2007; 63(2):332-41. DOI:10.1111/j.1541-0420.2006.00726.x · 1.52 Impact Factor