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Revista Colombiana de Estadística

Print version ISSN 0120-1751

Rev.Colomb.Estad. vol.33 no.1 Bogotá Jan./June 2010


Appraisal of Several Methods to Model Time to Multiple Events per Subject: Modelling Time to Hospitalizations and Death

Revisión de varios métodos para modelar tiempo a múltiples eventos por sujeto: modelamiento de tiempo a hospitalizaciones y muerte


1Medtronic Bakken Research Center, Cardiac Rhythm Disease Management, Clinical Outcomes, Research and Biometry, Maastricht, Netherlands. Biostatistician. Email:
2Medtronic Bakken Research Center, Cardiac Rhythm Disease Management, Clinical Outcomes, Research and Biometry, Maastricht, Netherlands. Principal Statistician. Email:


During the disease-recovery process of many diseases, such as in Heart Failure (HF), often more than one type of event plays a role. Some clinical trials use the combined endpoint of death and a secondary event; for instance, HF-related hospitalizations. This is often analyzed with time-to-first-event survival analysis which ignores possible subsequent events, such as several HF-related hospitalizations. Accounting for multiple events provides more detailed information on the disease-control process, and allows a more precise understanding of the prognosis of patients.
In this paper we explore and illustrate several modelling strategies to study time to repeated events of disease-related hospitalizations and death per subject. Marginal models are revised in order to account for intra-subject correlation and competing risks. Finally, we recommend a Multi-state model which allows a flexible modelling strategy that incorporates important features in the analysis of HF-related hospitalizations and death, and at the same time extends relevant characteristics of the Andersen & Gill (1982), Wei et al. (1989) and Prentice et al. (1981) models.

Key words: Survival analysis, Competing risks, Correlated observations, Marginal models.


Algunos ensayos clínicos para estudiar el efecto de nuevos tratamientos en pacientes con insuficiencia cardiaca (IC) se basan en la evaluación de hospitalizaciones relacionadas con IC y muerte. Frecuentemente el análisis se enfoca en el tiempo a la primera ocurrencia de alguno de estos dos desenlaces. Este tipo de análisis ignora importantes eventos como nuevas hospitalizaciones relacionadas con IC, que permiten una mejor descripción y compresión del proceso de recuperación de estos pacientes.
En este trabajo se describen y exploran varias estrategias para el análisis de tiempo a repetidas hospitalizaciones relacionadas con IC y tiempo a la muerte. Se estudian modelos marginales para incorporar la correlación intra-sujeto y riesgos competitivos propios de este tipo de ensayos clínicos. Finalmente, se recomienda un modelo multi-estado como una estrategia sencilla y flexible que incorpora elementos importantes en el análisis de hospitalizaciones relacionadas con IC y muerte, y a la vez extiende características relevantes de los modelos de Andersen & Gill (1982), Wei et al. (1989) and Prentice et al. (1981).

Palabras clave: análisis de sobrevida, riesgos competitivos, observaciones correlacionadas, modelos marginales.

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[Recibido en enero de 2009. Aceptado en marzo de 2010]

Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

    AUTHOR  = {Castañeda, Javier and Gerritse, Bart},
    TITLE   = {{Appraisal of Several Methods to Model Time to Multiple Events per Subject: Modelling Time to Hospitalizations and Death}},
    JOURNAL = {Revista Colombiana de Estadística},
    YEAR    = {2010},
    volume  = {33},
    number  = {1},
    pages   = {43-61}

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