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Published in: Lifetime Data Analysis 4/2023

20-01-2023

Estimation and testing for clustered interval-censored bivariate survival data with application using the semi-parametric version of the Clayton–Oakes model

Authors: Bernard Rosner, Camden Bay, Robert J. Glynn, Gui-shuang Ying, Maureen G. Maguire, Mei-Ling Ting Lee

Published in: Lifetime Data Analysis | Issue 4/2023

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Abstract

The Kaplan–Meier estimator is ubiquitously used to estimate survival probabilities for time-to-event data. It is nonparametric, and thus does not require specification of a survival distribution, but it does assume that the risk set at any time t consists of independent observations. This assumption does not hold for data from paired organ systems such as occur in ophthalmology (eyes) or otolaryngology (ears), or for other types of clustered data. In this article, we estimate marginal survival probabilities in the setting of clustered data, and provide confidence limits for these estimates with intra-cluster correlation accounted for by an interval-censored version of the Clayton–Oakes model. We develop a goodness-of-fit test for general bivariate interval-censored data and apply it to the proposed interval-censored version of the Clayton–Oakes model. We also propose a likelihood ratio test for the comparison of survival distributions between two groups in the setting of clustered data under the assumption of a constant between-group hazard ratio. This methodology can be used both for balanced and unbalanced cluster sizes, and also when the cluster size is informative. We compare our test to the ordinary log rank test and the Lin-Wei (LW) test based on the marginal Cox proportional Hazards model with robust standard errors obtained from the sandwich estimator. Simulation results indicate that the ordinary log rank test over-inflates type I error, while the proposed unconditional likelihood ratio test has appropriate type I error and higher power than the LW test. The method is demonstrated in real examples from the Sorbinil Retinopathy Trial, and the Age-Related Macular Degeneration Study. Raw data from these two trials are provided.

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Appendix
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Metadata
Title
Estimation and testing for clustered interval-censored bivariate survival data with application using the semi-parametric version of the Clayton–Oakes model
Authors
Bernard Rosner
Camden Bay
Robert J. Glynn
Gui-shuang Ying
Maureen G. Maguire
Mei-Ling Ting Lee
Publication date
20-01-2023
Publisher
Springer US
Published in
Lifetime Data Analysis / Issue 4/2023
Print ISSN: 1380-7870
Electronic ISSN: 1572-9249
DOI
https://doi.org/10.1007/s10985-022-09588-y

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