Regression analysis of multivariate incomplete failure time data by modeling marginal distributions
Abstract
Many survival studies record the times to two or more distinct failures on each subject. The failures may be events of different natures or may be repetitions of the same kind of event. In this article, we consider the regression analysis of such multivariate failure time observations. Each marginal distribution of the failure times is formulated by a Cox proportional hazards model. No specific structure of dependence among the distinct failure times on each subject is imposed. The regression parameters in the Cox models are estimated by maximizing the failure-specific partial likelihoods. The resulting estimators are shown to be asymptotically jointly normal with a covariance matrix that can be consistently estimated. Simultaneous inferential procedures are then proposed. Extensive Monte Carlo studies indicate that the normal approximation is adequate for practical use. The new methods allow time-dependent covariates, missing observations, and arbitrary patterns of censorship. They are illustrated with two real-life examples. For recurrent failure time data, various regression methods have been proposed in the literature. These methods, however, generally assume stringent structures of dependence among the recurrences of each subject. Moreover, as shown in the present article, they are rather sensitive to model misspecification.
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As pre-specified supportive analyses, the modified Wei-Lin-Weissfeld method (Li and Lagakos modification) was used to calculate hazard ratios for the time to the first, second, or third event.
“As pre-specified supportive analyses, we used the modified Wei-Lin-Weissfeld method (Li and Lagakos modification) to calculate hazard ratios for the time to the first, second, or third event (48,49).”
From Effects of Icosapent Ethyl on Total Ischemic Events (2019) · cites this paper as [48]
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Self-citation
- Authors
- Wei, L. J., Lin, D. Y., & Weissfeld, L.
- Affiliations
- University of Wisconsin–Madison (US)
- Harvard University (US)
- University of Michigan (US)
- ORCID
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 1989-12
- Volume
- 84
- Issue
- 408
- Pages
- 1065-1073
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W2092648747
- Cited by
- 1,868
- References
- 31
- Citations by year
- 2026: 29 · 2025: 45 · 2024: 33 · 2023: 33 · 2022: 76 · 2021: 67 · 2020: 74 · 2019: 66 · 2018: 68 · 2017: 52 · 2016: 83 · 2015: 79 · 2014: 104 · 2013: 91 · 2012: 78
- FWCI
- 8.37
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of the American Statistical Association (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Keywords
- multivariate failure time data, marginal distributions, Cox proportional hazards model, asymptotic normality, simultaneous inference, time-varying covariates, missing data, censorship, recurrent events, dependence structure
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