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Stat Methods Med Res. 2018 Jul 31:962280218790107. doi: 10.1177/0962280218790107. [Epub ahead of print]

A joint model for recurrent events and a semi-competing risk in the presence of multi-level clustering.

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1 Department of Biostatistics, Yale School of Public Health, New Haven, CT, USA.
2 Department of Internal Medicine, Yale School of Medicine, West Haven, CT, USA.
3 VA Cooperative Studies Program Coordinating Center, West Haven, CT, USA.


Clinical trial designs often include multiple levels of clustering in which patients are nested within clinical sites and recurrent outcomes are nested within patients who may also experience a semi-competing risk. Traditional survival methods that analyze these processes separately may lead to erroneous inferences as they ignore possible dependencies. To account for the association between recurrent events and a semi-competing risk in the presence of two levels of clustering, we developed a semi-parametric joint model. The Gaussian quadrature with a piecewise constant baseline hazard was used to estimate the unspecified baseline hazards and the likelihood. Simulations showed that the proposed joint model has good statistical properties (i.e. <5% bias and 95% coverage) compared to the shared frailty and joint frailty models when informative censoring and multiple levels of clustering were present. The proposed method was applied to data from an AIDS clinical trial to investigate the impact of antiretroviral treatment on recurrent AIDS-defining events in the presence of a semi-competing risk of death and multi-level clustering and showed a significant dependency between AIDS-defining events and death at the patient level but not at the clinic level.


Recurrent events; clustering; multi-level; semi-competing risk


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