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Joint longitudinal hurdle and time-to-event models: an application related to viral load and duration of the first treatment regimen in patients with HIV initiating therapy.

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posted on 2017-09-01, 15:48 authored by Samuel L. Brilleman, Michael J. Crowther, Margaret T. May, Mark Gompels, Keith R. Abrams
Shared parameter joint models provide a framework under which a longitudinal response and a time to event can be modelled simultaneously. A common assumption in shared parameter joint models has been to assume that the longitudinal response is normally distributed. In this paper, we instead propose a joint model that incorporates a two-part 'hurdle' model for the longitudinal response, motivated in part by longitudinal response data that is subject to a detection limit. The first part of the hurdle model estimates the probability that the longitudinal response is observed above the detection limit, whilst the second part of the hurdle model estimates the mean of the response conditional on having exceeded the detection limit. The time-to-event outcome is modelled using a parametric proportional hazards model, assuming a Weibull baseline hazard. We propose a novel association structure whereby the current hazard of the event is assumed to be associated with the current combined (expected) outcome from the two parts of the hurdle model. We estimate our joint model under a Bayesian framework and provide code for fitting the model using the Bayesian software Stan. We use our model to estimate the association between HIV RNA viral load, which is subject to a lower detection limit, and the hazard of stopping or modifying treatment in patients with HIV initiating antiretroviral therapy.


This paper presents independent research funded by the National Institute for Health Research (NIHR). The views expressed are those of the authors and not necessarily those of the NHS, the NIHR or the Department of Health. SLB was funded in part by an NIHR Methods Fellowship (MET 12–20). MJC was part funded by a NIHR Doctoral Research Fellowship (DRF-2012-05-409). MM was supported by the UK Medical Research Council (MRC) [grant number MR/J002380/1] and the UK Department for International Development (DFID) under the MRC/DFID Concordat agreement and is also part of the EDCTP2 programme supported by the European Union. We would also like to thank the patients and clinical teams for their contribution.



Statistics in Medicine, 2016, 35 (20), pp. 3583-3594

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/Organisation/COLLEGE OF MEDICINE, BIOLOGICAL SCIENCES AND PSYCHOLOGY/School of Medicine/Department of Health Sciences


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