title: 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.
abstract: 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. Copyright © 2016 John Wiley & Sons, Ltd.
authors.affiliation: Department of Epidemiology and Preventive Medicine, Monash University, Alfred Centre, 99 Commercial Road, Melbourne, VIC, 3004, Australia.|Victorian Centre for Biostatistics (ViCBiostat), Melbourne, VIC, Australia.
authors.forename: Samuel L
authors.initials: SL
authors.lastname: Brilleman
authors.affiliation: Department of Health Sciences, University of Leicester, Adrian Building, University Road, Leicester, LE1 7RH, U.K.|Department of Medical Epidemiology and Biostatistics, Karolinska Institutet, Box 281, S-171 77, Stockholm, Sweden.
authors.forename: Michael J
authors.initials: MJ
authors.lastname: Crowther
authors.affiliation: School of Social and Community Medicine, University of Bristol, Canynge Hall, 39 Whatley Road, Bristol, BS8 2PS, U.K.
authors.forename: Margaret T
authors.initials: MT
authors.lastname: May
authors.affiliation: North Bristol NHS Trust, Bristol, U.K.
authors.forename: Mark
authors.initials: M
authors.lastname: Gompels
authors.affiliation: Department of Health Sciences, University of Leicester, Adrian Building, University Road, Leicester, LE1 7RH, U.K.
authors.forename: Keith R
authors.initials: KR
authors.lastname: Abrams
mesh_terms: D000998:Antiviral Agents / Q000627:therapeutic use; D001499:Bayes Theorem; D004334:Drug Administration Schedule; D015658:HIV Infections / Q000188:drug therapy* / Q000821:virology; D006801:Humans; D008137:Longitudinal Studies; D015233:Models, Statistical; D016016:Proportional Hazards Models; D019562:Viral Load
chemical_list: D000998:Antiviral Agents
keywords: censoring; detection limit; hurdle model; joint model; shared parameter model