The CASCADE Collaboration: joint modeling of bivariate longitudinal data with informative dropout and left-censoring, with application to the evolution of CD4+ cell count and HIV RNA viral load in response to treatment of HIV infection
Several methodological issues occur in the context of the longitudinal study of HIV markers evolution. Three of them are of particular importance: (i) correlation between CD4+ T lymphocytes (CD4+) and plasma HIV RNA; (ii) left-censoring of HIV RNA due to a lower quantification limit; (iii) and potential informative dropout. We propose a likelihood inference for a parametric joint model including a bivariate linear mixed model for the two markers and a lognormal survival model for the time to drop out. We apply the model to data from patients starting antiretroviral treatment in the CASCADE collaboration where all of the three issues needed to be addressed.
[Show abstract][Hide abstract] ABSTRACT: HIV dynamics studies, based on differential equations, have significantly improved the knowledge on HIV infection. While first studies used simplified short-term dynamic models, recent works considered more complex long-term models combined with a global analysis of whole patient data based on nonlinear mixed models, increasing the accuracy of the HIV dynamic analysis. However statistical issues remain, given the complexity of the problem. We proposed to use the SAEM (stochastic approximation expectation-maximization) algorithm, a powerful maximum likelihood estimation algorithm, to analyze simultaneously the HIV viral load decrease and the CD4 increase in patients using a long-term HIV dynamic system. We applied the proposed methodology to the prospective COPHAR2-ANRS 111 trial. Very satisfactory results were obtained with a model with latent CD4 cells defined with five differential equations. One parameter was fixed, the 10 remaining parameters (eight with between-patient variability) of this model were well estimated. We showed that the efficacy of nelfinavir was reduced compared to indinavir and lopinavir.
"This topic was also studied by Jacobsen and Keiding (1995), Gill et al. (1997) and Nielsen (2000). The problematic of non-ignorable m.l.i.d. has prompted the development of joint models, in which the m.l.i.d. was included, for instance in a model proposed by Diggle and Kenward (1994); see Thiébaut et al. (2005) for a recent example. The aim of this paper is to study ignorability in the context of stochastic processes: these processes may be counting processes but also continuous state-space processes, such as diffusion processes. "
[Show abstract][Hide abstract] ABSTRACT: We develop a study of ignorability and conditions thereof for likelihood
inference in the framework of stochastic processes. We define a coarsening
model for processes which includes discrete-time observations as well as
censored continuous-time observations and applies to continuous state-space
processes as well as counting processes. For preparing the work we recall
formulas for manipulating marginal and conditional likelihood ratios (which can
apply to stochastic processes). Ignorability is defined in terms of local
equality of two likelihood ratios. We give static conditions of ignorability
and then dynamical conditions which are more interpretable. We illustrate the
use of the dynamical conditions of ignorability in problems of censoring,
missing data and joint modelling.
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