A shared-parameter continuous-time hidden Markov and survival model for longitudinal data with informative dropout

A shared-parameter approach for jointly modeling longitudinal and survival data is proposed. With respect to available approaches, it allows for time-varying random effects that affect both the longitudinal and the survival processes. The distribution of these random effects is modeled according to a continuous-time hidden Markov chain so that transitions may occur at any time point. For maximum likelihood estimation, we propose an algorithm based on a discretization of time until censoring in an arbitrary number of time windows. The observed information matrix is used to obtain standard errors. We illustrate the approach by simulation, even with respect to the effect of the number of time windows on the precision of the estimates, and by an application to data about patients suffering from mildly dilated cardiomyopathy

A Review on Joint Models in Biometrical Research

In some fields of biometrical research joint modelling of longitudinal measures and event time data has become very popular. This article reviews the work in that area of recent fruitful research by classifying approaches on joint models in three categories: approaches with focus on serial trends, approaches with focus on event time data and approaches with equal focus on both outcomes. Typically longitudinal measures and event time data are modelled jointly by introducing shared random effects or by considering conditional distributions together with marginal distributions. We present the approaches in an uniform nomenclature, comment on sub-models applied to longitudinal measures and event time data outcomes individually and exemplify applications in biometrical research

Joint models for nonlinear longitudinal profiles in the presence of informative censoring

Malaria is the parasitic disease which affects the most humans, with Plasmodium falciparum malaria being responsible for the majority of severe malaria and malaria related deaths. The asexual form of the parasite causes the signs and symptoms associated with malaria infection. The sexual form of the parasite, also known as a gametocyte, is the stage responsible for infectivity of the human host (patient) to the mosquito vector, and thus ongoing transmission of malaria and the spread of antimalarial drug resistance. Historically malaria therapeutic efficacy studies have focused mainly on the clearance of asexual parasites. However, malaria in a community can only be truly combated if a treatment program is implemented which is able to clear both asexual and sexual parasites effectively. In this thesis focus will be on the modeling of the key features of gametocytemia. Particular emphasis will be on the modeling of the time to gametocyte emergence, the density of gametocytes and the duration of gametocytemia. It is also of interest to investigate the impact of the administered treatment on the aforementioned features. Gametocyte data has several interesting features. Firstly, the distribution of gametocyte data is zero-inflated with a long tail to the right. The observed longitudinal gametocyte profile also has a nonlinear relationship with time. In addition, since most malaria intervention studies are not designed to optimally measure the evolution of the longitudinal gametocyte profile, there are very few observation points in the time period where the gametocyte profile is expected to peak. Gametocyte data collected from malaria intervention studies are also affected by informative censoring, which leads to incomplete gametocyte profiles. An example of informative censoring is when a patient who experiences treatment failure is “rescued", and withdrawn, from the study in order to receive alternative treatment. This patient can be considered to be in worse health as compared to the patients who remain in this study. There are also competing risks of exit from the study, as a patient can either experience treatment failure or be lost to follow-up. The above mentioned features of gametocyte data make it a statistically appealing dataset to analyze. In literature there are several modeling techniques which can be used to analyze individual features of the data. These techniques include standard survival models for modeling the time to gametocyte emergence and the duration of gametocytemia. The longitudinal nonlinear gametocyte profile would typically be modeled using nonlinear mixed effect models. These nonlinear models could then subsequently be extended to accommodate the zero-inflation in the data, by changing the underlying assumption around the distribution of the response variable. However, it is important to note that these standard techniques do not account for informative censoring. Failure to account for informative censoring leads to bias in parameter estimates. Joint modeling techniques can be used to account for informative censoring. The joint models applied in this thesis combined the longitudinal nonlinear gametocyte densities and the time to censoring due to either lost to follow up or treatment failure. The data analyzed in this thesis were collected from a series of clinical trials conducted be- tween 2002 and 2004 in Mozambique and the Mpumulanga province of South Africa. These trials were a part of the South East African Combination Antimalarial Therapy (SEACAT) evaluation of the phased introduction of combination anti-malarial therapy, nested in the Lubombo Spatial Development Initiative. The aim of these studies was primarily to measure the efficacy of sulfadoxine-pyrimethamine (SP) and a combination of artesunate and sulfadoxine-pyrimethamine (ACT), in eliminating asexual parasites in patients. The patients enrolled in the study had uncomplicated malaria, at a time of increasing resistance to sulfadoxine-pyrimethamine (SP) treatment. Blood samples were taken from patients during the course of 6 weeks on days 0, 1, 2, 3, 7, 14, 21, 28 and 42. Analysis of these blood samples provided longitudinal measurements for asexual 1 parasite densities, gametocyte densities, sulfadoxine drug concentrations and pyrimethamine drug concentrations. The gametocyte data collected in this study was initially analyzed using standard survival modeling techniques. Non-parametric Cox regression models and parametric survival models were applied to the data as part of this initial investigation. These models were used to investigate the factors which affected the time to gametocyte emergence. Subsequently, using the subset of the population which experienced gametocytemia, accelerated failure time models were applied to investigate the factors which affected the duration of gametocytemia. It is evident that the findings from the aforementioned duration investigation would only be able to provide valid duration estimates for patients who were detected to have gametocytemia. This work was extended to allow for population level duration estimates by incorporating the prevalence of gametocytemia into the estimation of duration, for generic patients with specific covariate patterns. The prevalence of gametocytemia was modeled using an underlying binomial distribution. The delta method was subsequently used to derive confidence intervals for the population level duration estimates which were associated with specific covariate patterns. An investigation into the factors affecting the early withdrawal of patients from the study was also conducted. Early exit from the study arose either through loss to follow-up (LTFU) or through treatment failure. The longitudinal gametocyte profile was modeled using joint modeling techniques. The resulting joint model used shared random effects to combine a Weibull survival model, describing the cause- specific hazards of patient exit from the study, with a nonlinear zero-adjusted gamma mixed effect model for the longitudinal gametocyte profile. This model was used to impute the incomplete gametocyte profiles, after adjusting for informative censoring. These imputed profiles were then used to estimate the duration of gametocytemia. It was found, in this thesis, that treatment had a very strong effect on the hazard of gametocyte emergence, density of gametocytes and the duration of gametocytemia. Patients who received a combination of sulfadoxine-pyrimethamine and artesunate were found to have significantly lower hazards of gametocyte emergence, lower predicted durations of gametocytemia and lower predicted longitudinal gametocyte densities as compared to patients who received sulfadoxine-pyrimethamine treatment only

Longitudinal quantile regression in presence of informative drop-out through longitudinal-survival joint modeling

We propose a joint model for a time-to-event outcome and a quantile of a continuous response repeatedly measured over time. The quantile and survival processes are associated via shared latent and manifest variables. Our joint model provides a flexible approach to handle informative drop-out in quantile regression. A general Monte Carlo Expectation Maximization strategy based on importance sampling is proposed, which is directly applicable under any distributional assumption for the longitudinal outcome and random effects, and parametric and non-parametric assumptions for the baseline hazard. Model properties are illustrated through a simulation study and an application to an original data set about dilated cardiomyopathies