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

Doctoral Thesis


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University of Cape Town

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 An example of informative censoring is when a patient who experiences treatment failure is “rescued", and withdrawn, from the study in order to receive alternative treatment.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.