Joint Modeling of Longitudinal Ordinal Data on Quality of Life and Survival

<p>Joint models for longitudinal and survival data have been widely discussed in the literature. This thesis proposes a joint model using a stereotype model for the longitudinal ordinal responses and a Cox proportional hazards model for survival time. Our current joint model has a new feature since no literature has examined the joint model under the stereotype model. The stereotype model can improve the fit by adding extra score parameters, but it still has the advantage of requiring only a single parameter to describe the effect of a predictor on the item response levels. We give an example to model longitudinal ordinal data and survival data for patients being followed up after treatments. The main focus is on modeling both the quality of life data and the survival data simultaneously with a goal of understanding the association between the two processes over time. These two models are linked through a latent variable that characterizes the quality of life of an individual and is assumed to underlie the hazard rate. In other words, the latent variable serves as a shared variable in the joint model. We present the joint model in two different aspects: one based on a Bayesian approach and the other one a semiparametric approach using the EM algorithm. For the Bayesian approach, the latent variable is treated as a continuous variable and is assumed to have a multivariate normal distribution. The partial survival likelihood function is used in the survival component of the Bayesian joint model, while the full likelihood function is considered in the semiparametric joint model. In the latter approach the baseline hazard is assumed to be a step function and has no parametric form. The latent variable in the semiparametric joint model is then treated as a discrete variable. We illustrate our methodologies by analyzing data from the Staccato study, a randomized trial to compare two treatment methods, for Human Immunodeficiency Virus (HIV) infection of Thai patients on Highly Active Antiretroviral Therapy (HAART), in which the quality of life was assessed with a HIV Medical Outcome Study (MOS-HIV) questionnaire. Furthermore, we extend the study further to the case of multiple failure types in the survival component. Thus, the extension of the joint model consists of the stereotype model and the competing risks model. The Bayesian method is employed to estimate all unknown parameters in this extended joint model. The results we obtained are consistent for both the Bayesian joint model and the semiparametric joint model. Both models show that patients who had a better quality of life were associated with a lower hazard of HIV progression. Patients on continuous treatment also had a lower hazard of HIV progression compared with patients on CD4-guided interruption treatment.</p>

Joint Modeling of Longitudinal Ordinal Data on Quality of Life and Survival

<p>Joint models for longitudinal and survival data have been widely discussed in the literature. This thesis proposes a joint model using a stereotype model for the longitudinal ordinal responses and a Cox proportional hazards model for survival time. Our current joint model has a new feature since no literature has examined the joint model under the stereotype model. The stereotype model can improve the fit by adding extra score parameters, but it still has the advantage of requiring only a single parameter to describe the effect of a predictor on the item response levels. We give an example to model longitudinal ordinal data and survival data for patients being followed up after treatments. The main focus is on modeling both the quality of life data and the survival data simultaneously with a goal of understanding the association between the two processes over time. These two models are linked through a latent variable that characterizes the quality of life of an individual and is assumed to underlie the hazard rate. In other words, the latent variable serves as a shared variable in the joint model. We present the joint model in two different aspects: one based on a Bayesian approach and the other one a semiparametric approach using the EM algorithm. For the Bayesian approach, the latent variable is treated as a continuous variable and is assumed to have a multivariate normal distribution. The partial survival likelihood function is used in the survival component of the Bayesian joint model, while the full likelihood function is considered in the semiparametric joint model. In the latter approach the baseline hazard is assumed to be a step function and has no parametric form. The latent variable in the semiparametric joint model is then treated as a discrete variable. We illustrate our methodologies by analyzing data from the Staccato study, a randomized trial to compare two treatment methods, for Human Immunodeficiency Virus (HIV) infection of Thai patients on Highly Active Antiretroviral Therapy (HAART), in which the quality of life was assessed with a HIV Medical Outcome Study (MOS-HIV) questionnaire. Furthermore, we extend the study further to the case of multiple failure types in the survival component. Thus, the extension of the joint model consists of the stereotype model and the competing risks model. The Bayesian method is employed to estimate all unknown parameters in this extended joint model. The results we obtained are consistent for both the Bayesian joint model and the semiparametric joint model. Both models show that patients who had a better quality of life were associated with a lower hazard of HIV progression. Patients on continuous treatment also had a lower hazard of HIV progression compared with patients on CD4-guided interruption treatment.</p>

Dynamic Predictions From Longitudinal CD4 Count Measures And Time To Death of HIV/AIDS Patients Using a Bayesian Joint Model

Background: Personalised or stratified medicine has played an increasingly important role in improving bio-medical care in recent years. A Bayesian joint modelling approach to dynamic prediction of HIV progression and mortality allows such individualised predictions to be made for HIV patients, based on monitoring of their CD4 counts. This study aims to provide predictions of patient-specific trajectories of HIV disease progression and survival.Methods: Longitudinal data on 254 HIV/AIDS patients who received ART between 2009 and 2014, and who had at least one CD4 count observed, were employed in a Bayesian joint model of disease progression, as measured by CD4 counts, and survival, to obtain individualised dynamic predictions of both processes that were updated at each visit time in the follow-up period. Different forms of association structure that relate the longitudinal CD4 biomarker and time to death were assessed; and predictions were averaged over the different models using Bayesian model averaging.Results: A total of 254 subjects were observed in the dataset with a median age of 30 years (interquartile range, IQR, 26–38). The individual follow-up times ranged from 1 to 120 months, with a median of 22 months and IQR 7 -39 months. The median baseline CD4 count was 129 cells/mm3 (IQR 61–247 cells/mm3). From the joint model with highest posterior weight, subjects whose functional status was working were significantly associated with a higher baseline CD4 count (β = 1.86; 95% CI: 0.65 3.04) whereas subjects who were bedridden were significantly associated with a lower baseline CD4 count (estimated effect β = -3.54; 95% CI: -5.65, -1.39), compared to ambulatory patients. A unit increase in weight of the individual increased the mean square root CD4 measurement by 0.06. The estimates of the association structure parameters from all three models considered indicated that the HIV mortality hazard at any time point is associated with the current underlying value of the CD4 count at the same time point. The model with highest posterior weight also had a time-dependent slope, indicating that HIV mortality is also associated with the rate of change in CD4 count. From both the model-averaged predictions and the highest posterior weight model alone, an increase in CD4 count was predicted at different visit times from the dynamic predictions. It was also found that there was an increase in the width of prediction intervals as time progressed.Conclusions: Functional status, weight and alcohol intake are important contributing factors that affect the mean square root of CD4 measurements. For this particular dataset, model averaging the dynamic predictions resulted in only one of the hypothesised association structures having non-zero weight at the majority of time points for each individual. The predictions were therefore similar whether we averaged them over models or derived them from the highest posterior weight model alone. We also observed that the parameter estimates in the both the CD4 count and survival sub-models showed slight variability between the postulated association structures.

Bayesian estimation of population size and overlap from random subsamples

Counting the number of species, items, or genes that are shared between two sets is a simple calculation when sampling is complete. However, when only partial samples are available, quantifying the overlap between two sets becomes an estimation problem. Furthermore, to calculate normalized measures of β-diversity, such as the Jaccard and Sorenson-Dice indices, one must also estimate the total sizes of the sets being compared. Previous efforts to address these problems have assumed knowledge of total population sizes and then used Bayesian methods to produce unbiased estimates with quantified uncertainty. Here, we address populations of unknown size and show that this produces systematically better estimates--both in terms of central estimates and quantification of uncertainty in those estimates. We further show how to use species count data to refine estimates of population size in a Bayesian joint model of populations and overlap.