Bayesian regression analysis of data with random effects covariates from nonlinear longitudinal measurements

© 2015 Elsevier Inc. Joint models for a wide class of response variables and longitudinal measurements consist on a mixed-effects model to fit longitudinal trajectories whose random effects enter as covariates in a generalized linear model for the primary response. They provide a useful way to assess association between these two kinds of data, which in clinical studies are often collected jointly on a series of individuals and may help understanding, for instance, the mechanisms of recovery of a certain disease or the efficacy of a given therapy. When a nonlinear mixed-effects model is used to fit the longitudinal trajectories, the existing estimation strategies based on likelihood approximations have been shown to exhibit some computational efficiency problems (De la Cruz et al., 2011). In this article we consider a Bayesian estimation procedure for the joint model with a nonlinear mixed-effects model for the longitudinal data and a generalized linear model for the primary response. The proposed prior structure allows for the implementation of an MCMC sampler. Moreover, we consider that the errors in the longitudinal model may be correlated. We apply our method to the analysis of hormone levels measured at the early stages of pregnancy that can be used to predict normal versus abnormal pregnancy outcomes. We also conduct a simulation study to assess the importance of modelling correlated errors and quantify the consequences of model misspecification

Prediction of Coronary Artery Disease Risk Based on Multiple Longitudinal Biomarkers

In the last decade, few topics in the area of cardiovascular disease (CVD) research have received as much attention as risk prediction. One of the well-documented risk factors for CVD is high blood pressure (BP). Traditional CVD risk prediction models consider BP levels measured at a single time and such models form the basis for current clinical guidelines for CVD prevention. However, in clinical practice, BP levels are often observed and recorded in a longitudinal fashion. Information on BP trajectories can be powerful predictors for CVD events. We consider joint modeling of time to coronary artery disease and individual longitudinal measures of systolic and diastolic BPs in a primary care cohort with up to 20 years of follow-up. We applied novel prediction metrics to assess the predictive performance of joint models. Predictive performances of proposed joint models and other models were assessed via simulations and illustrated using the primary care cohort

Joint Models for Multiple Longitudinal Processes and Time-to-event Outcome

Joint models are statistical tools for estimating the association between time-to-event and longitudinal outcomes. One challenge to the application of joint models is its computational complexity. Common estimation methods for joint models include a two-stage method, Bayesian and maximum-likelihood methods. In this work, we consider joint models of a time-to-event outcome and multiple longitudinal processes and develop a maximum-likelihood estimation method using the expectation–maximization algorithm. We assess the performance of the proposed method via simulations and apply the methodology to a data set to determine the association between longitudinal systolic and diastolic blood pressure measures and time to coronary artery disease

Review and Comparison of Computational Approaches for Joint Longitudinal and Time‐to‐Event Models

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/151312/1/insr12322.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/151312/2/insr12322_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/151312/3/Supplement_ReviewComputationalJointModels_final.pd

Joint modeling of bivariate time to event data with semi-competing risk

Indiana University-Purdue University Indianapolis (IUPUI)Survival analysis often encounters the situations of correlated multiple events including the same type of event observed from siblings or multiple events experienced by the same individual. In this dissertation, we focus on the joint modeling of bivariate time to event data with the estimation of the association parameters and also in the situation of a semi-competing risk. This dissertation contains three related topics on bivariate time to event mod els. The first topic is on estimating the cross ratio which is an association parameter between bivariate survival functions. One advantage of using cross-ratio as a depen dence measure is that it has an attractive hazard ratio interpretation by comparing two groups of interest. We compare the parametric, a two-stage semiparametric and a nonparametric approaches in simulation studies to evaluate the estimation perfor mance among the three estimation approaches. The second part is on semiparametric models of univariate time to event with a semi-competing risk. The third part is on semiparametric models of bivariate time to event with semi-competing risks. A frailty-based model framework was used to accommodate potential correlations among the multiple event times. We propose two estimation approaches. The first approach is a two stage semiparametric method where cumulative baseline hazards were estimated by nonparametric methods first and used in the likelihood function. The second approach is a penalized partial likelihood approach. Simulation studies were conducted to compare the estimation accuracy between the proposed approaches. Data from an elderly cohort were used to examine factors associated with times to multiple diseases and considering death as a semi-competing risk

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

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

Methods for non-proportional hazards in clinical trials: A systematic review

For the analysis of time-to-event data, frequently used methods such as the log-rank test or the Cox proportional hazards model are based on the proportional hazards assumption, which is often debatable. Although a wide range of parametric and non-parametric methods for non-proportional hazards (NPH) has been proposed, there is no consensus on the best approaches. To close this gap, we conducted a systematic literature search to identify statistical methods and software appropriate under NPH. Our literature search identified 907 abstracts, out of which we included 211 articles, mostly methodological ones. Review articles and applications were less frequently identified. The articles discuss effect measures, effect estimation and regression approaches, hypothesis tests, and sample size calculation approaches, which are often tailored to specific NPH situations. Using a unified notation, we provide an overview of methods available. Furthermore, we derive some guidance from the identified articles. We summarized the contents from the literature review in a concise way in the main text and provide more detailed explanations in the supplement (page 29)

Semiparametric Bayesian Modeling of Multivariate Average Bioequivalence

Bioequivalence trials are usually conducted to compare two or more formulations of a drug. Simultaneous assessment of bioequivalence on multiple endpoints is called multivariate bioequivalence. Despite the fact that some tests for multivariate bioequivalence are suggested, current practice usually involves univariate bioequivalence assessments ignoring the correlations between the endpoints such as AUC and Cmax. In this paper we develop a semiparametric Bayesian test for bioequivalence under multiple endpoints. Specifically, we show how the correlation between the endpoints can be incorporated in the analysis and how this correlation affects the inference. Resulting estimates and posterior probabilities ``borrow strength\u27\u27 from one another where the amount and direction of the strength borrowed are determined by the prior correlations. The method developed is illustrated using a real data set

BAYESIAN BASED SEMIPARAMETRIC MULTIDIMENSIONAL APPROACHES TO ANALYSIS PARKINSON\u27S DISEASE

In the slow progression of Parkinson\u27s Disease (PD), impairments arise and affect multiple domains (e.g., motor, cognitive, and behavioral). Mixed types, multivariate longitudinal data are commonly used in PD studies. Challenges exist in assessing PD status and investigating disease progression due to lack of biomarkers and ubiquitous impairment in the disease. We proposed a model framework by combining the semi-parametric approach and multi- dimensional framework, and used the proposed model to investigate the heterogeneous disease development and the non-linear treatment effects in the multiple domains predefined in PD. Furthermore, we extended the semi-parametric multidimensional approach to the data with multi-types endpoints. We investigated the multi-type events (competing risks) simultaneously with longitudinal profile in presence of impairment across domains and domain specific heterogeneous disease progression. Our approach provides an explicit framework for defining and estimating the impaired covariate effects, the association between domain specific longitudinal profile and multi-type endpoints. Lastly, we addressed the missing data in PD. We extended the multidimensional joint model to missing data by analyzing two missingness patterns (intermittent and monotone missingness) jointly in domain levels. We provided a statistical method for simultaneous likelihood inference on missing data in presence of two missingness patterns and two missing mechanisms, missing at random (MAR) and missing not at random (MNAR). In summary, the studies in this dissertation add to current PD studies by focusing on those ignored or not fully addressed problems in PD. The applications in longitudinal data, survival data and missing data promote this framework usability in public health research