A Bayesian Framework for Functional Mapping through Joint Modeling of Longitudinal and Time-to-Event Data

Bayesian joint modelling of longitudinal and time to event data: a methodological review

BACKGROUND

In clinical research, there is an increasing interest in joint modelling of longitudinal and time-to-event data, since it reduces bias in parameter estimation and increases the efficiency of statistical inference. Inference and prediction from frequentist approaches of joint models have been extensively reviewed, and due to the recent popularity of data-driven Bayesian approaches, a review on current Bayesian estimation of joint model is useful to draw recommendations for future researches.

METHODS

We have undertaken a comprehensive review on Bayesian univariate and multivariate joint models. We focused on type of outcomes, model assumptions, association structure, estimation algorithm, dynamic prediction and software implementation.

RESULTS

A total of 89 articles have been identified, consisting of 75 methodological and 14 applied articles. The most common approach to model the longitudinal and time-to-event outcomes jointly included linear mixed effect models with proportional hazards. A random effect association structure was generally used for linking the two sub-models. Markov Chain Monte Carlo (MCMC) algorithms were commonly used (93% articles) to estimate the model parameters. Only six articles were primarily focused on dynamic predictions for longitudinal or event-time outcomes.

CONCLUSION

Methodologies for a wide variety of data types have been proposed; however the research is limited if the association between the two outcomes changes over time, and there is also lack of methods to determine the association structure in the absence of clinical background knowledge. Joint modelling has been proved to be beneficial in producing more accurate dynamic prediction; however, there is a lack of sufficient tools to validate the prediction.

Dirichlet Lasso: A Bayesian approach to variable selection

Selection of the most important predictor variables in regression analysis is one of the key problems statistical research has been concerned with for long time. In this article, we propose the methodology, Dirichlet Lasso (abbreviated as DLASSO) to address this issue in a Bayesian framework. In many modern regression settings, large set of predictor variables are grouped and the coefficients belonging to any one of these groups are either all redundant or all important in predicting the response; we say in those cases that the predictors exhibit a group structure. We show that DLASSO is particularly useful where the group structure is not fully known. We exploit the clustering property of Dirichlet Process priors to infer the possibly missing group information. The Dirichlet Process has the advantage of simultaneously clustering the variable coefficients and selecting the best set of predictor variables. We compare the predictive performance of DLASSO to Group Lasso and ordinary Lasso with real data and simulation studies. Our results demonstrate that the predictive performance of DLASSO is almost as good as that of Group Lasso when group label information is given; and superior to the ordinary Lasso for missing group information. For high dimensional data (e.g., genetic data) with missing group information, DLASSO will be a powerful approach of variable selection since it provides a superior predictive performance and higher statistical accuracy.

A semiparametric approach to simultaneous covariance estimation for bivariate sparse longitudinal data

Estimation of the covariance structure for irregular sparse longitudinal data has been studied by many authors in recent years but typically using fully parametric specifications. In addition, when data are collected from several groups over time, it is known that assuming the same or completely different covariance matrices over groups can lead to loss of efficiency and/or bias. Nonparametric approaches have been proposed for estimating the covariance matrix for regular univariate longitudinal data by sharing information across the groups under study. For the irregular case, with longitudinal measurements that are bivariate or multivariate, modeling becomes more difficult. In this article, to model bivariate sparse longitudinal data from several groups, we propose a flexible covariance structure via a novel matrix stick-breaking process for the residual covariance structure and a Dirichlet process mixture of normals for the random effects. Simulation studies are performed to investigate the effectiveness of the proposed approach over more traditional approaches. We also analyze a subset of Framingham Heart Study data to examine how the blood pressure trajectories and covariance structures differ for the patients from different BMI groups (high, medium, and low) at baseline.

Association mapping in crop plants: opportunities and challenges

The research area of association mapping (AM) is currently receiving major attention for genetic studies of quantitative traits in all major crops. However, the level of success and utility of AM achieved for crop improvement is not comparable to that in the area of human health care for diagnosis of complex human diseases. These AM studies in plants, as in humans, became possible due to the availability of DNA-based molecular markers and a variety of sophisticated statistical tools that are evolving on a regular basis. In this chapter, we first briefly review the significance of a variety of populations that are used in AM studies, then briefly describe the molecular markers and high-throughput genotyping strategies, and finally describe the approaches used for AM studies. The major part of the chapter is, however, devoted to analysis of reasons why the results of AM have been underutilized in plant breeding. We also examine the opportunities available and challenges faced while using AM for crop improvement programs. This includes a detailed discussion of the issues that have plagued AM studies, and the solutions that have become available to deal with these issues, so that in future, the results of AM studies may prove increasingly fruitful for crop improvement programs.

Statistical challenges in the analysis of dynamic traits: implications for pharmacogenomic clinics

Analysis of dynamic traits is statistically challenging for several reasons. Since most of the dynamic traits result in irregular sparse longitudinal measurements, a unified approach for jointly modeling the mean trajectories and the underlying covariance structure is essential. When the traits are bivariate or multivariate in nature, modeling the covariance structure is really challenging. For the pharmacogenomic clinics, it is extremely important to have a comprehensive study of the whole biological system. In other words, if the traits under consideration result in some events (e.g., death, disease), then a joint analysis is required for the observed dynamic traits and the event-time. In statistics, there is a vast literature on such joint modeling using parametric, nonparametric and semiparametric approaches. In this article, we will discuss different aspects of modeling the longitudinal traits, their limitations and importance to pharmacogenomic clinics.