Just Another Gibbs Sampling (JAGS) is a convenient tool to draw posterior samples using Markov Chain Monte Carlo for Bayesian modeling. However, the built-in function dinterval() to model censored data misspecifies the computation of deviance function, which may limit its usage to perform likelihood based model comparison. To establish an automatic approach to specify the correct deviance function in JAGS, we propose a simple alternative modeling strategy to implement Bayesian model selection for analysis of censored outcomes. The proposed approach is applicable to a broad spectrum of data types, which include survival data and many other right-, left- and interval-censored Bayesian model structures.
The aim of this work is the comparison of the performance of the three popular software platforms JAGS, NIMBLE and Stan. These probabilistic programming languages are able to automatically generate samples from the posterior distribution of interest using MCMC algorithms, starting from the specification of a Bayesian model, i.e. the likelihood and the prior. The final goal is to present a detailed analysis of their strengths and weaknesses to statisticians or applied scientists. In this way, we wish to contribute to make them fully aware of the pros and cons of this software. We carry out a sy…
This paper describes and illustrates the functionality of the baker R package. The package estimates a suite of nested partially-latent class models (NPLCM) for multivariate binary responses that are observed under a case-control design. The baker package allows researchers to flexibly estimate population-level class prevalences and posterior probabilities of class membership for individual cases. Estimation is accomplished by calling a cross-platform automatic Bayesian inference software JAGS through a wrapper R function that parses model specifications and data inputs. The baker package prov…
A flexible quantile mixed-effects model for censored outcomes
Syneos Health；Department of Mathematical Statistics and Actuarial Science, University of the Free State（自由州大学数学统计与精算科学系）；I-BioStat, KU Leuven（KU鲁汶大学生物统计研究所）；Department of Statistics and Actuarial Science, University of Stellenbosch（斯泰伦博斯大学统计与精算科学系）
Continuous-time multi-state survival models can be used to describe health-related processes over time. In the presence of interval-censored times for transitions between the living states, the likelihood is constructed using transition probabilities. Models can be specified using parametric or semi-parametric shapes for the hazards. Semi-parametric hazards can be fitted using $P$-splines and penalised maximum likelihood estimation. This paper presents a method to estimate flexible multi-state models which allows for parametric and semi-parametric hazard specifications. The estimation is based…
In contrast to the popular Cox model which presents a multiplicative covariate effect specification on the time to event hazards, the semiparametric additive risks model (ARM) offers an attractive additive specification, allowing for direct assessment of the changes or the differences in the hazard function for changing value of the covariates. The ARM is a flexible model, allowing the estimation of both time-independent and time-varying covariates. It has a nonparametric component and a regression component identified by a finite-dimensional parameter. This chapter presents an efficient appro…
An R package for specifying and estimating linear latent variable models is presented. The philosophy of the implementation is to separate the model specification from the actual data, which leads to a dynamic and easy way of modeling complex hierarchical structures. Several advanced features are implemented including robust standard errors for clustered correlated data, multigroup analyses, non-linear parameter constraints, inference with incomplete data, maximum likelihood estimation with censored and binary observations, and instrumental variable estimators. In addition an extensive simulat…
We propose a class of transformation hazard models for right-censored failure time data. It includes the proportional hazards model (Cox) and the additive hazards model (Lin and Ying) as special cases. Due to the requirement of a nonnegative hazard function, multidimensional parameter constraints must be imposed in the model formulation. In the Bayesian paradigm, the nonlinear parameter constraint introduces many new computational challenges. We propose a prior through a conditional-marginal specification, in which the conditional distribution is univariate, and absorbs all of the nonlinear pa…
Multistate models can be used to describe transitions over time across states. In the presence of interval-censored times for transitions, the likelihood is constructed using transition probabilities. Models are specified using proportional hazards model for the transitions. Time-dependency is usually defined by parametric models, which can be too restrictive. Nonparametric hazards specification with splines allow for flexible modelling of time-dependency without making strong model assumptions. Penalised maximum likelihood is used to estimate the models. Selecting the optimal amount of smooth…
Individuals often respond differently to identical treatments, and characterizing such variability in treatment response is an important aim in the practice of personalized medicine. In this article, we describe a non-parametric accelerated failure time model that can be used to analyze heterogeneous treatment effects (HTE) when patient outcomes are time-to-event. By utilizing Bayesian additive regression trees and a mean-constrained Dirichlet process mixture model, our approach offers a flexible model for the regression function while placing few restrictions on the baseline hazard. Our non-p…
This paper studies the identification and estimation of weighted average derivatives of conditional location functionals including conditional mean and conditional quantiles in settings where either the outcome variable or a regressor is interval-valued. Building on Manski and Tamer (2002) who study nonparametric bounds for mean regression with interval data, we characterize the identified set of weighted average derivatives of regression functions. Since the weighted average derivatives do not rely on parametric specifications for the regression functions, the identified set is well-defined w…
The mean residual life function is a key functional for a survival distribution. It has a practically useful interpretation as the expected remaining lifetime given survival up to a particular time point, and it also characterizes the survival distribution. However, it has received limited attention in terms of inference methods under a probabilistic modeling framework. We seek to provide general inference methodology for mean residual life regression. Survival data often include a set of predictor variables for the survival response distribution, and in many cases it is natural to include the…
We apply Gaussian process (GP) regression, which provides a powerful non-parametric probabilistic method of relating inputs to outputs, to survival data consisting of time-to-event and covariate measurements. In this context, the covariates are regarded as the `inputs' and the event times are the `outputs'. This allows for highly flexible inference of non-linear relationships between covariates and event times. Many existing methods, such as the ubiquitous Cox proportional hazards model, focus primarily on the hazard rate which is typically assumed to take some parametric or semi-parametric fo…
Robust statistical data modelling under potential model mis-specification often requires leaving the parametric world for the nonparametric. In the latter, parameters are infinite dimensional objects such as functions, probability distributions or infinite vectors. In the Bayesian nonparametric approach, prior distributions are designed for these parameters, which provide a handle to manage the complexity of nonparametric models in practice. However, most modern Bayesian nonparametric models seem often out of reach to practitioners, as inference algorithms need careful design to deal with the …
Bayesian nonparametric methods are a popular choice for analysing survival data due to their ability to flexibly model the distribution of survival times. These methods typically employ a nonparametric prior on the survival function that is conjugate with respect to right-censored data. Eliciting these priors, particularly in the presence of covariates, can be challenging and inference typically relies on computationally intensive Markov chain Monte Carlo schemes. In this paper, we build on recent work that recasts Bayesian inference as assigning a predictive distribution on the unseen values …
