A Bayesian semiparametric survival model with longitudinal markers

A Bayesian semi-parametric model for learning biomarker trajectories and changepoints in the preclinical phase of Alzheimer's disease

It has become consensus that mild cognitive impairment (MCI), one of the early symptoms onset of Alzheimer's disease (AD), may appear 10 or more years after the emergence of neuropathological abnormalities. Therefore, understanding the progression of AD biomarkers and uncovering when brain alterations begin in the preclinical stage, while patients are still cognitively normal, are crucial for effective early detection and therapeutic development. In this paper, we develop a Bayesian semiparametric framework that jointly models the longitudinal trajectory of the AD biomarker with a changepoint relative to the occurrence of symptoms onset, which is subject to left truncation and right censoring, in a heterogeneous population. Furthermore, unlike most existing methods assuming that everyone in the considered population will eventually develop the disease, our approach accounts for the possibility that some individuals may never experience MCI or AD, even after a long follow-up time. We evaluate the proposed model through simulation studies and demonstrate its clinical utility by examining an important AD biomarker, ptau181, using a dataset from the Biomarkers of Cognitive Decline Among Normal Individuals (BIOCARD) study.

Harnessing repeated measurements of predictor variables for clinical risk prediction: a review of existing methods

BACKGROUND

Clinical prediction models (CPMs) predict the risk of health outcomes for individual patients. The majority of existing CPMs only harness cross-sectional patient information. Incorporating repeated measurements, such as those stored in electronic health records, into CPMs may provide an opportunity to enhance their performance. However, the number and complexity of methodological approaches available could make it difficult for researchers to explore this opportunity. Our objective was to review the literature and summarise existing approaches for harnessing repeated measurements of predictor variables in CPMs, primarily to make this field more accessible for applied researchers.

METHODS

MEDLINE, Embase and Web of Science were searched for articles reporting the development of a multivariable CPM for individual-level prediction of future binary or time-to-event outcomes and modelling repeated measurements of at least one predictor. Information was extracted on the following: the methodology used, its specific aim, reported advantages and limitations, and software available to apply the method.

RESULTS

The search revealed 217 relevant articles. Seven methodological frameworks were identified: time-dependent covariate modelling, generalised estimating equations, landmark analysis, two-stage modelling, joint-modelling, trajectory classification and machine learning. Each of these frameworks satisfies at least one of three aims: to better represent the predictor-outcome relationship over time, to infer a covariate value at a pre-specified time and to account for the effect of covariate change.

CONCLUSIONS

The applicability of identified methods depends on the motivation for including longitudinal information and the method's compatibility with the clinical context and available patient data, for both model development and risk estimation in practice.

Joint analysis of longitudinal and survival AIDS data with a spatial fraction of long-term survivors: A Bayesian approach

A typical survival analysis with time-dependent covariates usually does not take into account the possible random fluctuations or the contamination by measurement errors of the variables. Ignoring these sources of randomness may cause bias in the estimates of the model parameters. One possible way for overcoming that limitation is to consider a longitudinal model for the time-varying covariates jointly with a survival model for the time to the event of interest, thereby taking advantage of the complementary information flowing between these two-model outcomes. We employ here a Bayesian hierarchical approach to jointly model spatial-clustered survival data with a fraction of long-term survivors along with the repeated measurements of CD4⁺ T lymphocyte counts for a random sample of 500 HIV/AIDS individuals collected in all the 27 states of Brazil during the period 2002-2006. The proposed Bayesian joint model comprises two parts: on the one hand, a flexible model using Penalized Splines to better capture the nonlinear behavior of the different CD4 profiles over time; on the other hand, a spatial cure model to cope with the set of long-term survivor individuals. Our findings show that joint models considering this set of patients were the ones with the best performance comparatively to the more traditional survival approach. Moreover, the use of spatial frailties allowed us to map the heterogeneity in the disease risk among the Brazilian states.

A Bayesian approach to joint analysis of multivariate longitudinal data and parametric accelerated failure time

Impairment caused by Parkinson's disease (PD) is multidimensional (e.g., sensoria, functions, and cognition) and progressive. Its multidimensional nature precludes a single outcome to measure disease progression. Clinical trials of PD use multiple categorical and continuous longitudinal outcomes to assess the treatment effects on overall improvement. A terminal event such as death or dropout can stop the follow-up process. Moreover, the time to the terminal event may be dependent on the multivariate longitudinal measurements. In this article, we consider a joint random-effects model for the correlated outcomes. A multilevel item response theory model is used for the multivariate longitudinal outcomes and a parametric accelerated failure time model is used for the failure time because of the violation of proportional hazard assumption. These two models are linked via random effects. The Bayesian inference via MCMC is implemented in 'BUGS' language. Our proposed method is evaluated by a simulation study and is applied to DATATOP study, a motivating clinical trial to determine if deprenyl slows the progression of PD.

Joint model for a diagnostic test without a gold standard in the presence of a dependent terminal event

Breast cancer patients after breast conservation therapy often develop ipsilateral breast tumor relapse (IBTR), whose classification (true local recurrence versus new ipsilateral primary tumor) is subject to error, and there is no available gold standard. Some patients may die because of breast cancer before IBTR develops. Because this terminal event may be related to the individual patient's unobserved disease status and time to IBTR, the terminal mechanism is non-ignorable. This article presents a joint analysis framework to model the binomial regression with misclassified binary outcome and the correlated time to IBTR, subject to a dependent terminal event and in the absence of a gold standard. Shared random effects are used to link together two survival times. The proposed approach is evaluated by a simulation study and is applied to a breast cancer data set consisting of 4477 breast cancer patients. The proposed joint model can be conveniently fit using adaptive Gaussian quadrature tools implemented in SAS 9.3 (SAS Institute Inc., Cary, NC, USA) procedure NLMIXED.

Bayesian inference for longitudinal data with non-parametric treatment effects

We consider inference for longitudinal data based on mixed-effects models with a non-parametric Bayesian prior on the treatment effect. The proposed non-parametric Bayesian prior is a random partition model with a regression on patient-specific covariates. The main feature and motivation for the proposed model is the use of covariates with a mix of different data formats and possibly high-order interactions in the regression. The regression is not explicitly parameterized. It is implied by the random clustering of subjects. The motivating application is a study of the effect of an anticancer drug on a patient's blood pressure. The study involves blood pressure measurements taken periodically over several 24-h periods for 54 patients. The 24-h periods for each patient include a pretreatment period and several occasions after the start of therapy.

Bayesian Nonparametric Inference - Why and How

We review inference under models with nonparametric Bayesian (BNP) priors. The discussion follows a set of examples for some common inference problems. The examples are chosen to highlight problems that are challenging for standard parametric inference. We discuss inference for density estimation, clustering, regression and for mixed effects models with random effects distributions. While we focus on arguing for the need for the flexibility of BNP models, we also review some of the more commonly used BNP models, thus hopefully answering a bit of both questions, why and how to use BNP.

Joint latent class models for longitudinal and time-to-event data: a review

Most statistical developments in the joint modelling area have focused on the shared random-effect models that include characteristics of the longitudinal marker as predictors in the model for the time-to-event. A less well-known approach is the joint latent class model which consists in assuming that a latent class structure entirely captures the correlation between the longitudinal marker trajectory and the risk of the event. Owing to its flexibility in modelling the dependency between the longitudinal marker and the event time, as well as its ability to include covariates, the joint latent class model may be particularly suited for prediction problems. This article aims at giving an overview of joint latent class modelling, especially in the prediction context. The authors introduce the model, discuss estimation and goodness-of-fit, and compare it with the shared random-effect model. Then, dynamic predictive tools derived from joint latent class models, as well as measures to evaluate their dynamic predictive accuracy, are presented. A detailed illustration of the methods is given in the context of the prediction of prostate cancer recurrence after radiation therapy based on repeated measures of Prostate Specific Antigen.

Rubbery Polya Tree

Polya trees (PT) are random probability measures which can assign probability 1 to the set of continuous distributions for certain specifications of the hyperparameters. This feature distinguishes the PT from the popular Dirichlet process (DP) model which assigns probability 1 to the set of discrete distributions. However, the PT is not nearly as widely used as the DP prior. Probably the main reason is an awkward dependence of posterior inference on the choice of the partitioning subsets in the definition of the PT. We propose a generalization of the PT prior that mitigates this undesirable dependence on the partition structure, by allowing the branching probabilities to be dependent within the same level. The proposed new process is not a PT anymore. However, it is still a tail-free process and many of the prior properties remain the same as those for the PT.

CENTER-ADJUSTED INFERENCE FOR A NONPARAMETRIC BAYESIAN RANDOM EFFECT DISTRIBUTION

Dirichlet process (DP) priors are a popular choice for semiparametric Bayesian random effect models. The fact that the DP prior implies a non-zero mean for the random effect distribution creates an identifiability problem that complicates the interpretation of, and inference for, the fixed effects that are paired with the random effects. Similarly, the interpretation of, and inference for, the variance components of the random effects also becomes a challenge. We propose an adjustment of conventional inference using a post-processing technique based on an analytic evaluation of the moments of the random moments of the DP. The adjustment for the moments of the DP can be conveniently incorporated into Markov chain Monte Carlo simulations at essentially no additional computational cost. We conduct simulation studies to evaluate the performance of the proposed inference procedure in both a linear mixed model and a logistic linear mixed effect model. We illustrate the method by applying it to a prostate specific antigen dataset. We provide an R function that allows one to implement the proposed adjustment in a post-processing step of posterior simulation output, without any change to the posterior simulation itself.