Bayesian estimators for conditional hazard functions

Bayesian semi-parametric inference for clustered recurrent events with zero inflation and a terminal event

Recurrent events are common in clinical studies and are often subject to terminal events. In pragmatic trials, participants are often nested in clinics and can be susceptible or structurally unsusceptible to the recurrent events. We develop a Bayesian shared random effects model to accommodate this complex data structure. To achieve robustness, we consider the Dirichlet processes to model the residual of the accelerated failure time model for the survival process as well as the cluster-specific shared frailty distribution, along with an efficient sampling algorithm for posterior inference. Our method is applied to a recent cluster randomized trial on fall injury prevention.

MEASURING PERFORMANCE FOR END-OF-LIFE CARE

Although not without controversy, readmission is entrenched as a hospital quality metric with statistical analyses generally based on fitting a logistic-Normal generalized linear mixed model. Such analyses, however, ignore death as a competing risk, although doing so for clinical conditions with high mortality can have profound effects; a hospital's seemingly good performance for readmission may be an artifact of it having poor performance for mortality. in this paper we propose novel multivariate hospital-level performance measures for readmission and mortality that derive from framing the analysis as one of cluster-correlated semi-competing risks data. We also consider a number of profiling-related goals, including the identification of extreme performers and a bivariate classification of whether the hospital has higher-/lower-than-expected readmission and mortality rates via a Bayesian decision-theoretic approach that characterizes hospitals on the basis of minimizing the posterior expected loss for an appropriate loss function. in some settings, particularly if the number of hospitals is large, the computational burden may be prohibitive. To resolve this, we propose a series of analysis strategies that will be useful in practice. Throughout, the methods are illustrated with data from CMS on N = 17,685 patients diagnosed with pancreatic cancer between 2000-2012 at one of J = 264 hospitals in California.

On a new piecewise regression model with cure rate: Diagnostics and application to medical data

In this article, we discuss an extension of the classical negative binomial cure rate model with piecewise exponential distribution of the time to event for concurrent causes, which enables the modeling of monotonic and non-monotonic hazard functions (ie, the shape of the hazard function is not assumed as in traditional parametric models). This approach produces a flexible cure rate model, depending on the choice of time partition. We discuss local influence on this negative binomial power piecewise exponential model. We report on Monte Carlo simulation studies and application of the model to real melanoma and leukemia datasets.

Bayesian group sequential enrichment designs based on adaptive regression of response and survival time on baseline biomarkers

Precision medicine relies on the idea that, for a particular targeted agent, only a subpopulation of patients is sensitive to it and thus may benefit from it therapeutically. In practice, it is often assumed based on preclinical data that a treatment-sensitive subpopulation is known, and moreover that the agent is substantively efficacious in that subpopulation. Due to important differences between preclinical settings and human biology, however, data from patients treated with a new targeted agent often show that one or both of these assumptions are false. This paper provides a Bayesian randomized group sequential enrichment design that compares an experimental treatment to a control based on survival time and uses early response as an ancillary outcome to assist with adaptive variable selection and enrichment. Initially, the design enrolls patients under broad eligibility criteria. At each interim decision, submodels for regression of response and survival time on a baseline covariate vector and treatment are fit; variable selection is used to identify a covariate subvector that characterizes treatment-sensitive patients and determines a personalized benefit index, and comparative superiority and futility decisions are made. Enrollment of each cohort is restricted to the most recent adaptively identified treatment-sensitive patients. Group sequential decision cutoffs are calibrated to control overall type I error and account for the adaptive enrollment restriction. The design provides a basis for precision medicine by identifying a treatment-sensitive subpopulation, if it exists, and determining whether the experimental treatment is superior to the control in that subpopulation. A simulation study shows that the proposed design reliably identifies a sensitive subpopulation, yields much higher generalized power compared to several existing enrichment designs and a conventional all-comers group sequential design, and is robust.

Hierarchical models for semi-competing risks data with application to quality of end-of-life care for pancreatic cancer

Readmission following discharge from an initial hospitalization is a key marker of quality of health care in the United States. For the most part, readmission has been studied among patients with 'acute' health conditions, such as pneumonia and heart failure, with analyses based on a logistic-Normal generalized linear mixed model (Normand et al., 1997). Naïve application of this model to the study of readmission among patients with 'advanced' health conditions such as pancreatic cancer, however, is problematic because it ignores death as a competing risk. A more appropriate analysis is to imbed such a study within the semi-competing risks framework. To our knowledge, however, no comprehensive statistical methods have been developed for cluster-correlated semi-competing risks data. To resolve this gap in the literature we propose a novel hierarchical modeling framework for the analysis of cluster-correlated semi-competing risks data that permits parametric or non-parametric specifications for a range of components giving analysts substantial flexibility as they consider their own analyses. Estimation and inference is performed within the Bayesian paradigm since it facilitates the straightforward characterization of (posterior) uncertainty for all model parameters, including hospital-specific random effects. Model comparison and choice is performed via the deviance information criterion and the log-pseudo marginal likelihood statistic, both of which are based on a partially marginalized likelihood. An efficient computational scheme, based on the Metropolis-Hastings-Green algorithm, is developed and had been implemented in the SemiCompRisks R package. A comprehensive simulation study shows that the proposed framework performs very well in a range of data scenarios, and outperforms competitor analysis strategies. The proposed framework is motivated by and illustrated with an on-going study of the risk of readmission among Medicare beneficiaries diagnosed with pancreatic cancer. Using data on n=5,298 patients at J=112 hospitals in the six New England states between 2000-2009, key scientific questions we consider include the role of patient-level risk factors on the risk of readmission and the extent of variation in risk across hospitals not explained by differences in patient case-mix.

Assessment of critical exposure and outcome windows in time-to-event analysis with application to air pollution and preterm birth study

In reproductive epidemiology, there is a growing interest to examine associations between air pollution exposure during pregnancy and the risk of preterm birth (PTB). One important research objective is to identify critical periods of exposure and estimate the associated effects at different stages of pregnancy. However, population studies have reported inconsistent findings. This may be due to limitations from the standard analytic approach of treating PTB as a binary outcome without considering time-varying exposures together over the course of pregnancy. To address this research gap, we present a Bayesian hierarchical model for conducting a comprehensive examination of gestational air pollution exposure by estimating the joint effects of weekly exposures during different vulnerable periods. Our model also treats PTB as a time-to-event outcome to address the challenge of different exposure lengths among ongoing pregnancies. The proposed model is applied to a dataset of geocoded birth records in the Atlanta metropolitan area between 1999-2005 to examine the risk of PTB associated with gestational exposure to ambient fine particulate matter [Formula: see text]m in aerodynamic diameter (PM[Formula: see text]). We find positive associations between PM[Formula: see text] exposure during early and mid-pregnancy, and evidence that associations are stronger for PTBs occurring around week 30.

Bayesian Semi-parametric Analysis of Semi-competing Risks Data: Investigating Hospital Readmission after a Pancreatic Cancer Diagnosis

In the U.S., the Centers for Medicare and Medicaid Services uses 30-day readmission, following hospitalization, as a proxy outcome to monitor quality of care. These efforts generally focus on treatable health conditions, such as pneumonia and heart failure. Expanding quality of care systems to monitor conditions for which treatment options are limited or non-existent, such as pancreatic cancer, is challenging because of the non-trivial force of mortality; 30-day mortality for pancreatic cancer is approximately 30%. In the statistical literature, data that arise when the observation of the time to some non-terminal event is subject to some terminal event are referred to as 'semi-competing risks data'. Given such data, scientific interest may lie in at least one of three areas: (i) estimation/inference for regression parameters, (ii) characterization of dependence between the two events, and (iii) prediction given a covariate profile. Existing statistical methods focus almost exclusively on the first of these; methods are sparse or non-existent, however, when interest lies with understanding dependence and performing prediction. In this paper we propose a Bayesian semi-parametric regression framework for analyzing semi-competing risks data that permits the simultaneous investigation of all three of the aforementioned scientific goals. Characterization of the induced posterior and posterior predictive distributions is achieved via an efficient Metropolis-Hastings-Green algorithm, which has been implemented in an R package. The proposed framework is applied to data on 16,051 individuals diagnosed with pancreatic cancer between 2005-2008, obtained from Medicare Part A. We found that increased risk for readmission is associated with a high comorbidity index, a long hospital stay at initial hospitalization, non-white race, male, and discharge to home care.

Hierarchical dynamic time-to-event models for post-treatment preventive care data on breast cancer survivors

This paper considers modelling data arising in post-treatment preventive care settings, where cancer patients who have undergone disease-directed treatment discontinue seeking preventive care services. Clinicians and public health researchers are interested in explaining such behavioural patterns by modelling the time-to-receiving care while accounting for several patient and treatment attributes. A key feature of such data is that a noticeable number of patients would never return for screening, a concept subtly different from censoring, where an individual does not return for screening in the given time frame of the study. Models distinguishing between these two concepts are known as cure rate models and are often preferred for data where a significant part of the population never experienced the endpoint. Building upon recent work on hierarchical cure model framework we propose modelling a sequence of latent events with a piecewise exponential distribution that remedies oversmoothing encountered in existing models with different latent distributions. We investigate simultaneous regression on the cure fraction and the latent event distribution and derive a flexible class of semiparametric cure rate models.

The separation of timescales in Bayesian survival modeling of the time-varying effect of a time-dependent exposure

In this paper, we apply flexible Bayesian survival analysis methods to investigate the risk of lymphoma associated with kidney transplantation among patients with end-stage renal disease. Of key interest is the potentially time-varying effect of a time-dependent exposure: transplant status. Bayesian modeling of the baseline hazard and the effect of transplant requires consideration of 2 timescales: time since study start and time since transplantation, respectively. Previous related work has not dealt with the separation of multiple timescales. Using a hierarchical model for the hazard function, both timescales are incorporated via conditionally independent stochastic processes; smoothing of each process is specified via intrinsic conditional Gaussian autoregressions. Features of the corresponding posterior distribution are evaluated from draws obtained via a Metropolis-Hastings-Green algorithm.

Bayesian dynamic models for survival data with a cure fraction

In this paper, we propose a new class of semi-parametric cure rate models. Specifically, we construct dynamic models for piecewise hazard functions over a finite partition of the time axis. Allowing the size of partition and the levels of baseline hazard to be random, our proposed models provide a great flexibility in controlling the degree of parametricity in the right tail of the survival distribution and the amount of correlations among the log-baseline hazard levels. Several properties of the proposed models are derived, and propriety of the implied posteriors with improper noninformative priors for regression coefficients based on the proposed models is established for the fixed partition of the time axis. In addition, an efficient reversible jump computational algorithm is developed for carrying out posterior computation. A real data set from a melanoma clinical trial is analyzed in detail to further demonstrate the proposed methodology.

Bayesian modeling of time-varying and waning exposure effects

In epidemiologic studies, there is often interest in assessing the association between exposure history and disease incidence. For many diseases, incidence may depend not only on cumulative exposure, but also on the ages at which exposure occurred. This article proposes a flexible Bayesian approach for modeling age-varying and waning exposure effects. The Cox model is generalized to allow the hazard of disease to depend on an integral, across the exposed ages, of a piecewise polynomial function of age, multiplied by an exponential decay term. Linearity properties of the model facilitate posterior computation via a Gibbs sampler, which generalizes previous algorithms for Cox regression with time-dependent covariates. The approach is illustrated by an application to the study of protective effects of breastfeeding on incidence of childhood asthma.