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

An augmented illness-death model for semi-competing risks with clinically immediate terminal events

Preeclampsia is a pregnancy-associated condition posing risks of both fetal and maternal mortality and morbidity that can only resolve following delivery and removal of the placenta. Because in its typical form preeclampsia can arise before delivery, but not after, these two events exemplify the time-to-event setting of "semi-competing risks" in which a non-terminal event of interest is subject to the occurrence of a terminal event of interest. The semi-competing risks framework presents a valuable opportunity to simultaneously address two clinically meaningful risk modeling tasks: (i) characterizing risk of developing preeclampsia, and (ii) characterizing time to delivery after onset of preeclampsia. However, some people with preeclampsia deliver immediately upon diagnosis, while others are admitted and monitored for an extended period before giving birth, resulting in two distinct trajectories following the non-terminal event, which we call "clinically immediate" and "non-immediate" terminal events. Though such phenomena arise in many clinical contexts, to-date there have not been methods developed to acknowledge the complex dependencies between such outcomes, nor leverage these phenomena to gain new insight into individualized risk. We address this gap by proposing a novel augmented frailty-based illness-death model with a binary submodel to distinguish risk of immediate terminal event following the non-terminal event. The model admits direct dependence of the terminal event on the non-terminal event through flexible regression specification, as well as indirect dependence via a shared frailty term linking each submodel. We develop an efficient Bayesian sampler for estimation and corresponding model fit metrics, and derive formulae for dynamic risk prediction. In an extended example using pregnancy outcome data from an electronic health record, we demonstrate the proposed model's direct applicability to address a broad range of clinical questions.

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.

Direct and indirect treatment effects in the presence of semicompeting risks

Semicompeting risks refer to the phenomenon that the terminal event (such as death) can censor the nonterminal event (such as disease progression) but not vice versa. The treatment effect on the terminal event can be delivered either directly following the treatment or indirectly through the nonterminal event. We consider 2 strategies to decompose the total effect into a direct effect and an indirect effect under the framework of mediation analysis in completely randomized experiments by adjusting the prevalence and hazard of nonterminal events, respectively. They require slightly different assumptions on cross-world quantities to achieve identifiability. We establish asymptotic properties for the estimated counterfactual cumulative incidences and decomposed treatment effects. We illustrate the subtle difference between these 2 decompositions through simulation studies and two real-data applications in the Supplementary Materials.

Competing Risk Modeling with Bivariate Varying Coefficients to Understand the Dynamic Impact of COVID-19

The coronavirus disease 2019 (COVID-19) pandemic has exerted a profound impact on patients with end-stage renal disease relying on kidney dialysis to sustain their lives. A preliminary analysis of dialysis patient postdischarge hospital readmissions and deaths in 2020 revealed that the COVID-19 effect has varied significantly with postdischarge time and time since the pandemic onset. However, the complex dynamics cannot be characterized by existing varying coefficient models. To address this issue, we propose a bivariate varying coefficient model for competing risks, where tensor-product B-splines are used to estimate the surface of the COVID-19 effect. An efficient proximal Newton algorithm is developed to facilitate the fitting of the new model to the massive data for Medicare beneficiaries on dialysis. Difference-based anisotropic penalization is introduced to mitigate model overfitting and effect wiggliness; a cross-validation method is derived to determine optimal tuning parameters. Hypothesis testing procedures are designed to examine whether the COVID-19 effect varies significantly with postdischarge time and the time since the pandemic onset, either jointly or separately. Applications to Medicare dialysis patients demonstrate the real-world performance of the proposed methods. Simulation experiments are conducted to evaluate the estimation accuracy, type I error rate, statistical power, and model selection procedures. Supplementary materials for this article are available online.

Trends and ethnic differences in stroke recurrence and mortality in a biethnic population, 2000-2019: a novel application of an illness-death model

PURPOSE

To estimate temporal trends in post-stroke outcomes in Mexican Americans (MAs) and non-Hispanic whites (NHWs).

METHODS

We included first-ever ischemic strokes from a population-based study in South Texas (n = 5343, 2000-2019). We applied an illness-death model with three jointly specified Cox-type models to estimate ethnic differences and ethnic-specific temporal trends in recurrence (first stroke to recurrence), recurrence-free mortality (first stroke to death without recurrence), recurrence-affected mortality (first stroke to death with recurrence), and postrecurrence mortality (recurrence to death).

RESULTS

MAs had higher rates of postrecurrence mortality than NHWs in 2019 but lower rates in 2000. One-year risk of this outcome increased in MAs and decreased in NHWs, resulting in ethnic differences changing from -14.9% (95% CI -35.9%, -2.8%) in 2000 to 9.1% (1.7%, 18.9%) in 2018. For recurrence-free mortality, lower rates were observed in MAs until 2013. Ethnic differences in 1-year risk changed from -3.3% (95% CI -4.9%, -1.6%) in 2000 to -1.2% (-3.1%, 0.8%) in 2018. For stroke recurrence and recurrence-affected mortality, significant ethnic disparities persisted over the study period.

CONCLUSIONS

An ethnic disparity in postrecurrence mortality was newly identified, driven by the increasing trend in MAs but a decreasing trend in NHWs.

Predicting the Risk of Alzheimer's Disease and Related Dementia in Patients with Mild Cognitive Impairment Using a Semi-Competing Risk Approach

Alzheimer's disease (AD) and AD-related dementias (AD/ADRD) are a group of progressive neurodegenerative diseases. The progression of AD can be conceptualized as a continuum in which patients progress from normal cognition to preclinical AD (i.e., no symptoms but biological changes in the brain) to mild cognitive impairment (MCI) due to AD (i.e., mild symptoms but not interfere with daily activities), followed by increasing severity of dementia due to AD. Early detection and prediction models for the transition of MCI to AD/ADRD are needed, and efforts have been made to build predictions of MCI conversion to AD/ADRD. However, most existing studies developing such prediction models did not consider the competing risks of death, which may result in biased risk estimates. In this study, we aim to develop a prediction model for AD/ADRD among patients with MCI considering the competing risks of death using a semi-competing risk approach.

Analysis of hospital readmissions with competing risks

The 30-day hospital readmission rate has been used in provider profiling for evaluating inter-provider care coordination, medical cost effectiveness, and patient quality of life. Current profiling analyzes use logistic regression to model 30-day readmission as a binary outcome, but one disadvantage of this approach is that this outcome is strongly affected by competing risks (e.g., death). Thus, one, perhaps unintended, consequence is that if two facilities have the same rates of readmission, the one with the higher rate of competing risks will have the lower 30-day readmission rate. We propose a discrete time competing risk model wherein the cause-specific readmission hazard is used to assess provider-level effects. This approach takes account of the timing of events and focuses on the readmission rates which are of primary interest. The quality measure, then is a standardized readmission ratio, akin to a standardized mortality ratio. This measure is not systematically affected by the rate of competing risks. To facilitate the estimation and inference of a large number of provider effects, we develop an efficient Blockwise Inversion Newton algorithm, and a stabilized robust score test that overcomes the conservative nature of the classical robust score test. An application to dialysis patients demonstrates improved profiling, model fitting, and outlier detection over existing methods.

Modeling semi-competing risks data as a longitudinal bivariate process

As individuals age, death is a competing risk for Alzheimer's disease (AD) but the reverse is not the case. As such, studies of AD can be placed within the semi-competing risks framework. Central to semi-competing risks, and in contrast to standard competing risks , is that one can learn about the dependence structure between the two events. To-date, however, most methods for semi-competing risks treat dependence as a nuisance and not a potential source of new clinical knowledge. We propose a novel regression-based framework that views the two time-to-event outcomes through the lens of a longitudinal bivariate process on a partition of the time scales of the two events. A key innovation of the framework is that dependence is represented in two distinct forms, local and global dependence, both of which have intuitive clinical interpretations. Estimation and inference are performed via penalized maximum likelihood, and can accommodate right censoring, left truncation, and time-varying covariates. An important consequence of the partitioning of the time scale is that an ambiguity regarding the specific form of the likelihood contribution may arise; a strategy for sensitivity analyses regarding this issue is described. The framework is then used to investigate the role of gender and having ≥1 apolipoprotein E (APOE) ε4 allele on the joint risk of AD and death using data from the Adult Changes in Thought study.

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.

Joint analysis of longitudinal measurements and spatially clustered competing risks HIV/AIDS data

The joint modeling of repeated measurements and time-to-event provides a general framework to describe better the link between the progression of disease through longitudinal measurements and time-to-event outcome. In the survival data, a sample of individuals is frequently grouped into clusters. In some applications, these clusters could be arranged spatially, for example, based on geographical regions. There are two benefits of considering spatial variation in these data, enhancing the efficiency and accuracy of the parameters estimations, and investigating the survivorship spatial pattern. On the other hand, in survival data, there is a situation that subjects are supposed to experience more than one type of event potentially, but the occurrence of one type of event prevents the occurrence of the others. In this article, we considered a Bayesian joint model of longitudinal and competing risks outcomes for spatially clustered HIV/AIDS data. The data were from a registry-based study carried in Hamadan Province, Iran, from December 1997 to June 2020. In this joint model, a linear mixed effects model was used for the longitudinal submodel and a cause-specific hazard model with spatial and spatial-risk random effects was used for the survival submodel. Also, a latent structure was defined by random effects to link both event times and longitudinal processes. We used a univariate intrinsic conditional autoregressive (ICAR) distribution and a multivariate ICAR distribution for modeling the areal spatial and spatial-risk random effects, respectively. The performance of our proposed model using simulation studies and analysis of HIV/AIDS data were assessed.

Bayesian survival analysis with BUGS

Survival analysis is one of the most important fields of statistics in medicine and biological sciences. In addition, the computational advances in the last decades have favored the use of Bayesian methods in this context, providing a flexible and powerful alternative to the traditional frequentist approach. The objective of this article is to summarize some of the most popular Bayesian survival models, such as accelerated failure time, proportional hazards, mixture cure, competing risks, multi-state, frailty, and joint models of longitudinal and survival data. Moreover, an implementation of each presented model is provided using a BUGS syntax that can be run with JAGS from the R programming language. Reference to other Bayesian R-packages is also discussed.

A dependent Dirichlet process model for survival data with competing risks

In this paper, we first propose a dependent Dirichlet process (DDP) model using a mixture of Weibull models with each mixture component resembling a Cox model for survival data. We then build a Dirichlet process mixture model for competing risks data without regression covariates. Next we extend this model to a DDP model for competing risks regression data by using a multiplicative covariate effect on subdistribution hazards in the mixture components. Though built on proportional hazards (or subdistribution hazards) models, the proposed nonparametric Bayesian regression models do not require the assumption of constant hazard (or subdistribution hazard) ratio. An external time-dependent covariate is also considered in the survival model. After describing the model, we discuss how both cause-specific and subdistribution hazard ratios can be estimated from the same nonparametric Bayesian model for competing risks regression. For use with the regression models proposed, we introduce an omnibus prior that is suitable when little external information is available about covariate effects. Finally we compare the models' performance with existing methods through simulations. We also illustrate the proposed competing risks regression model with data from a breast cancer study. An R package "DPWeibull" implementing all of the proposed methods is available at CRAN.

A phase I-II design based on periodic and continuous monitoring of disease status and the times to toxicity and death

A Bayesian phase I-II dose-finding design is presented for a clinical trial with four coprimary outcomes that reflect the actual clinical observation process. During a prespecified fixed follow-up period, the times to disease progression, toxicity, and death are monitored continuously, and an ordinal disease status variable, including progressive disease (PD) as one level, is evaluated repeatedly by scheduled imaging. We assume a proportional hazards model with piecewise constant baseline hazard for each continuous variable and a longitudinal multinomial probit model for the ordinal disease status process and include multivariate patient frailties to induce association among the outcomes. A finite partition of the nonfatal outcome combinations during the follow-up period is constructed, and the utility of each set in the partition is elicited. Posterior mean utility is used to optimize each patient's dose, subject to a safety rule excluding doses with an unacceptably high rate of PD, severe toxicity, or death. A simulation study shows that, compared with the proposed design, a simpler design based on commonly used efficacy and toxicity outcomes obtained by combining the four variables described above performs poorly and has substantially smaller probabilities of correctly choosing truly optimal doses and excluding truly unsafe doses.

On shared gamma-frailty conditional Markov model for semicompeting risks data

Semicompeting risks data are a mixture of competing risks data and progressive state data. This type of data occurs when a nonterminal event is subject to truncation by a well-defined terminal event, but not vice versa. The shared gamma-frailty conditional Markov model (GFCMM) has been used to analyze semicompeting risks data because of its flexibility. There are two versions of this model: the restricted and the unrestricted model. Maximum likelihood estimation methodology has been proposed in the literature. However, we found through numerical experiments that the unrestricted model sometimes yields nonparametrically biased estimation. In this article, we provide a practical guideline for using the GFCMM in the analysis of semicompeting risk data that includes: (a) a score test to assess if the restricted model, which does not exhibit estimation problems, is reasonable under a proportional hazards assumption, and (b) a graphical illustration to justify whether the unrestricted model yields nonparametric estimation with substantial bias for cases where the test provides a statistical significant result against the restricted model. This guideline was applied to the Indianapolis-Ibadan Dementia Project data as an illustration to explore how dementia occurrence changes mortality risk.

Estimation and inference for semi-competing risks based on data from a nested case-control study

In semi-competing risks, the occurrence of some non-terminal event is subject to a terminal event, usually death. While existing methods for semi-competing risks data analysis assume complete information on all relevant covariates, data on at least one covariate are often not readily available in practice. In this setting, for standard univariate time-to-event analyses, researchers may choose from several strategies for sub-sampling patients on whom to collect complete data, including the nested case-control study design. Here, we consider a semi-competing risks analysis through the reuse of data from an existing nested case-control study for which risk sets were formed based on either the non-terminal or the terminal event. Additionally, we introduce the supplemented nested case-control design in which detailed data are collected on additional events of the other type. We propose estimation with respect to a frailty illness-death model through maximum weighted likelihood, specifying the baseline hazard functions either parametrically or semi-parametrically via B-splines. Two standard error estimators are proposed: (i) a computationally simple sandwich estimator and (ii) an estimator based on a perturbation resampling procedure. We derive the asymptotic properties of the proposed methods and evaluate their small-sample properties via simulation. The designs/methods are illustrated with an investigation of risk factors for acute graft-versus-host disease among N = 8838 patients undergoing hematopoietic stem cell transplantation, for which death is a significant competing risk.

Individual participant data meta-analysis of intervention studies with time-to-event outcomes: A review of the methodology and an applied example

Many randomized trials evaluate an intervention effect on time-to-event outcomes. Individual participant data (IPD) from such trials can be obtained and combined in a so-called IPD meta-analysis (IPD-MA), to summarize the overall intervention effect. We performed a narrative literature review to provide an overview of methods for conducting an IPD-MA of randomized intervention studies with a time-to-event outcome. We focused on identifying good methodological practice for modeling frailty of trial participants across trials, modeling heterogeneity of intervention effects, choosing appropriate association measures, dealing with (trial differences in) censoring and follow-up times, and addressing time-varying intervention effects and effect modification (interactions).We discuss how to achieve this using parametric and semi-parametric methods, and describe how to implement these in a one-stage or two-stage IPD-MA framework. We recommend exploring heterogeneity of the effect(s) through interaction and non-linear effects. Random effects should be applied to account for residual heterogeneity of the intervention effect. We provide further recommendations, many of which specific to IPD-MA of time-to-event data from randomized trials examining an intervention effect.We illustrate several key methods in a real IPD-MA, where IPD of 1225 participants from 5 randomized clinical trials were combined to compare the effects of Carbamazepine and Valproate on the incidence of epileptic seizures.

Is mortality readmissions bias a concern for readmission rates under the Hospital Readmissions Reduction Program?

OBJECTIVE

To determine whether the exclusion of patients who die from adjusted 30-day readmission rates influences readmission rate measures and penalties under the Hospital Readmission Reduction Program (HRRP).

DATA SOURCES/STUDY SETTING

100% Medicare fee-for-service claims over the period July 1, 2012, until June 30, 2015.

STUDY DESIGN

We examine the 30-day readmission risk across the three conditions targeted by the HRRP: acute myocardial infarction (AMI), congestive heart failure (CHF), and pneumonia. Using logistic regression, we estimate the readmission risk for three samples of patients: those who survived the 30-day period after their index admission, those who died over the 30-day period, and all patients who were admitted to see how they differ.

DATA COLLECTION/EXTRACTION METHODS

We identified and extracted data for Medicare fee-for-service beneficiaries admitted with primary diagnoses of AMI (N = 497 931), CHF (N = 1 047 552), and pneumonia (N = 850 552).

RESULTS

The estimated hospital readmission rates for the survived and nonsurvived patients differed by 5%-8%, on average. Incorporating these estimates into overall readmission risk for all admitted patients changes the likely penalty status for 9% of hospitals. However, this change is randomly distributed across hospitals and is not concentrated amongst any one type of hospital.

CONCLUSIONS

Not accounting for variations in mortality may result in inappropriate penalties for some hospitals. However, the effect of this bias is low due to low mortality rates amongst incentivized conditions and appears to be randomly distributed across hospital types.

SemiCompRisks: An R Package for the Analysis of Independent and Cluster-correlated Semi-competing Risks Data

Semi-competing risks refer to the setting where primary scientific interest lies in estimation and inference with respect to a non-terminal event, the occurrence of which is subject to a terminal event. In this paper, we present the R package SemiCompRisks that provides functions to perform the analysis of independent/clustered semi-competing risks data under the illness-death multi-state model. The package allows the user to choose the specification for model components from a range of options giving users substantial flexibility, including: accelerated failure time or proportional hazards regression models; parametric or non-parametric specifications for baseline survival functions; parametric or non-parametric specifications for random effects distributions when the data are cluster-correlated; and, a Markov or semi-Markov specification for terminal event following non-terminal event. While estimation is mainly performed within the Bayesian paradigm, the package also provides the maximum likelihood estimation for select parametric models. The package also includes functions for univariate survival analysis as complementary analysis tools.

Joint Shock/Death Risk Prediction Model for Patients Considering Implantable Cardioverter-Defibrillators

BACKGROUND

The risk of death or appropriate therapy varies widely among recipients of implantable cardioverter-defibrillators (ICDs). The goals of this study were to develop a risk prediction tool that jointly considers future outcome probabilities of ICD shock and death.

METHODS AND RESULTS

We performed a secondary analysis of patients receiving ICDs as part of the SCD-HeFT trial (Sudden Cardiac Death in Heart Failure Trial). We applied an illness-death regression model to jointly model both ICD shocks and death under the semi-competing risks framework, which predicts for each patient their probability of having received ICD shocks, dying, or both at any given point in time. Among 803 ICD recipients (mean age, 60 years; 23% women) followed for a median of 41.1 months, 430 (53.5%) patients completed the study without dying or receiving an ICD shock, 206 (25.7%) received at least 1 shock but survived, 113 (14.1%) died before experiencing a shock, and 54 (6.7%) received at least 1 shock and subsequently died. Predicted outcome probabilities based on baseline demographic and clinical variables reveal substantial heterogeneity in joint shock and death risks, both between patients at each time point and for each single patient across time. Overall, predictive performance for ICD shock and death individually was adequate, based on area under the curve at 5 years of 0.65 for shocks and of 0.79 for death.

CONCLUSIONS

Our analysis of outcomes after ICD implantation provides an alternative predictive model for individual risk of death or ICD shocks. If validated, this may provide a useful tool for individualized counseling regarding likely outcomes after device implantation, while also informing the design of further studies to focus the clinical effectiveness and cost-effectiveness of ICD therapy.

CLINICAL TRIAL REGISTRATION

URL: https://www.clinicaltrials.gov. Unique identifier: NCT00000609.

Bayesian Semiparametric Joint Regression Analysis of Recurrent Adverse Events and Survival in Esophageal Cancer Patients

We propose a Bayesian semiparametric joint regression model for a recurrent event process and survival time. Assuming independent latent subject frailties, we define marginal models for the recurrent event process intensity and survival distribution as functions of the subject's frailty and baseline covariates. A robust Bayesian model, called Joint-DP, is obtained by assuming a Dirichlet process for the frailty distribution. We present a simulation study that compares posterior estimates under the Joint-DP model to a Bayesian joint model with lognormal frailties, a frequentist joint model, and marginal models for either the recurrent event process or survival time. The simulations show that the Joint-DP model does a good job of correcting for treatment assignment bias, and has favorable estimation reliability and accuracy compared with the alternative models. The Joint-DP model is applied to analyze an observational dataset from esophageal cancer patients treated with chemo-radiation, including the times of recurrent effusions of fluid to the heart or lungs, survival time, prognostic covariates, and radiation therapy modality.

Optimizing natural killer cell doses for heterogeneous cancer patients on the basis of multiple event times

A sequentially adaptive Bayesian design is presented for a clinical trial of cord blood derived natural killer cells to treat severe hematologic malignancies. Given six prognostic subgroups defined by disease type and severity, the goal is to optimize cell dose in each subgroup. The trial has five co-primary outcomes, the times to severe toxicity, cytokine release syndrome, disease progression or response, and death. The design assumes a multivariate Weibull regression model, with marginals depending on dose, subgroup, and patient frailties that induce association among the event times. Utilities of all possible combinations of the nonfatal outcomes over the first 100 days following cell infusion are elicited, with posterior mean utility used as a criterion to optimize dose. For each subgroup, the design stops accrual to doses having an unacceptably high death rate, and at the end of the trial selects the optimal safe dose. A simulation study is presented to validate the design's safety, ability to identify optimal doses, and robustness, and to compare it to a simplified design that ignores patient heterogeneity.

Semi-Competing Risks Data Analysis: Accounting for Death as a Competing Risk When the Outcome of Interest Is Nonterminal

Hospital readmission is a key marker of quality of health care. Notwithstanding its widespread use, however, it remains controversial in part because statistical methods used to analyze readmission, primarily logistic regression and related models, may not appropriately account for patients who die before experiencing a readmission event within the time frame of interest. Toward resolving this, we describe and illustrate the semi-competing risks framework, which refers to the general setting where scientific interest lies with some nonterminal event (eg, readmission), the occurrence of which is subject to a terminal event (eg, death). Although several statistical analysis methods have been proposed for semi-competing risks data, we describe in detail the use of illness-death models primarily because of their relation to well-known methods for survival analysis and the availability of software. We also describe and consider in detail several existing approaches that could, in principle, be used to analyze semi-competing risks data, including composite end point and competing risks analyses. Throughout we illustrate the ideas and methods using data on N=49 763 Medicare beneficiaries hospitalized between 2011 and 2013 with a principle discharge diagnosis of heart failure.