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Many non-fatal events can be considered recurrent in that they can occur repeatedly over time, and some researchers may be interested in the trajectory and relative risk of non-fatal events. With the competing risk of death, the treatment effect on the mean number of recurrent events is non-identifiable since the observed mean is a function of both the recurrent event and terminal event processes. In this paper, we assume independence between the non-fatal and the terminal event process, conditional on the shared frailty, to fit a parametric model that recovers the trajectory of, and identifies the effect of treatment on, the non-fatal event process in the presence of the competing risk of death. Simulation studies are conducted to verify the reliability of our estimators. We illustrate the method and perform model diagnostics using the Carvedilol Prospective Randomized Cumulative Survival trial which involves heart-failure events. [ABSTRACT FROM AUTHOR]

Identifying and distinguishing risk factors for heterogeneous disease subtypes has been of great interest. However, missingness in disease subtypes is a common problem in those data analyses. Several methods have been proposed to deal with the missing data, including complete-case analysis, inverse-probability weighting, and multiple imputation. Although extant literature has compared these methods in missing problems, none has focused on the competing risk setting. In this paper, we discuss the assumptions required when complete-case analysis, inverse-probability weighting, and multiple imputation are used to deal with the missing failure subtype problem, focusing on how to implement these methods under various realistic scenarios in competing risk settings. Besides, we compare these three methods regarding their biases, efficiency, and robustness to model misspecifications using simulation studies. Our results show that complete-case analysis can be seriously biased when the missing completely at random assumption does not hold. Inverse-probability weighting and multiple imputation estimators are valid when we correctly specify the corresponding models for missingness and for imputation, and multiple imputation typically shows higher efficiency than inverse-probability weighting. However, in real-world studies, building imputation models for the missing subtypes can be more challenging than building missingness models. In that case, inverse-probability weighting could be preferred for its easy usage. We also propose two automated model selection procedures and demonstrate their usage in a study of the association between smoking and colorectal cancer subtypes in the Nurses' Health Study and Health Professional Follow-Up Study. [ABSTRACT FROM AUTHOR]

The performance of health care facilities (e.g. hospitals, transplant centers, etc.) is often evaluated through time-to-event outcomes. In this paper, we consider the case where, for each subject, the failure event is due to one of several mutually exclusive causes (competing risks). Since the distribution of patient characteristics may differ greatly by the center, some form of covariate adjustment is generally necessary in order for center-specific outcomes to be accurately compared (to each other or to an overall average). We propose a weighting method for comparing facility-specific cumulative incidence functions to an overall average. The method directly standardizes each facility's non-parametric cumulative incidence function through a weight function constructed from a multivariate prognostic score. We formally define the center effects and derive large-sample properties of the proposed estimator. We evaluate the finite sample performance of the estimator through simulation. The proposed method is applied to the end-stage renal disease setting to evaluate the center-specific pre-transplant mortality and transplant cumulative incidence functions from the Scientific Registry of Transplant Recipients. [ABSTRACT FROM AUTHOR]

For the analysis of competing risks data, three different types of hazard functions have been considered in the literature, namely the cause-specific hazard, the sub-distribution hazard, and the marginal hazard function. Accordingly, medical researchers can fit three different types of the Cox model to estimate the effect of covariates on each of the hazard function. While the relationship between the cause-specific hazard and the sub-distribution hazard has been extensively studied, the relationship to the marginal hazard function has not yet been analyzed due to the difficulties related to non-identifiability. In this paper, we adopt an assumed copula model to deal with the model identifiability issue, making it possible to establish a relationship between the sub-distribution hazard and the marginal hazard function. We then compare the two methods of fitting the Cox model to competing risks data. We also extend our comparative analysis to clustered competing risks data that are frequently used in medical studies. To facilitate the numerical comparison, we implement the computing algorithm for marginal Cox regression with clustered competing risks data in the R joint.Cox package and check its performance via simulations. For illustration, we analyze two survival datasets from lung cancer and bladder cancer patients. [ABSTRACT FROM AUTHOR]

In this paper, we consider joint modeling of repeated measurements and competing risks failure time data to allow for more than one distinct failure type in the survival endpoint. Hence, we can fit a cause-specific hazards submodel to allow for competing risks, with a separate latent association between longitudinal measurements and each cause of failure. We also consider the possible masked causes of failure in joint modeling of repeated measurements and competing risks failure time data. We also derive a score test to identify longitudinal biomarkers or surrogates for a time-to-event outcome in competing risks data which contain masked causes of failure. With a carefully chosen definition of complete data, the maximum likelihood estimation of the cause-specific hazard functions and of the masking probabilities is performed via an expectation maximization algorithm. The simulations are used to explore how the number of individuals, the number of time points per individual, and the functional form of the random effects from the longitudinal biomarkers considering heterogeneous baseline hazards in individuals influence the power to detect the association of a longitudinal biomarker and the survival time. [ABSTRACT FROM AUTHOR]

After the diagnosis of a disease, one major objective is to predict cumulative probabilities of events such as clinical relapse or death from the individual information collected up to a prediction time, usually including biomarker repeated measurements. Several competing estimators have been proposed, mainly from two approaches: joint modelling and landmarking. These approaches differ by the information used, the model assumptions and the complexity of the computational procedures. This paper aims to review the two approaches, precisely define the derived estimators of dynamic predictions and compare their performances notably in case of misspecification. The ultimate goal is to provide key elements for the use of individual dynamic predictions in clinical practice. Prediction of two competing causes of prostate cancer progression from the history of prostate-specific antigen is used as a motivated example. We formally define the quantity to estimate and its estimators, propose techniques to assess the uncertainty around predictions and validate them. We then conduct an in-depth simulation study compare the estimators in terms of prediction error, discriminatory power, efficiency and robustness to model assumptions. We show that prediction tools should be handled with care, in particular by properly specifying models and estimators. [ABSTRACT FROM AUTHOR]

Background: Patients with peripheral artery disease face high amputation and mortality risk. When assessing vascular outcomes, consideration of mortality as a competing risk is not routine. We hypothesize standard time-to-event methods will overestimate major amputation risk in chronic limb-threatening ischemia (CLTI) and non-CLTI. Methods : Patients undergoing peripheral vascular intervention from 2017 to 2018 were abstracted from the Vascular Quality Initiative registry and stratified by mean age (⩾ 75 vs < 75 years). Mortality and amputation data were obtained from Medicare claims. The 2-year cumulative incidence function (CIF) and risk of major amputation from standard time-to-event analysis (1 – Kaplan–Meier and Cox regression) were compared with competing risk analysis (Aalen–Johansen and Fine–Gray model) in CLTI and non-CLTI. Results : A total of 7273 patients with CLTI and 5095 with non-CLTI were included. At 2-year follow up, 13.1% of patients underwent major amputation and 33.4% died without major amputation in the CLTI cohort; 1.3% and 10.7%, respectively, in the non-CLTI cohort. In CLTI, standard time-to-event analysis overestimated the 2-year CIF of major amputation by 20.5% and 13.7%, respectively, in patients ⩾ 75 and < 75 years old compared with competing risk analysis. The standard Cox regression overestimated adjusted 2-year major amputation risk in patients ⩾ 75 versus < 75 years old by 7.0%. In non-CLTI, the CIF was overestimated by 7.1% in patients ⩾ 75 years, and the adjusted risk was overestimated by 5.1% compared with competing risk analysis. Conclusions : Standard time-to-event analysis overestimates the incidence and risk of major amputation, especially in CLTI. Competing risk analyses are alternative approaches to estimate accurately amputation risk in vascular outcomes research. [ABSTRACT FROM AUTHOR]

Living in recovery housing can improve addiction recovery and desistance outcomes. This study examined whether retention in recovery housing and types of discharge outcomes (completed, "neutral," and "negative" outcomes) differed for clients with recent criminal legal system (CLS) involvement. Using data from 101 recovery residences certified by the Virginia Association of Recovery Residences based on 1,978 individuals completing the REC-CAP assessment, competing risk analyses (cumulative incidence function, restricted mean survival time, and restricted mean time lost) followed by the marginalization of effects were implemented to examine program outcomes at final discharge. Residents with recent CLS involvement were more likely to be discharged for positive reasons (successful completion of their goals) and premature/negative reasons (e.g., disciplinary releases) than for neutral reasons. Findings indicate that retention for 6–18 months is essential to establish and maintain positive discharge outcomes, and interventions should be developed to enhance retention in recovery residents with recent justice involvement. [ABSTRACT FROM AUTHOR]

Competing risks data often occur within a center in multi-center clinical trials where the event times within a center may be correlated due to unobserved factors across individuals. In this paper, we consider the cause-specific proportional hazards model with a shared frailty to model the association between the event times within a center in the framework of competing risks. We use a hierarchical likelihood approach, which does not require any intractable integration over the frailty terms. In a clinical trial, cause of death information may not be observed for some patients. In such a case, analyses through exclusion of cases with missing cause of death may lead to biased inferences. We propose a hierarchical likelihood approach for fitting the cause-specific proportional hazards model with a shared frailty in the presence of missing cause of failure. We use multiple imputation methods to address missing cause of death information under the assumption of missing at random. Simulation studies show that the proposed procedures perform well, even if the imputation model is misspecified. The proposed methods are illustrated with data from EORTC trial 30791 conducted by European Organization for Research and Treatment of Cancer (EORTC). [ABSTRACT FROM AUTHOR]

Competing risks data often exist within a center in multi-center randomized clinical trials where the treatment effects or baseline risks may vary among centers. In this paper, we propose a subdistribution hazard regression model with multivariate frailty to investigate heterogeneity in treatment effects among centers from multi-center clinical trials. For inference, we develop a hierarchical likelihood (or h-likelihood) method, which obviates the need for an intractable integration over the frailty terms. We show that the profile likelihood function derived from the h-likelihood is identical to the partial likelihood, and hence it can be extended to the weighted partial likelihood for the subdistribution hazard frailty models. The proposed method is illustrated with a dataset from a multi-center clinical trial on breast cancer as well as with a simulation study. We also demonstrate how to present heterogeneity in treatment effects among centers by using a confidence interval for the frailty for each individual center and how to perform a statistical test for such heterogeneity using a restricted h-likelihood. [ABSTRACT FROM AUTHOR]

Most competing hazards models are based on the rather strong assumption that alternative destinations are stochastically independent. Individual-specific unmeasured risk factors that are shared by two or more alternatives are, as a result, ruled out. The present paper develops a generalization of the standard discrete-time competing hazards model that allows for the types of stochastic dependencies resulting from shared unmeasured risk factors. An empirical example is provided using the process by which young women form their first conjugal residential union, with married and unmarried cohabitation representing the competing alternatives. The results suggest considerable and significant similarity of the alternatives in terms of the unmeasurables. It is also shown that, as a result, the independence assumption leads to substantially biased estimates of the net marriage and net cohabitation survival function. While the model does require a temporal independence assumption, Monte Carlo simulations indicate that the biases introduced by violations of this assumption are confined primarily to the estimates for time-varying covariates. Estimates for other covariates and the cross-destination correlation coefficient, itself, are relatively robust. [ABSTRACT FROM AUTHOR]

We compared methods to project absolute risk, the probability of experiencing the outcome of interest in a given projection interval accommodating competing risks, for a person from the target population with missing predictors. Without missing data, a perfectly calibrated model gives unbiased absolute risk estimates in a new target population, even if the predictor distribution differs from the training data. However, if predictors are missing in target population members, a reference dataset with complete data is needed to impute them and to estimate absolute risk, conditional only on the observed predictors. If the predictor distributions of the reference data and the target population differ, this approach yields biased estimates. We compared the bias and mean squared error of absolute risk predictions for seven methods that assume predictors are missing at random (MAR). Some methods imputed individual missing predictors, others imputed linear predictor combinations (risk scores). Simulations were based on real breast cancer predictor distributions and outcome data. We also analyzed a real breast cancer dataset. The largest bias for all methods resulted from different predictor distributions of the reference and target populations. No method was unbiased in this situation. Surprisingly, violating the MAR assumption did not induce severe biases. Most multiple imputation methods performed similarly and were less biased (but more variable) than a method that used a single expected risk score. Our work shows the importance of selecting predictor reference datasets similar to the target population to reduce bias of absolute risk predictions with missing risk factors. [ABSTRACT FROM AUTHOR]

We present a nonparametric method for estimating the conditional future state entry probabilities and distributions of state entry time conditional on a past state visit when data are subject to dependent censorings in a progressive multistate model where Markovianity of the system is not assumed. These estimators are constructed using the competing risk techniques with risk sets consisting of fractional observations and inverse probability of censoring weights. The fractional observations correspond to estimates of the number of persons who ultimately enter a state from which the future state in question can be reached in one step. We then address the corresponding regression problem by combining these marginal estimators with the pseudo-value approach. The performance of our regression scheme is studied using a comprehensive simulation study. An analysis of existing data on graft-versus-host disease for bone marrow transplant individuals is presented using our novel methodology. A second analysis of another well-known data set on burn patients is also included. [ABSTRACT FROM AUTHOR]

This paper deals with the competing risks model as a special case of a multi-state model. The properties of the model are reviewed and contrasted to the so-called latent failure time approach. The relation between the competing risks model and right-censoring is discussed and regression analysis of the cumulative incidence function briefly reviewed. Two real data examples are presented and a guide to the practitioner is given. [ABSTRACT FROM AUTHOR]

Hepatocellular carcinoma (HCC) is one of the most fatal cancers in the world. There is an urgent need to understand the molecular background of HCC to facilitate the identification of biomarkers and discover effective therapeutic targets. Published transcriptomic studies have reported a large number of genes that are individually significant for HCC. However, reliable biomarkers remain to be determined. In this study, built on max-linear competing risk factor models, we developed a machine learning analytical framework to analyze transcriptomic data to identify the most miniature set of differentially expressed genes (DEGs). By analyzing 9 public whole-transcriptome datasets (containing 1184 HCC samples and 672 nontumor controls), we identified 5 critical differentially expressed genes (DEGs) (ie, CCDC107, CXCL12, GIGYF1, GMNN, and IFFO1) between HCC and control samples. The classifiers built on these 5 DEGs reached nearly perfect performance in identification of HCC. The performance of the 5 DEGs was further validated in a US Caucasian cohort that we collected (containing 17 HCC with paired nontumor tissue). The conceptual advance of our work lies in modeling gene-gene interactions and correcting batch effect in the analytic framework. The classifiers built on the 5 DEGs demonstrated clear signature patterns for HCC. The results are interpretable, robust, and reproducible across diverse cohorts/populations with various disease etiologies, indicating the 5 DEGs are intrinsic variables that can describe the overall features of HCC at the genomic level. The analytical framework applied in this study may pave a new way for improving transcriptome profiling analysis of human cancers. [ABSTRACT FROM AUTHOR]

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Simulation studies play an important role in evaluating the performance of statistical models developed for analyzing complex survival data such as those with competing risks and clustering. This article aims to provide researchers with a basic understanding of competing risks data generation, techniques for inducing cluster-level correlation, and ways to combine them together in simulation studies, in the context of randomized clinical trials with a binary exposure or treatment. We review data generation with competing and semi-competing risks and three approaches of inducing cluster-level correlation for time-to-event data: the frailty model framework, the probability transform, and Moran's algorithm. Using exponentially distributed event times as an example, we discuss how to introduce cluster-level correlation into generating complex survival outcomes, and illustrate multiple ways of combining these methods to simulate clustered, competing and semi-competing risks data with pre-specified correlation values or degree of clustering. [ABSTRACT FROM AUTHOR]

Hepatocellular carcinoma (HCC) is one of the most fatal cancers in the world. There is an urgent need to understand the molecular background of HCC to facilitate the identification of biomarkers and discover effective therapeutic targets. Published transcriptomic studies have reported a large number of genes that are individually significant for HCC. However, reliable biomarkers remain to be determined. In this study, built on max-linear competing risk factor models, we developed a machine learning analytical framework to analyze transcriptomic data to identify the most miniature set of differentially expressed genes (DEGs). By analyzing 9 public whole-transcriptome datasets (containing 1184 HCC samples and 672 nontumor controls), we identified 5 critical differentially expressed genes (DEGs) (ie, CCDC107, CXCL12, GIGYF1, GMNN, and IFFO1) between HCC and control samples. The classifiers built on these 5 DEGs reached nearly perfect performance in identification of HCC. The performance of the 5 DEGs was further validated in a US Caucasian cohort that we collected (containing 17 HCC with paired nontumor tissue). The conceptual advance of our work lies in modeling gene-gene interactions and correcting batch effect in the analytic framework. The classifiers built on the 5 DEGs demonstrated clear signature patterns for HCC. The results are interpretable, robust, and reproducible across diverse cohorts/populations with various disease etiologies, indicating the 5 DEGs are intrinsic variables that can describe the overall features of HCC at the genomic level. The analytical framework applied in this study may pave a new way for improving transcriptome profiling analysis of human cancers. [ABSTRACT FROM AUTHOR]

Competing risk analyses have been widely used for the analysis of in-hospital mortality in which hospital discharge is considered as a competing event. The competing risk model assumes that more than one cause of failure is possible, but there is only one outcome of interest and all others serve as competing events. However, hospital discharge and in-hospital death are two outcomes resulting from the same disease process and patients whose disease conditions were stabilized so that inpatient care was no longer needed were discharged. We therefore propose to use cure models, in which hospital discharge is treated as an observed "cure" of the disease. We consider both the mixture cure model and the promotion time cure model and extend the models to allow cure status to be known for those who were discharged from the hospital. An EM algorithm is developed for the mixture cure model. We also show that the competing risk model, which treats hospital discharge as a competing event, is equivalent to a promotion time cure model. Both cure models were examined in simulation studies and were applied to a recent cohort of COVID-19 in-hospital patients with diabetes. The promotion time model shows that statin use improved the overall survival; the mixture cure model shows that while statin use reduced the in-hospital mortality rate among the susceptible, it improved the cure probability only for older but not younger patients. Both cure models show that treatment was more beneficial among older patients. [ABSTRACT FROM AUTHOR]

In the context of competing risks data, the subdistribution hazard ratio has limited clinical interpretability to measure treatment effects. An alternative is the difference in restricted mean times lost (RMTL), which gives the mean time lost to a specific cause of failure between treatment groups. In non-randomized studies, the average causal effect is conventionally used for decision-making about treatment and public health policies. We show how the difference in RMTL can be estimated by contrasting the integrated cumulative incidence functions from a Fine-Gray model. We also show how the difference in RMTL can be estimated by using inverse probability of treatment weighting and contrasts between weighted non-parametric estimators of the area below the cumulative incidence. We use pseudo-observation approaches to estimate both component models and we integrate them into a doubly-robust estimator. We demonstrate that this estimator is consistent when either component is correctly specified. We conduct simulation studies to assess its finite-sample performance and demonstrate its inherited consistency property from its component models. We also examine the performance of this estimator under varying degrees of covariate overlap and under a model misspecification of nonlinearity. We apply the proposed method to assess biomarker-treatment interaction in subpopulations of the POPLAR and OAK randomized controlled trials of second-line therapy for advanced non-small-cell lung cancer. [ABSTRACT FROM AUTHOR]

In studies analyzing competing time-to-event outcomes, interest often lies in both estimating the effects of baseline covariates on the cause-specific hazards and predicting cumulative incidence functions. When missing values occur in these baseline covariates, they may be discarded as part of a complete-case analysis or multiply imputed. In the latter case, the imputations may be performed either compatibly with a substantive model pre-specified as a cause-specific Cox model [substantive model compatible fully conditional specification (SMC-FCS)], or approximately so [multivariate imputation by chained equations (MICE)]. In a large simulation study, we assessed the performance of these three different methods in terms of estimating cause-specific regression coefficients and predicting cumulative incidence functions. Concerning regression coefficients, results provide further support for use of SMC-FCS over MICE, particularly when covariate effects are large and the baseline hazards of the competing events are substantially different. Complete-case analysis also shows adequate performance in settings where missingness is not outcome dependent. With regard to cumulative incidence prediction, SMC-FCS and MICE are performed more similarly, as also evidenced in the illustrative analysis of competing outcomes following a hematopoietic stem cell transplantation. The findings are discussed alongside recommendations for practising statisticians. [ABSTRACT FROM AUTHOR]

We compare two multi-state modelling frameworks that can be used to represent dates of events following hospital admission for people infected during an epidemic. The methods are applied to data from people admitted to hospital with COVID-19, to estimate the probability of admission to intensive care unit, the probability of death in hospital for patients before and after intensive care unit admission, the lengths of stay in hospital, and how all these vary with age and gender. One modelling framework is based on defining transition-specific hazard functions for competing risks. A less commonly used framework defines partially-latent subpopulations who will experience each subsequent event, and uses a mixture model to estimate the probability that an individual will experience each event, and the distribution of the time to the event given that it occurs. We compare the advantages and disadvantages of these two frameworks, in the context of the COVID-19 example. The issues include the interpretation of the model parameters, the computational efficiency of estimating the quantities of interest, implementation in software and assessing goodness of fit. In the example, we find that some groups appear to be at very low risk of some events, in particular intensive care unit admission, and these are best represented by using 'cure-rate' models to define transition-specific hazards. We provide general-purpose software to implement all the models we describe in the flexsurv R package, which allows arbitrarily flexible distributions to be used to represent the cause-specific hazards or times to events. [ABSTRACT FROM AUTHOR]

In the opioid research, predicting the risk of overdose or other adverse outcomes from opioid prescription patterns can help health professionals identify high-risk individuals. Challenges may arise in modeling the exposure-time-response association if the intensity, duration, and timing of exposure vary among subjects, and if exposures have a cumulative or latency effect on the risk. Further challenges may arise when the data involve competing risks, where subjects may fail from one of multiple events and failure from one precludes the risk of experiencing others. In this study, we proposed a competing risks regression model via subdistribution hazards to directly estimate the association between longitudinal patterns of opioid exposure and cumulative incidence of opioid overdose. The model incorporated weighted cumulative effects of the exposure and used penalized splines in the partial likelihood equation to estimate the weights flexibly. The proposed model is able to distinguish different opioid prescription patterns even though these patterns have the same overall intensity during the study period. Performance of the model was evaluated through simulation. [ABSTRACT FROM AUTHOR]

Multi-state models provide an extension of the usual survival/event-history analysis setting. In the medical domain, multi-state models give the possibility of further investigating intermediate events such as relapse and remission. In this work, a further extension is proposed using relative survival, where mortality due to population causes (i.e. non-disease-related mortality) is evaluated. The objective is to split all mortality in disease and non-disease-related mortality, with and without intermediate events, in datasets where cause of death is not recorded or is uncertain. To this end, population mortality tables are integrated into the estimation process, while using the basic relative survival idea that the overall mortality hazard can be written as a sum of a population and an excess part. Hence, we propose an upgraded non-parametric approach to estimation, where population mortality is taken into account. Precise definitions and suitable estimators are given for both the transition hazards and probabilities. Variance estimating techniques and confidence intervals are introduced and the behaviour of the new method is investigated through simulations. The newly developed methodology is illustrated by the analysis of a cohort of patients followed after an allogeneic hematopoietic stem cell transplantation. The work has been implemented in the R package mstate. [ABSTRACT FROM AUTHOR]

Why do governments choose to fund pro-government militias (PGMs) if doing so could extend costly civil conflict? While PGMs are active in a majority of civil wars, their impact on conflict termination remains poorly understood. We argue that the choice to fund PGMs is a strategic one for states and part of their efforts to influence wartime dynamics and conflict termination. We hypothesize that PGMs' impact on conflict termination is conditional on whether they are government funded. Government-funded PGMs help states to ward off costly negotiations and encourage the rebellion's gradual dissolution. Using competing risks analyses on civil wars ending between 1981 and 2007, we find robust evidence that PGM funding affects conflict outcomes. [ABSTRACT FROM AUTHOR]

Competing risks models are attractive tools to analyze time-to-event data where several causes of an event are competing. However, a complexity may arise when, for instance, some subjects experience the event of interest but the causes are not known. Assuming that unknown causes of events are missing at random, we developed a novel constrained maximum penalized likelihood method for fitting semi-parametric cause-specific Cox regression models. Here, penalty functions were used to smooth the baseline hazards. An appealing feature of this approach is that all the relevant estimands in competing risks models are estimated including cause-specific hazard ratios, cause-specific baseline hazards, and cumulative incidence functions. Asymptotic results for these estimators were also developed, allowing for direct inferences. The proposed method was compared with some existing methods through a simulation study. A real data example was analyzed using the new method to evaluate the association of age at diagnosis with melanoma-death and non-melanoma-death in patients diagnosed with thin melanoma (tumour thickness ≤ 1.0 mm). An R function for our proposed method is currently available on GitHub and will be included in the R package "survivalMPL" at CRAN. [ABSTRACT FROM AUTHOR]

This study investigates the determinants of voluntary and involuntary head coach turnovers using a large dataset of some 6,500 coach-game observations from Major League Soccer over 2004–2019. The duration analysis results show that team performance related to expected playoff qualification and performance expectations matter for both types of separations. Moreover, the findings reveal that coach reputation decreases dismissal probabilities, while coach age increases quit rates. The results of this study will be of particular interest to Major League Soccer team owners and managers as well as for business management outside the sports industry. [ABSTRACT FROM AUTHOR]

Propensity score matching is widely used to determine the effects of treatments in observational studies. Competing risk survival data are common to medical research. However, there is a paucity of propensity score matching studies related to competing risk survival data with missing causes of failure. In this study, we provide guidelines for estimating the treatment effect on the cumulative incidence function when using propensity score matching on competing risk survival data with missing causes of failure. We examined the performances of different methods for imputing the data with missing causes. We then evaluated the gain from the missing cause imputation in an extensive simulation study and applied the proposed data imputation method to the data from a study on the risk of hepatocellular carcinoma in patients with chronic hepatitis B and chronic hepatitis C. [ABSTRACT FROM AUTHOR]

The assessment of prognostic markers is key to the improvement of therapeutic strategies for cancer patients. Some promising markers may fail to be applied in clinical practice, or some useless markers may be applied, because of misleading results ensuing from inadequate planning of the study and/or from an oversimplified statistical analysis. This commentary illustrates and discusses the main issues involved in planning an effective clinical study and the subsequent statistical analysis for the prognostic evaluation of a cancer marker. Another aim is to extend the most applied statistical models (ie, those using Kaplan-Meier and Cox) to enable the choice of the best-suited methods for study endpoints. Specifically, for tumor-centered endpoints like tumor recurrence, the issue of competing risks is highlighted. For markers measured on a continuous numerical scale, a loss of relevant prognostic information may occur by setting arbitrary cutoffs; thus, the methods to analyze the original scale are explained. Furthermore, because the P -value is not a sufficient criterion to assess the usefulness of a marker in clinical practice, measures for evaluating the ability of the marker to discriminate between "good" and "bad" prognoses are illustrated. Several tumor markers are considered both in human and veterinary medicine. Given the similarity between markers for human breast cancer and canine mammary cancer, an application of the statistical methods discussed within the article to a public dataset from human breast cancer patients is shown. [ABSTRACT FROM AUTHOR]

Background: No studies have assessed changes in employment survival in multiple sclerosis (MS) populations over recent decades, including the introduction of disease-modifying therapies (DMTs). Objectives: To evaluate factors associated with leaving employment due to MS; to assess whether the risk of leaving employment has changed over recent decades in Australia, stratified by MS phenotype. Methods: We included 1240 participants who were working before MS diagnosis. Information on employment status, reasons for leaving employment and year of leaving were collected. Data were analysed using competing risk survival analysis. Results: Males, progressive MS, lower education level and older age at diagnosis were associated with a higher sub-distribution hazard of leaving employment. Compared to the period before 2010, the sub-distribution hazard during 2010–2016 for relapsing-remitting multiple sclerosis (RRMS) was reduced by 43% (sub-distribution hazard ratio (sHR) 0.67, 95% confidence interval (CI): 0.50 to 0.90), while no significant reduction was seen for primary-progressive multiple sclerosis (PPMS) (sHR 1.25, 95% CI: 0.72 to 2.16) or secondary-progressive multiple sclerosis (SPMS) (sHR 1.37, 95% CI: 0.84 to 2.25). Conclusion: Males, people with progressive MS and those of lower education level were at higher risk of leaving employment. The differential changed risk of leaving employment between people with different MS phenotype after 2010 coincides with the increased usage of high-efficacy DMTs for RRMS. [ABSTRACT FROM AUTHOR]

Standard tests for the Cox model, such as the likelihood ratio test or the Wald test, do not perform well in situations, where the number of covariates is substantially higher than the number of observed events. This issue is perpetuated in competing risks settings, where the number of observed occurrences for each event type is usually rather small. Yet, appropriate testing methodology for competing risks survival analysis with few events per variable is missing. In this article, we show how to extend the global test for survival by Goeman et al. to competing risks and multistate models[Per journal style, abstracts should not have reference citations. Therefore, can you kindly delete this reference citation.]. Conducting detailed simulation studies, we show that both for type I error control and for power, the novel test outperforms the likelihood ratio test and the Wald test based on the cause-specific hazards model in settings where the number of events is small compared to the number of covariates. The benefit of the global tests for competing risks survival analysis and multistate models is further demonstrated in real data examples of cancer patients from the European Society for Blood and Marrow Transplantation. [ABSTRACT FROM AUTHOR]

Hospital readmission rate is a ubiquitous measure of efficiency and quality. Individuals with life-limiting illnesses account heavily for admissions but evaluation is complicated by high-mortality rates. We report a retrospective cohort study examining the association between palliative care (PC) and readmissions while controlling for postdischarge mortality with a competing risks approach. Eligible participants were adult inpatients admitted to an academic, safety-net medical center (2009-2015) with at least one diagnosis of cancer, heart failure, chronic obstructive pulmonary disease, liver failure, kidney failure, AIDS/HIV, and selected neurodegenerative conditions. PC was associated with reduced 30-, 60-, and 90-day readmissions (subhazard ratios = 0.57, 0.53, and 0.52, respectively [all p < .001]). Hospital PC is associated with a reduction in readmissions, and this is not explained by higher mortality among PC patients. Performance measures only counting those alive at a given end point may underestimate systematically the effects of treatments with a high-mortality rate. [ABSTRACT FROM AUTHOR]

The cause-specific cumulative incidence function quantifies the subject-specific disease risk with competing risk outcome. With longitudinally collected biomarker data, it is of interest to dynamically update the predicted cumulative incidence function by incorporating the most recent biomarker as well as the cumulating longitudinal history. Motivated by a longitudinal cohort study of chronic kidney disease, we propose a framework for dynamic prediction of end stage renal disease using multivariate longitudinal biomarkers, accounting for the competing risk of death. The proposed framework extends the local estimation-based landmark survival modeling to competing risks data, and implies that a distinct sub-distribution hazard regression model is defined at each biomarker measurement time. The model parameters, prediction horizon, longitudinal history and at-risk population are allowed to vary over the landmark time. When the measurement times of biomarkers are irregularly spaced, the predictor variable may not be observed at the time of prediction. Local polynomial is used to estimate the model parameters without explicitly imputing the predictor or modeling its longitudinal trajectory. The proposed model leads to simple interpretation of the regression coefficients and closed-form calculation of the predicted cumulative incidence function. The estimation and prediction can be implemented through standard statistical software with tractable computation. We conducted simulations to evaluate the performance of the estimation procedure and predictive accuracy. The methodology is illustrated with data from the African American Study of Kidney Disease and Hypertension. [ABSTRACT FROM AUTHOR]

Australia is currently undergoing significant social policy reform under the introduction of a personalized scheme for disability services: the National Disability Insurance Scheme (NDIS). This article explores the growing administrative burdens placed on disability providers operating under the new scheme, using an Australia-wide survey of the disability sector. The 2018 National Disability Services survey of the disability sector reveals that administrative burden is the most commented on challenge for providers. Moreover, providers linked this burden to questions concerning their financial sustainability and ability to continue to offer services within the NDIS. In this article, we explore the sources of these administrative burdens and their relationships with the institutional logics at play in the NDIS. In addition to documenting the impact of system change on the Australian disability service sector, this article raises questions regarding institutional hybridity within personalization schemes more broadly and whether they are a source of tension, innovation, or both. [ABSTRACT FROM AUTHOR]

Pseudo-values provide a method to perform regression analysis for complex quantities with right-censored data. A further complication, interval-censored data, appears when events such as dementia are studied in an epidemiological cohort. We propose an extension of the pseudo-value approach for interval-censored data based on a semi-parametric estimator computed using penalised likelihood and splines. This estimator takes interval-censoring and competing risks into account in an illness-death model. We apply the pseudo-value approach to three mean value parameters of interest in studies of dementia: the probability of staying alive and non-demented, the restricted mean survival time without dementia and the absolute risk of dementia. Simulation studies are conducted to examine properties of pseudo-values based on this semi-parametric estimator. The method is applied to the French cohort PAQUID, which included more than 3,000 non-demented subjects, followed for dementia for more than 25 years. [ABSTRACT FROM AUTHOR]

An accurate assessment of drug safety or effectiveness in pharmaco-epidemiology requires defining an etiologically correct time-varying exposure model, which specifies how previous drug use affects the hazard of the event of interest. An additional challenge is to account for the multitude of mutually exclusive events that may be associated with the use of a given drug. To simultaneously address both challenges, we develop, and validate in simulations, a new approach that combines flexible modeling of the cumulative effects of time-varying exposures with competing risks methodology to separate the effects of the same drug exposure on different outcomes. To account for the dosage, duration and timing of past exposures, we rely on a spline-based weighted cumulative exposure modeling. We also propose likelihood ratio tests to test if the cumulative effects of past exposure on the hazards of the competing events are the same or different. Simulation results indicate that the estimated event-specific weight functions are reasonably accurate, and that the proposed tests have acceptable type I error rate and power. In real-life application, the proposed method indicated that recent use of antihypertensive drugs may reduce the risk of stroke but has no effect on the hazard of coronary heart disease events. [ABSTRACT FROM AUTHOR]

We aim to close a methodological gap in analyzing durations of successive events that are subject to induced dependent censoring as well as competing-risk censoring. In the Bipolar Disorder Center for Pennsylvanians study, some patients who managed to recover from their symptomatic entry later developed a new depressive or manic episode. It is of great clinical interest to quantify the association between time to recovery and time to recurrence in patients with bipolar disorder. The estimation of the bivariate distribution of the gap times with independent censoring has been well studied. However, the existing methods cannot be applied to failure times that are censored by competing causes such as in the Bipolar Disorder Center for Pennsylvanians study. Bivariate cumulative incidence function has been used to describe the joint distribution of parallel event times that involve multiple causes. To the best of our knowledge, however, there is no method available for successive events with competing-risk censoring. Therefore, we extend the bivariate cumulative incidence function to successive events data, and propose non-parametric estimators of the bivariate cumulative incidence function and the related conditional cumulative incidence function. Moreover, an odds ratio measure is proposed to describe the cause-specific dependence, leading to the development of a formal test for independence of successive events. Simulation studies demonstrate that the estimators and tests perform well for realistic sample sizes, and our methods can be readily applied to the Bipolar Disorder Center for Pennsylvanians study. [ABSTRACT FROM AUTHOR]

Inferring processes or constructs from performance data is a major hallmark of cognitive psychometrics. Particularly, diffusion modeling of response times (RTs) from correct and erroneous responses using the Wiener distribution has become a popular measurement tool because it provides a set of psychologically interpretable parameters. However, an important precondition to identify all of these parameters is a sufficient number of RTs from erroneous responses. In the present article, we show by simulation that the parameters of the Wiener distribution can be recovered from tasks yielding very high or even perfect response accuracies using the shifted Wald distribution. Specifically, we argue that error RTs can be modeled as correct RTs that have undergone censoring by using techniques from parametric survival analysis. We illustrate our reasoning by fitting the Wiener and (censored) shifted Wald distribution to RTs from six participants who completed a Go/No-go task. In accordance with our simulations, diffusion modeling using the Wiener and the shifted Wald distribution yielded identical parameter estimates when the number of erroneous responses was predicted to be low. Moreover, the modeling of error RTs as censored correct RTs substantially improved the recovery of these diffusion parameters when premature trial timeout was introduced to increase the number of omission errors. Thus, the censored shifted Wald distribution provides a suitable means for diffusion modeling in situations when the Wiener distribution cannot be fitted without parametric constraints. [ABSTRACT FROM AUTHOR]

We propose a cause-specific quantile residual life regression where the cause-specific quantile residual life, defined as the inverse of the cumulative incidence function of the residual life distribution of a specific type of events of interest conditional on a fixed time point, is log-linear in observable covariates. The proposed test statistic for the effects of prognostic factors does not involve estimation of the improper probability density function of the cause-specific residual life distribution under competing risks. The asymptotic distribution of the test statistic is derived. Simulation studies are performed to assess the finite sample properties of the proposed estimating equation and the test statistic. The proposed method is illustrated with a real dataset from a clinical trial on breast cancer. [ABSTRACT FROM AUTHOR]

We examine the value of price commitment in a non-profit organization using individual-level purchases over a series of concert performances. To decide on a pricing policy, the performing arts organization must be able to accurately measure when each ticket will be sold and what type of audience will purchase the tickets for each performance. We use a competing hazards framework to model the timing of ticket purchases when customer segments differ in their valuations and arrival times. We show that the customer purchase likelihoods change based on the prices observed earlier in the season. Hence, price commitment can aid in improving sales, revenues, and customer visits. In particular, we show that price commitment to a decreasing monotone discount policy can improve the revenues in the range 2.1%-6.7% per concert. [ABSTRACT FROM AUTHOR]

Mortality rates in Markov models, as used in health economic studies, are often estimated from summary statistics that allow limited adjustment for confounders. If interventions are targeted at multiple diseases and/or risk factors, these mortality rates need to be combined in a single model. This requires them to be mutually adjusted to avoid ‘double counting’ of mortality. We present a mathematical modeling approach to describe the joint effect of mutually dependent risk factors and chronic diseases on mortality in a consistent manner. Most importantly, this approach explicitly allows the use of readily available external data sources. An additional advantage is that existing models can be smoothly expanded to encompass more diseases/risk factors. To illustrate the usefulness of this method and how it should be implemented, we present a health economic model that links risk factors for diseases to mortality from these diseases, and describe the causal chain running from these risk factors (e.g., obesity) through to the occurrence of disease (e.g., diabetes, CVD) and death. Our results suggest that these adjustment procedures may have a large impact on estimated mortality rates. An improper adjustment of the mortality rates could result in an underestimation of disease prevalence and, therefore, disease costs. [ABSTRACT FROM AUTHOR]

Competing risks arise in medical research when subjects are exposed to various types or causes of death. Data from large cohort studies usually exhibit subsets of regressors that are missing for some study subjects. Furthermore, such studies often give rise to censored data. In this article, a carefully formulated likelihood-based technique for the regression analysis of right-censored competing risks data when two of the covariates are discrete and partially missing is developed. The approach envisaged here comprises two models: one describes the covariate effects on both long-term incidence and conditional latencies for each cause of death, whilst the other deals with the observation process by which the covariates are missing. The former is formulated with a well-established mixture model and the latter is characterised by copula-based bivariate probability functions for both the missing covariates and the missing data mechanism. The resulting formulation lends itself to the empirical assessment of non-ignorability by performing sensitivity analyses using models with and without a non-ignorable component. The methods are illustrated on a 20-year follow-up involving a prostate cancer cohort from the National Cancer Institutes Surveillance, Epidemiology, and End Results program. [ABSTRACT FROM AUTHOR]

We propose a cost-effective sampling design and estimating procedure for validating personal risk models using right-censored cohort data. Validation involves using each subject's covariates, as ascertained at cohort entry, in a risk model (specified independently of the data) to assign him/her a probability of an adverse outcome within a future time period. Subjects are then grouped according to the magnitudes of their assigned risks, and within each group, the mean assigned risk is compared with the probability of outcome occurrence as estimated using the follow-up data. Such validation presents two complications. First, in the presence of right-censoring, estimating the probability of developing the outcomes before death requires competing risk analysis. Second, for rare outcomes, validation using the full cohort requires assembling covariates and assigning risks to thousands of subjects. This can be costly when some covariates involve analyzing biological specimens. A two-stage sampling design addresses this problem by assembling covariates and assigning risks only to those subjects most informative for estimating key parameters. We use this design to estimate the outcome probabilities needed to evaluate model performance and we provide theoretical and bootstrap estimates of their variances. We also describe how to choose two-stage designs with minimal efficiency loss for a parameter of interest when the quantities determining optimality are unknown at the time of design. We illustrate these methods by using subjects in the California Teachers Study to validate ovarian cancer risk models. We find that a design with optimal efficiency for one performance parameter need not be so for others, and trade-offs will be required. A two-stage design that samples all outcome-positive subjects and more outcome-negative than censored subjects will perform well in most circumstances. The methods are implemented in Risk Model Assessment Program, an R program freely available at http://med.stanford.edu/epidemiology/two-stage.html. [ABSTRACT FROM AUTHOR]

In lifetimes studies, the occurrence of an event (such as tumor detection or death) might be caused by one of many competing causes. Moreover, both the number of causes and the time-to-event associated with each cause are not usually observable. The number of causes can be zero, corresponding to a cure fraction. In this article, we propose a method of estimating the numerical characteristics of unobservable stages (such as initiation, promotion and progression) of carcinogenesis from data on tumor size at detection in the presence of latent competing causes. To this end, a general survival model for spontaneous carcinogenesis under a hybrid latent activation scheme has been developed to allow for a simple pattern of the dynamics of tumor growth. It is assumed that a tumor becomes detectable when its size attains some threshold level (proliferation of tumorais cells (or descendants) generated by the malignant cell), which is treated as a random variable. We assume the number of initiated cells and the number of malignant cells (competing causes) both to follow weighted Poisson distributions. The advantage of this model is that it incorporates into the analysis characteristics of the stage of tumor progression as well as the proportion of initiated cells that had been 'promoted' to the malignant ones and the proportion of malignant cells that die before tumor induction. The lifetimes corresponding to each competing cause are assumed to follow a Weibull distribution. Parameter estimation of the proposed model is discussed through the maximum likelihood estimation method. A simulation study has been carried out in order to examine the coverage probabilities of the confidence intervals. Finally, we illustrate the usefulness of the proposed model by applying it to a real data involving malignant melanoma. [ABSTRACT FROM AUTHOR]

We propose vertical modelling as a natural approach to the problem of analysis of competing risks data when failure types are missing for some individuals. Under a natural missing-at-random assumption for these missing failure types, we use the observed data likelihood to estimate its parameters and show that the all-cause hazard and the relative hazards appearing in vertical modelling are indeed key quantities of this likelihood. This fact has practical implications in that it suggests vertical modelling as a simple and attractive method of analysis in competing risks with missing causes of failure; all individuals are used in estimating the all-cause hazard and only those with non-missing cause of failure for relative hazards. The relative hazards also appear in a multiple imputation approach to the same problem proposed by Lu and Tsiatis and in the EM algorithm. We compare the vertical modelling approach with the method of Goetghebeur and Ryan for a breast cancer data set, highlighting the different aspects they contribute to the data analysis. [ABSTRACT FROM AUTHOR]

Background Survival after a stroke is lower for Indigenous than other stroke patients in Australia. It is not known whether recurrence is more common for Indigenous patients, or whether their higher prevalence of comorbidity affects their lower survival. Aims This study aimed to investigate the stroke recurrence and role of comorbidities in adverse stroke outcomes (recurrence and death) for Indigenous compared with other Australians. Methods A retrospective cohort study of first hospitalization for stroke ( n = 2105) recorded in Northern Territory hospital inpatient data between 1996 and 2011 was conducted. For the multivariable analyses of adverse outcomes, logistic regression was used for case fatality and competing risk analysis for recurrent stroke and long-term death. Comorbidities (identified from inpatient diagnosis data) were analyzed using the Charlson Comorbidity Index (modified for stroke outcomes). Results Prevalence of comorbidities, case fatality, incidence of re-hospitalization for recurrent stroke, and long-term death rate were higher for Indigenous than non-Indigenous stroke patients. Adjustment for comorbidity in multivariable analyses considerably reduced Indigenous patients' excess risk for case fatality (odds ratio: 1·25, 0·88-1·78) and long-term death (standard hazard ratio: 1·27, 1·01-1·61) (but not recurrence), implying that their excess risk of death was in part due to higher comorbidity prevalence. Conclusion Indigenous stroke patients have higher prevalence of comorbidities than non-Indigenous stroke patients, which explained part of the disparity in both case fatality and long-term survival but did not explain the disparity in stroke recurrence at all. [ABSTRACT FROM AUTHOR]

Although member states are obliged to transpose directives into domestic law in a conformable manner and receive considerable time for their transposition activities, we identify three levels of transposition outcomes for EU directives: conformable, partially conformable and non-conformable. Compared with existing transposition models, which do not distinguish between different transposition outcomes, we examine the factors influencing each transposition process by means of a competing risk analysis. We find that preference-related factors, in particular the disagreement of a member state and the Commission regarding a directive’s outcome, play a much more strategic role than has to date acknowledged in the transposition literature. Whereas disagreement of a member state delays conformable transposition, it speeds up non-conformable transposition. Disagreement of the Commission only prolongs the transposition process. We therefore conclude that a stronger focus on an effective sanctioning mechanism is warranted for safeguarding compliance with directives. [ABSTRACT FROM PUBLISHER]

Advancements in technology coupled with the perception of diminished public tolerance for casualties have increased the prominence and popularity of aerial bombing as a coercive tool, particularly for the United States. Despite interest from policy makers and support from the public, there has been little scholarly assessment of these coercive episodes. How successful are air campaigns, and what are the prospects for the future? In this article, I focus on the factors that cause bombing campaigns to end. To explore what leads to campaign termination, I highlight the theoretical significance of the political characteristics of both the attacker and the adversary. Using competing risks duration analysis to examine both failed and successful bombing campaigns from 1917 through 1999, I find that a democratic government on either side of the coercive equation increases the likelihood of campaigns ending. [ABSTRACT FROM AUTHOR]

Our article was merely pointing out the shortcomings of Kaplan-Meier analysis and the importance of competing events when comparing results. It is appreciated that [1] suggest the use of net failure (Kaplan-Meier) when describing failure rates or selecting the implant with the greatest longevity. 3 Boeckstyns MEH, Merser S, Cool P. Reporting implant survival. [Extracted from the article]