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Regression methodology has been well developed for competing risks data with continuous event times, both for the cause-specific hazard and cumulative incidence functions. However, in many applications, including those from the Surveillance, Epidemiology, and End Results (SEER) program of the National Cancer Institute, the event times may be observed discretely. Naive application of continuous time regression methods to such data is not appropriate. We propose maximum likelihood inferences for estimation of model parameters for the discrete time cause-specific hazard functions, develop predictions for the associated cumulative incidence functions, and derive consistent variance estimators for the predicted cumulative incidence functions. The methods are readily implemented using standard software for generalized estimating equations, where models for different causes may be fitted separately. For the SEER data, it may be desirable to model different event types on different time scales and the methods are generalized to accommodate such scenarios, extending earlier work on continuous time data. Simulation studies demonstrate that the methods perform well in realistic set-ups. The methodology is illustrated with stage III colon cancer data from SEER.

The present paper discusses modeling and analysis of recurrent event data with competing risks. We propose non parametric estimation of cumulative incidence functions of recurrent event competing risks model. Asymptotic properties of the proposed estimators are established. Simulation procedures are carried out to asses the finite sample properties of the proposed estimators. The proposed method is applied to a real-life data.

This paper studies the Cox model with time-varying coefficients for cause-specific hazard functions when the causes of failure are subject to missingness. Inverse probability weighted and augmented inverse probability weighted estimators are investigated. The latter is considered as a two-stage estimator by directly utilizing the inverse probability weighted estimator and through modeling available auxiliary variables to improve efficiency. The asymptotic properties of the two estimators are investigated. Hypothesis testing procedures are developed to test the null hypotheses that the covariate effects are zero and that the covariate effects are constant. We conduct simulation studies to examine the finite sample properties of the proposed estimation and hypothesis testing procedures under various settings of the auxiliary variables and the percentages of the failure causes that are missing. These simulation results demonstrate that the augmented inverse probability weighted estimators are more efficient than the inverse probability weighted estimators and that the proposed testing procedures have the expected satisfactory results in sizes and powers. The proposed methods are illustrated using the Mashi clinical trial data for investigating the effect of randomization to formula-feeding versus breastfeeding plus extended infant zidovudine prophylaxis on death due to mother-to-child HIV transmission in Botswana.

In this paper we extend the bivariate hazard ratio to multivariate competing risks data and show that it is equivalent to the cause-specific cross hazard ratio. Two approaches are proposed to estimate these two equivalent association measures. One extends the plug-in estimator, and the other adapts the pseudo-likelihood estimator for bivariate survival data to multivariate competing risks data. The asymptotic properties of the extended estimators are established by using empirical processes techniques. The extended plug-in and pseudo-likelihood estimators have comparable performance with the existing U-statistic when the data have no tied events. However, in many applications, there are tied events in which all the three estimators are found to produce biased results. To our best knowledge, we are not aware of any association analysis for multivariate competing risks data that has considered tied events. Hence we propose a modified U-statistic to specifically handle tied observations. The modified U-statistic clearly outperforms the other estimators when there are rounding errors. All methods are applied to the Cache County Study to examine mother–child and sibship associations in dementia among this aging population, where the event times are rounded to the nearest integers. The modified U performs consistently with our simulation results and provides more reliable results in the presence of tied events.

Cause-specific hazard functions are employed to analyze a semi-Markov model which could be used to describe data arising from clinical trials or certain types of observational studies. The use of these hazard functions to fit a set of data arising from N possibly incomplete case histories is shown to have several notable advantages over the approach adopted by Lagakos, Sommer, and Zelen (1978). /// L'auteur suggère l'emploi de fonctions associées aux causes spécifiques de risque dans le but d'analyser un modèle semi-Markovien servant à décrire des données provenant de tests ou d'observations cliniques. Il démontre comment l'utilisation de ces fonctions peut servir à analyser les données issues de N histoires cliniques possiblement incomplètes. Cette approche comporte plusieurs avantages, comparativement à celle favorisée par Lagakos, Sommer et Zelen (1978).

Cox's (1972) proportional hazards model is applied to a prospective study of infection in aplastic anaemia and acute leukaemia patients following bone marrow transplantation. The usefulness of time-dependent covariates and cause-specific hazard functions is highlighted.

Introduction Tuberculosis (TB) remains the most common opportunistic infection and leading cause of death among individuals living with HIV/AIDS in Ethiopia. Its significant impact on morbidity and mortality underscores the crucial link between these two diseases. While the advent of antiretroviral therapy (ART) has led to a dramatic decline in mortality rates among HIV/AIDS patients, TB continues to pose a substantial threat. This study aims to estimate the probability of death due to TB among HIV/AIDS patients on ART, considering the presence of various competing risks, including diarrhea, other infections, and unknown/unspecified causes. Also we have assessed the effects of prognostic factors on HIV/AIDS cause specific deaths, compared with the death from other competing risks, and exploring leading cause of death among HIV/AIDS patients on Antiretroviral Therapy. Methods Data from a retrospective research examining the effectiveness of antiretroviral therapy (ART) in Ethiopia were used in this investigation. The data came from medical records of patients who were part of the national ART program. A total of 39,590 records were gathered between October 2019 and March 2020 from all regions of Ethiopia as well as the administration cities of Addis Ababa and Dire Dawa. The study facilities were grouped using a multi-stage sample technique and simple random selection was used to select health facility and a person record from medical records. In the presence of the competing causes of death, Cause specific hazard, subdistribution hazard model and flexible parametric proportional hazard model have been used to assess the effect of covariates on the risk of death, with the cmprisk package in R4.3.2 software. Results Out of the total 1212 deaths, 542(44.7%) died competing with other opportunistic infection (TE-Esophageal Candidiasis, TO-oral, CT-CNS Toxoplasmosis, CM-Crypotococcal Meningitis…), 421 (34.7%) died due to tuberculosis and the remaining death were unknown/Not specified infection 222(18.3%) and diarrhea 27(2.2%). Rates of mortality caused by tuberculosis, competing with other opportunistic infection, diarrhea and unknown/Not specified were 3.5, 4.5, 0.2 and 1.8 per 1000 person-months, respectively. Having a higher CD4 count at diagnosis, responding to combination antiretroviral treatment (cART) six months after start, and having prophylactic treatment for pneumocystis pneumonia (PCP) decreased the risk of tuberculosis, other opportunistic infections, and unidentified and diarrheal causes of death. However, older age, late HIV.AIDS diagnosis, and the last HIV/AIDS WHO clinical stages increased the hazard of tuberculosis and other opportunistic disease mortality. Additionally, male gender, older age and last HIV clinical stages increased the mortality HIV/AIDS patients. Conclusion The findings of this study demonstrated that TB, an opportunistic infection, was the primary cause of death in HIV/AIDS patients, despite the presence of several competing risks, such as diarrhea, other infections, and an undetermined or unclear cause. It's important to use effective techniques to quickly detect those who have HIV or AIDS and provide them with care and treatment to increase their chances of surviving.

In this article we study a joint model for longitudinal measurements and competing risks survival data. Our joint model provides a flexible approach to handle possible nonignorable missing data in the longitudinal measurements due to dropout. It is also an extension of previous joint models with a single failure type, offering a possible way to model informatively censored events as a competing risk. Our model consists of a linear mixed effects submodel for the longitudinal outcome and a proportional cause-specific hazards frailty submodel (Prentice et al., 1978, Biometrics 34, 541-554) for the competing risks survival data, linked together by some latent random effects. We propose to obtain the maximum likelihood estimates of the parameters by an expectation maximization (EM) algorithm and estimate their standard errors using a profile likelihood method. The developed method works well in our simulation studies and is applied to a clinical trial for the scleroderma lung disease. /// Dans ce papier, nous étudions un modèle conjoint pour des mesures longitudinales et des données de survie à risques compétitifs. Notre modèle conjoint fournit une approche souple pour prendre en compte les données manquantes possiblement non ignorables dans les mesures longitudinales dues aux sorties d'étude. Il s'agit aussi d'une extension des modèles conjoints précédents avec un seul type d'événements, offrant une voie possible pour modéliser les événements censurés informativement comme un risque compétitif. Notre modèle consiste en un sous-modèle linéaire à effets mixtes pour le critère longitudinal et un sous-modèle de fragilité à risques proportionnels cause spécifique (Prentice et al., 1978, Biometrics 34, 541-554) pour les données de survie à risques compétitifs, liés l'un à l'autre par des effets aléatoires latents. Nous proposons d'obtenir les estimations du maximum de vraisemblance des paramètres par un algorithme EM et d'estimer leurs écartstypes en utilisant une méthode de vraisemblance profilée. La méthode développée fonctionne bien dans nos études de simulation et est appliquée à un essai clinique sur les atteintes pulmonaires de la sclérodermie.

Background Multi-state models are complex stochastic models which focus on pathways defined by the temporal and sequential occurrence of numerous events of interest. In particular, the so-called illness-death models are especially useful for studying probabilities associated to diseases whose occurrence competes with other possible diseases, health conditions or death. They can be seen as a generalization of the competing risks models, which are widely used to estimate disease-incidences among populations with a high risk of death, such as elderly or cancer patients. The main advantage of the aforementioned illness-death models is that they allow the treatment of scenarios with non-terminal competing events that may occur sequentially, which competing risks models fail to do. Methods We propose an illness-death model using Cox proportional hazards models with Weibull baseline hazard functions, and applied the model to a study of recurrent hip fracture. Data came from the PREV2FO cohort and included 34491 patients aged 65 years and older who were discharged alive after a hospitalization due to an osteoporotic hip fracture between 2008-2015. We used a Bayesian approach to approximate the posterior distribution of each parameter of the model, and thus cumulative incidences and transition probabilities. We also compared these results with a competing risks specification. Results Posterior transition probabilities showed higher probabilities of death for men and increasing with age. Women were more likely to refracture as well as less likely to die after it. Free-event time was shown to reduce the probability of death. Estimations from the illness-death and the competing risks models were identical for those common transitions although the illness-death model provided additional information from the transition from refracture to death. Conclusions We illustrated how multi-state models, in particular illness-death models, may be especially useful when dealing with survival scenarios which include multiple events, with competing diseases or when death is an unavoidable event to consider. Illness-death models via transition probabilities provide additional information of transitions from non-terminal health conditions to absorbing states such as death, what implies a deeper understanding of the real-world problem involved compared to competing risks models.

Background Several studies have shown positive associations between higher WBC count and deaths from all-causes, CHD, stroke and cancer among occidental populations or developed countries of Asia. No study on the association of WBC count with all-cause and cause-specific mortality in Chinese populations was reported. We studied this using prospective data from a large Chinese cohort. Methods We used prospective data from the Guangzhou Biobank Cohort Study (GBCS), a total of 29,925 participants in present study. A Cox proportional hazards regression model was used to estimate the hazard ratios (HR) and 95% confidence interval (CI). Results The hazard ratios (HR) for all-cause, CHD, and respiratory disease mortality for the highest decile of WBC count (women > 8.2 × 10 9 /L; men > 8.8 × 10 9 /L) was 1.83 (95% confidence interval (CI) 1.54, 2.17), 3.02 (95% CI 1.84, 4.98) and 2.52 (95% CI 1.49, 4.27), respectively, after adjusting for multiple potential confounders. The associations were similar when deaths during the first 2 years of follow-up were excluded. After further adjusting for pulmonary function, the highest decile of WBC count was associated with 90% higher risk of respiratory disease mortality (HR 1.90, 95% CI 1.08, 3.33). No evidence for an association between higher WBC count and cancer mortality was found. Sub-type analysis showed that only granulocyte count remained significantly predictive of all-cause, CHD, and respiratory disease mortality. Conclusions Elevated WBC, specifically granulocyte, count was associated with all-cause, CHD and respiratory mortality in southern Chinese. Further investigation is warranted to clarify whether decreasing inflammation would attenuate WBC count associated mortality.