Subdistribution hazard models for competing risks in discrete time

Biostatistics ◽  
2018 ◽  
Vol 21 (3) ◽  
pp. 449-466 ◽  
Author(s):  
Moritz Berger ◽  
Matthias Schmid ◽  
Thomas Welchowski ◽  
Steffen Schmitz-Valckenberg ◽  
Jan Beyersmann
Keyword(s):  
Competing Risks ◽  
Discrete Time ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Model Parameters ◽  
Subdistribution Hazard ◽  
Ml Estimation ◽  
Modeling Approach ◽  
Hazards Model ◽  
Event Times

Summary A popular modeling approach for competing risks analysis in longitudinal studies is the proportional subdistribution hazards model by Fine and Gray (1999. A proportional hazards model for the subdistribution of a competing risk. Journal of the American Statistical Association94, 496–509). This model is widely used for the analysis of continuous event times in clinical and epidemiological studies. However, it does not apply when event times are measured on a discrete time scale, which is a likely scenario when events occur between pairs of consecutive points in time (e.g., between two follow-up visits of an epidemiological study) and when the exact lengths of the continuous time spans are not known. To adapt the Fine and Gray approach to this situation, we propose a technique for modeling subdistribution hazards in discrete time. Our method, which results in consistent and asymptotically normal estimators of the model parameters, is based on a weighted ML estimation scheme for binary regression. We illustrate the modeling approach by an analysis of nosocomial pneumonia in patients treated in hospitals.

scholarly journals Competing risks’ analysis in cardiovascular disease epidemiology; – Τhe case of ATTICA study (2002-2012)

2020 ◽  
pp. 19-25
Author(s):  
Thomas Tsiampalis ◽  
Demosthenes Panagiotakos
Keyword(s):  
Cardiovascular Disease ◽  
Competing Risks ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Cox Model ◽  
Survival Function ◽  
Gray Model ◽  
Disease Epidemiology ◽  
Hazards Model ◽  
One To One

Background: In studies of all-cause mortality, a one-to-one relation connects the hazard with the survival and as a consequence the regression models which focus on the hazard, such as the proportional hazards model, immediately dictate how the covariates relate to the survival function, as well. However, these two concepts and their one-to-one relation are totally different in the context of competing risks, where the terms of cause-specific hazard and cumulative incidence function appear. Objective: The aim of the present work was to present two of the most popular methods (cause-specific hazard model and Fine & Gray model) through an application on cardiovascular disease epidemiology (CVD), as well as, to narratively review more recent publications, based on either the frequentist, or the Bayesian approach to inference. Methods: A narrative review of the most widely used methods in the competing risks setting was conducted, extended to more recent publications. For the application, our interest lied in modeling the risk of Coronary Heart Disease in the presence of vascular stroke, by using the cause-specific hazard and the Fine & Gray models, two of most commonly encountered approaches. Results-Conclusions: After the implementation of these two approaches in the context of competing risks in CVD epidemiology, it is noted that while the use of the Fine & Gray model includes information about the existence of a competing risk, the interpretation of the results is not as easy as in the case of the cause-specific risk Cox model.

scholarly journals A competing risks model with time‐varying heterogeneity and simultaneous failure

2020 ◽  
Vol 11 (2) ◽  
pp. 535-577 ◽  
Author(s):  
Ruixuan Liu
Keyword(s):  
Competing Risks ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Estimation Procedure ◽  
Time Varying ◽  
Competing Risks Model ◽  
Hazards Model ◽  
Competing Risks Data ◽  
Passage Times ◽  
Lévy Subordinators

This paper proposes a new bivariate competing risks model in which both durations are the first passage times of dependent Lévy subordinators with exponential thresholds and multiplicative covariates effects. Our specification extends the mixed proportional hazards model, as it allows for the time‐varying heterogeneity represented by the unobservable Lévy processes and it generates the simultaneous termination of both durations with positive probability. We obtain nonparametric identification of all model primitives given competing risks data. A flexible semiparametric estimation procedure is provided and illustrated through the analysis of a real dataset.

A comparison of a linear and proportional hazards approach to analyse discrete longevity data in dairy cows

2000 ◽  
Vol 70 (2) ◽  
pp. 197-206 ◽  
Author(s):  
R. Lubbers ◽  
S. Brotherstone ◽  
V.P. Ducrocq ◽  
P.M. Visscher
Keyword(s):  
Discrete Time ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Weibull Model ◽  
Logarithmic Scale ◽  
Data Set ◽  
Breeding Values ◽  
Hazards Model ◽  
Estimated Breeding Values ◽  
The Uk

AbstractThe objective of this study was to compare two methods for analysis of longevity in dairy cattle. The first method, currently used for routine genetic evaluation in the UK, uses a linear model to analyse lifespan, i.e. the number of lactations a cow has survived or is expected to survive. The second method was based on the concept of proportional hazard, i.e. modelling the conditional survival probability of a cow as a function of time. Comparisons were based on estimated heritabilities, ranking of estimated breeding values of sires, estimated effects of covariates used in the final models, and the distribution of residuals. The same data set, 21497 observations on the number of lactations cows had survived, was used for both analyses, even in the presence of censored observations. Cows in the data were progeny of 487 sires. Heritability estimates for lifespan or survival were approximately 0·06 for both methods, using the definition of heritability on a logarithmic scale for the proportional hazards model. Correlations between breeding values for sires were high, with absolute values ranging from 0·93 to 0·98, depending on the model fitted. It was concluded that it may be justified to use the standard Weibull model even for discrete time measures such as the number of completed lactations, but that more research is needed in the area of discrete time variates.

scholarly journals Reduced rank proportional hazards model for competing risks

Biostatistics ◽  
2005 ◽  
Vol 6 (3) ◽  
pp. 465-478 ◽  
Author(s):  
M. Fiocco ◽  
H. Putter ◽  
J. C. van Houwelingen
Keyword(s):  
Competing Risks ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Reduced Rank ◽  
Hazards Model

Analysing multicentre competing risks data with a mixed proportional hazards model for the subdistribution

2006 ◽  
Vol 25 (24) ◽  
pp. 4267-4278 ◽  
Author(s):  
Sandrine Katsahian ◽  
Matthieu Resche-Rigon ◽  
Sylvie Chevret ◽  
Raphaël Porcher
Keyword(s):  
Competing Risks ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Hazards Model ◽  
Competing Risks Data ◽  
Mixed Proportional Hazards

scholarly journals Competing Risks Copula Models for Unemployment Duration: An Application to a German Hartz Reform

2017 ◽  
Vol 6 (1) ◽  
Author(s):  
Simon M.S. Lo ◽  
Gesine Stephan ◽  
Ralf A. Wilke
Keyword(s):  
Competing Risks ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Cox Proportional Hazards ◽  
Cox Proportional Hazards Model ◽  
Unemployment Duration ◽  
Copula Models ◽  
Covariate Effects ◽  
Hazards Model ◽  
Special Cases

AbstractThe copula graphic estimator (CGE) for competing risks models has received little attention in empirical research, despite having been developed into a comprehensive research method. In this paper, we bridge the gap between theoretical developments and applied research by considering a general class of competing risks copula models, which nests popular models such as the Cox proportional hazards model, the semiparametric multivariate mixed proportional hazards model (MMPHM), and the CGE as special cases. Analyzing the effects of a German Hartz reform on unemployment duration, we illustrate that the CGE imposes fewer restrictions on partial covariate effects than standard methods do. Differences are less evident when a more flexible difference-in-differences estimator is applied. It is also found that the MMPHM estimates react more strongly to the choice of the copula than the CGE in terms of the shape of the treatment effect function over time. Thus, the MMPHM produces less robust results in our application.

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