Time-dependent covariates in the proportional subdistribution hazards model for competing risks.

Separate Cox analyses of all cause-specific hazards are the standard technique of choice to study the effect of a covariate in competing risks, but a synopsis of these results in terms of cumulative event probabilities is challenging. This difficulty has led to the development of the proportional subdistribution hazards model. If the covariate is known at baseline, the model allows for a summarizing assessment in terms of the cumulative incidence function. black Mathematically, the model also allows for including random time-dependent covariates, but practical implementation has remained unclear due to a certain risk set peculiarity. We use the intimate relationship of discrete covariates and multistate models to naturally treat time-dependent covariates within the subdistribution hazards framework. The methodology then straightforwardly translates to real-valued time-dependent covariates. As with classical survival analysis, including time-dependent covariates does not result in a model for probability functions anymore. Nevertheless, the proposed methodology provides a useful synthesis of separate cause-specific hazards analyses. We illustrate this with hospital infection data, where time-dependent covariates and competing risks are essential to the subject research question.

[1]  Nils Lid Hjort,et al.  On inference in parametric survival data models , 1992 .

[2]  M. Schumacher,et al.  Use of Multistate Models to Assess Prolongation of Intensive Care Unit Stay Due to Nosocomial Infection , 2006, Infection Control & Hospital Epidemiology.

[3]  S Chevret,et al.  A Note on Including Time‐dependent Covariate in Regression Model for Competing Risks Data , 2005, Biometrical journal. Biometrische Zeitschrift.

[4]  N. Keiding,et al.  Multi-state models for event history analysis , 2002, Statistical methods in medical research.

[5]  Somnath Datta,et al.  Validity of the Aalen–Johansen estimators of stage occupation probabilities and Nelson–Aalen estimators of integrated transition hazards for non-Markov models , 2001 .

[6]  R. Gray.  A Class of $K$-Sample Tests for Comparing the Cumulative Incidence of a Competing Risk , 1988 .

[7]  R. Gray.  Modeling Survival Data: Extending the Cox Model , 2002 .

[8]  J. Kalbfleisch,et al.  The Statistical Analysis of Failure Time Data , 1980 .

[9]  E. Martínez,et al.  Initial risk class and length of hospital stay in community-acquired pneumonia. , 2001, The European respiratory journal.

[10]  Dankmar Böhning,et al.  A comparison of three different models for estimating relative risk in meta‐analysis of clinical trials under unobserved heterogeneity , 2007, Statistics in medicine.

[11]  Martin Schumacher,et al.  Misspecified regression model for the subdistribution hazard of a competing risk by Latouche A, Boisson V, Chevret S and Porcher R. Statistics in Medicine 2006; DOI: 10.2002/sim.2600 , 2007, Statistics in medicine.

[12]  H Putter,et al.  Tutorial in biostatistics: competing risks and multi‐state models , 2007, Statistics in medicine.

[13]  J. Fine,et al.  Regression modeling of competing crude failure probabilities. , 2001, Biostatistics.

[14]  D.,et al.  Regression Models and Life-Tables , 2022 .

[15]  S Chevret,et al.  Misspecified regression model for the subdistribution hazard of a competing risk , 2007, Statistics in medicine.

[16]  References , 1971 .

[17]  Nicholas P. Jewell,et al.  AIDS epidemiology : methodological issues , 1993 .

[18]  Qi Jiang,et al.  Illustrating the Impact of a Time-Varying Covariate With an Extended Kaplan-Meier Estimator , 2005 .

[19]  John D. Kalbfleisch,et al.  The Statistical Analysis of Failure Data , 1986, IEEE Transactions on Reliability.

[20]  J. Klein,et al.  Statistical Models Based On Counting Process , 1994 .

[21]  Clive Osmond,et al.  Modern Statistical Methods in Chronic Disease Epidemiology. , 1988 .

[22]  J. de Irala-Estévez,et al.  Comparison of different methodological approaches to identify risk factors of nosocomial infection in intensive care units , 2001, Intensive Care Medicine.

[23]  Robert Gray,et al.  A Proportional Hazards Model for the Subdistribution of a Competing Risk , 1999 .

[24]  R. G. Cornell,et al.  Modern Statistical Methods in Chronic Disease Epidemiology. , 1988 .

[25]  Rupert G. Miller,et al.  Survival Analysis , 2022, The SAGE Encyclopedia of Research Design.

[26]  Mei-Jie Zhang,et al.  Direct Modelling of Regression Effects for Transition Probabilities in Multistate Models , 2007 .

[27]  J. Klein,et al.  Survival Analysis: Techniques for Censored and Truncated Data , 1997 .

[28]  R. Wilson.  Bacteria, antibiotics and COPD. , 2001, The European respiratory journal.

[29]  J. Fine,et al.  Parametric regression on cumulative incidence function. , 2007, Biostatistics.

[30]  Jason P. Fine,et al.  Direct parametric inference for the cumulative incidence function , 2006 .

[31]  John D. Kalbfleisch,et al.  Misspecified proportional hazard models , 1986 .

[32]  Richard D. Gill,et al.  Understanding Cox's regression model: a martingale approach : (preprint) , 1984 .

[33]  John P Klein,et al.  Regression Modeling of Competing Risks Data Based on Pseudovalues of the Cumulative Incidence Function , 2005, Biometrics.

[34]  Carl van Walraven,et al.  Time-dependent bias was common in survival analyses published in leading clinical journals. , 2004, Journal of clinical epidemiology.

[35]  J. Robins,et al.  Recovery of Information and Adjustment for Dependent Censoring Using Surrogate Markers , 1992 .

[36]  Sue E. Estroff,et al.  "Letter to the editor": Comment. , 1984 .

[37]  Aris Perperoglou,et al.  Book Review: Survival analysis, techniques for censored and truncated data, 2nd edition , 2005 .

[38]  Jens Perch Nielsen,et al.  A framework for consistent prediction rules based on markers , 1993 .