A competing risks approach for nonparametric estimation of transition probabilities in a non-Markov illness-death model

Competing risks model time to first event and type of first event. An example from hospital epidemiology is the incidence of hospital-acquired infection, which has to account for hospital discharge of non-infected patients as a competing risk. An illness-death model would allow to further study hospital outcomes of infected patients. Such a model typically relies on a Markov assumption. However, it is conceivable that the future course of an infected patient does not only depend on the time since hospital admission and current infection status but also on the time since infection. We demonstrate how a modified competing risks model can be used for nonparametric estimation of transition probabilities when the Markov assumption is violated.

[1]  Stephan Harbarth,et al.  The Importance of Good Data, Analysis, and Interpretation for Showing the Economics of Reducing Healthcare-Associated Infection , 2011, Infection Control & Hospital Epidemiology.

[2]  Martin Schumacher,et al.  Incidence densities in a competing events analysis. , 2010, American journal of epidemiology.

[3]  D. Dabrowska.  Multivariate Survival Analysis , 2005 .

[4]  Jason P. Fine,et al.  On semi-competing risks data , 2001 .

[5]  Anatoly Lisnianski,et al.  Recent Advances in System Reliability , 2012 .

[6]  Martin Schumacher,et al.  Estimating summary functionals in multistate models with an application to hospital infection data , 2011, Comput. Stat..

[7]  J Beyersmann,et al.  Multistate modelling to estimate the excess length of stay associated with meticillin-resistant Staphylococcus aureus colonisation and infection in surgical patients. , 2011, The Journal of hospital infection.

[8]  Mark J van der Laan,et al.  Locally Efficient Estimation With Bivariate Right-Censored Data , 2006 .

[9]  James M. Robins,et al.  Unified Methods for Censored Longitudinal Data and Causality , 2003 .

[10]  R. Prentice,et al.  Nonparametric Estimation of the Bivariate Survivor Function , 2019, The Statistical Analysis of Multivariate Failure Time Data.

[11]  Martin Schumacher,et al.  Application of multistate models in hospital epidemiology: Advances and challenges , 2011, Biometrical journal. Biometrische Zeitschrift.

[12]  Somnath Datta,et al.  Nonparametric Estimation of Marginal Temporal Functionals in a Multi-State Model , 2012 .

[13]  Niels Keiding,et al.  Independent Delayed Entry , 1992 .

[14]  Martin Schumacher,et al.  Competing Risks and Multistate Models with R , 2011 .

[15]  G A Satten,et al.  Nonparametric Estimation for the Three‐Stage Irreversible Illness–Death Model , 2000, Biometrics.

[16]  Zhiliang Ying,et al.  A simple nonparametric estimator of the bivariate survival function under univariate censoring , 1993 .

[17]  C. Umscheid,et al.  Estimating the Proportion of Healthcare-Associated Infections That Are Reasonably Preventable and the Related Mortality and Costs , 2011, Infection Control & Hospital Epidemiology.

[18]  M. Pepe,et al.  A qualifier Q for the survival function to describe the prevalence of a transient condition. , 1991, Statistics in medicine.

[19]  Related Topics,et al.  Survival analysis : state of the art , 1992 .

[20]  Thomas M Braun,et al.  Comparing the small sample performance of several variance estimators under competing risks , 2007, Statistics in medicine.

[21]  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 .

[22]  Winfried Stute,et al.  Consistent estimation under random censorship when covariables are present , 1993 .

[23]  Wei-Yann Tsai,et al.  A note on nonparametric estimators of the bivariate survival function under univariate censoring , 1998 .

[24]  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.

[25]  G. Satten,et al.  Estimation of Integrated Transition Hazards and Stage Occupation Probabilities for Non‐Markov Systems Under Dependent Censoring , 2002, Biometrics.

[26]  Niels Keiding,et al.  Statistical Models Based on Counting Processes , 1993 .

[27]  Odd O. Aalen,et al.  Estimating stage occupation probabilities in non-Markov models , 2007, Lifetime data analysis.

[28]  Ren Johansen.  An Empirical Transition Matrix for Non-homogeneous Markov Chains Based on Censored Observations , 1978 .

[29]  David V Glidden,et al.  Robust Inference for Event Probabilities with Non‐Markov Event Data , 2002, Biometrics.

[30]  A. Azzalini.  A class of distributions which includes the normal ones , 1985 .

[31]  Carmen Cadarso-Suárez,et al.  Nonparametric estimation of transition probabilities in a non-Markov illness–death model , 2006, Lifetime data analysis.

[32]  Martin Schumacher,et al.  A Note on Variance Estimation of the Aalen–Johansen Estimator of the Cumulative Incidence Function in Competing Risks, with a View towards Left‐Truncated Data , 2010, Biometrical journal. Biometrische Zeitschrift.