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

Lifetime Data Analysis

Volumn 20, Issue 4, 2014, Pages 495-513

  Allignol, Arthur ^a,c   Beyersmann, Jan ^b,c   Gerds, Thomas ^d   Latouche, Aurélien ^e  

^a UNIVERSITY OF FREIBURG   (Germany)

^b UNIVERSITY OF ULM   (Germany)

^c UNIVERSITY OF FREIBURG   (Germany)

^d UNIVERSITY OF COPENHAGEN   (Denmark)

^e Bioinformatique et Chimie Moléculaire   (France)

Author keywords

Markov assumption; Bivariate survival; Left truncation; Multi state model; Nosocomial infection

Indexed keywords

EID: 84879264072     PISSN: 13807870     EISSN: 15729249     Source Type: Journal    
DOI: 10.1007/s10985-013-9269-1     Document Type: Article

References (30)

1. Aalen O, Johansen S (1978) An empirical transition matrix for non-homogeneous Markov chains based on censored observations. Scand J Stat 5:141–150
2. Allignol A, Schumacher M, Beyersmann J (2010) 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. Biom J 52:126–137
3. Allignol A, Schumacher M, Beyersmann J (2011) Estimating summary functionals in multistate models with an application to hospital infection data. Comput Stat 26:181–197
4. Andersen P, Borgan Ø, Gill R, Keiding N (1993) Statistical models based on counting processes. Springer, New York
5. Azzalini A (1985) A class of distributions which includes the normal ones. Scand J Stat 12:171–178
6. Beyersmann J, Allignol A, Schumacher M (2012) Competing risks and multistate models with R. Springer, New York
7. Beyersmann J, Gastmeier P, Grundmann H, Bärwolff S, Geffers C, Behnke M, Rüden H, Schumacher M (2006) Use of multistate models to assess prolongation of intensive care unit stay due to nosocomial infection. Infect Control Hosp Epidemiol 27:493–499
8. Beyersmann J, Wolkewitz M, Allignol A, Grambauer N, Schumacher M (2011) Application of multistate models in hospital epidemiology: advances and challenges. Biom J 53:332–350
9. Braun T, Yuan Z (2007) Comparing the small sample performance of several variance estimators under competing risks. Stat Med 26:1170–1180
10. Datta S, Ferguson A (2012) Nonparametric estimation of marginal temporal functionals in a multi-state model. In: Lisnianski A, Frenkel I (eds) Recent advances in system reliability. Springer, New York
11. Datta S, Satten GA (2001) Validity of the Aalen–Johansen estimators of stage occupation probabilities and Nelson–Aalen estimators of integrated transition hazards for non-Markov models. Stat Probab Lett 55:403–411
12. Datta S, Satten GA (2002) Estimation of integrated transition hazards and stage occupation probabilities for non-markov systems under dependent censoring. Biometrics 58:792–792
13. Datta S, Satten GA, Datta S (2000) Nonparametric estimation for the three-stage irreversible illness-death model. Biometrics 56:841–847
14. De Angelis G, Allignol A, Murthy A, Wolkewitz M, Beyersmann J, Safran E, Schrenzel J, Pittet D, Harbarth S (2011) Multistate modelling to estimate the excess length of stay associated with meticillin-resistant staphylococcus aureus colonisation and infection in surgical patients. J Hosp Infect 78:86–91
15. Fine J, Jiang H, Chappell R (2001) On semi-competing risks data. Biometrika 88:907–919
16. Gill R (1992) Multivariate survival analysis. Theory Probab Appl 37:18–31
17. Glidden D (2002) Robust inference for event probabilities with non-Markov data. Biometrics 58:361–368
18. Grambauer N, Schumacher M, Dettenkofer M, Beyersmann J (2010) Incidence densities in a competing events analysis. Am J Epidemiol 172:1077–1084
19. Graves N, Barnett A, Halton K, Crnich C, Cooper B, Beyersmann J, Wolkewitz M, Samore M, Harbarth S (2011) The importance of good data, analysis, and interpretation for showing the economics of reducing healthcare-associated infection. Infect Control Hosp Epidemiol 32:927–928
20. Gunnes N, Borgan Ø, Aalen O (2007) Estimating stage occupation probabilities in non-markov models. Lifetime Data Anal 13:211–240
21. Keiding N (1992) Independent delayed entry. In: Klein J, Goel P (eds) Survival analysis: state of the art. Kluwer, Dordrecht, pp 309–326
22. Lin D, Ying Z (1993) A simple nonparametric estimator of the bivariate survival function under univariate censoring. Biometrika 80:573–581
23. Meira-Machado L, de Uña-Álvarez J, Cadarso-Suárez C (2006) Nonparametric estimation of transition probabilities in a non-Markov illness-death model. Lifetime Data Anal 12:325–344
24. Pepe M, Longton G, Thornquist M (1991) A qualifier $$q$$q for the survival function to describe the prevalence of a transient condition. Stat Med 10:413–421
25. Prentice R, Moodie Z, Wu J (2004) Nonparametric estimation of the bivariate survivor function. In: Lin D, Heagerty P (eds) Proceedings of the second Seattle Symposium in Biostatistics. Lecture notes in statistics, vol 179. Springer, New York, pp 113–142
26. Quale C, van der Laan M, Robins R (2006) Locally efficient estimation with bivariate right-censored data. J Am Stat Assoc 101:1076–1084
27. Stute W (1993) Consistent estimation under random censorship when covariables are present. J Multivar Stat 45:89–103
28. Tsai W, Crowley J (1998) A note on nonparametric estimators of the bivariate survival function under univariate censoring. Biometrika 85:573–580
29. Umscheid C, Mitchell M, Doshi J, Agarwal R, Williams K, Brennan P (2011) Estimating the proportion of healthcare-associated infections that are reasonably preventable and the related mortality and costs. Infect Control Hosp Epidemiol 32:101–114
30. van der Laan MJ, Robins JM (2003) Unified methods for censored longitudinal data and causality. Springer, New York