Competing risks and multistate models with R

Competing Risks and Multistate Models with R

Volumn , Issue , 2012, Pages 1-245

  Beyersmann, Jan ^a,b   Allignol, Arthur ^a,b   Schumacher, Martin ^a  

^a UNIVERSITY OF FREIBURG   (Germany)

^b UNIVERSITY OF FREIBURG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

COMPETING RISKS; EVENT HISTORY ANALYSIS; MULTI-STATE; MULTI-STATE MODEL; NONPARAMETRIC METHODS; SINGLE EVENT; SURVIVAL ANALYSIS;

RISK ASSESSMENT;

EID: 85037150396     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/978-1-4614-2035-4     Document Type: Book

References (138)

1. Aalen, O. (1980). A model for nonparametric regression analysis of counting processes. Springer Lecture Notes in Statistics, 2:1-25, Springer, New York.
2. Aalen, O. (1987). Dynamic modelling and causality. Scandinavian Actuarial Journal, pages 177-190.
3. Aalen, O., Borgan, O., and Fekjer, H. (2001). Covariate adjustment of event histories estimated from Markov chains: the additive approach. Biometrics, 57:993-1001.
4. Aalen, O., Borgan, Ø., and Gjessing, H. (2008). Event History Analysis. Springer, New York.
5. Aalen, O. and Johansen, S. (1978). An empirical transition matrix for nonhomogeneousMarkov chains based on censored observations. Scandinavian Journal of Statistics, 5:141-150.
6. Allignol, A. and Beyersmann, J. (2010). Software for fitting non-standard subdistribution hazards models. Biostatistics, 11(4):674-675.
7. Allignol, A., Beyersmann, J., and Schumacher, M. (2008). mvna: An R package for the Nelson-Aalen estimator in multistate models. R News, 8(2):48-50.
8. Allignol, A., Schumacher, M., and 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. Biometrical Journal, 52(1):126-137.
9. Allignol, A., Schumacher, M., and Beyersmann, J. (2011). Empirical transition matrix of multistate models: the etm package. Journal of Statistical Software, 38(4):1-15.
10. Allignol, A., Schumacher, M., and Beyersmann, J. (2011). Estimating summary functionals in multistate models with an application to hospital infection data. Computational Statistics, 26:181-197.
11. Allignol, A., Schumacher, M., Wanner, C., Drechsler, C., and Beyersmann, J. (2011). Understanding competing risks: a simulation point of view. BMC Medical Research Methodology. To appear.
12. Andersen, P. (1986). Time-dependent covariates and Markov processes. In Moolgavkar, S. and Prentice, R., editors, Modern Statistical Methods in Chronic Disease Epidemiology, pages 82-103. Wiley, New York.
13. Andersen, P., Abildstrøm, S., and Rosthøj, S. (2002). Competing risks as a multistate model. Statistical Methods in Medical Research, 11(2):203-215.
14. Andersen, P. and Borgan, Ø. (1985). Counting process models for life history data: A review. Scandinavian Journal of Statistics, 12:97-140.
15. Andersen, P., Borgan, Ø., Gill, R., and Keiding, N. (1993). Statistical Models Based on Counting Processes. Springer, New York.
16. Andersen, P. and Gill, R. (1982). Cox's regression model for counting processes: A large sample study. The Annals of Statistics, 10:1100-1120.
17. Andersen, P. and Keiding, N. (2002). Multi-state models for event history analysis. Statistical Methods in Medical Research, 11(2):91-115.
18. Andersen, P., Klein, J., and Rosthøj, S. (2003). Generalised linear models for correlated pseudo-observations with applications to multi-state models. Biometrika, 90(1):15-27.
19. Andersen, P. and Perme, M. (2008). Inference for outcome probabilities in multistate models. Lifetime Data Analysis, 14(4):405-431.
20. Andersen, P. and Perme, M. (2010). Pseudo-observations in survival analysis. Statistical Methods in Medical Research, 19(1):71-99.
21. Anderson, J., Cain, K., and Gelber, R. (1983). Analysis of survival by tumor response. Journal of Clinical Oncology, 1:710-719.
22. Anderson, J., Cain, K., and Gelber, R. (2008). Analysis of survival by tumor response and other comparisons of time-to-event by outcome variables. Journal of Clinical Oncology, 26(24):3913-3915.
23. Bajorunaite, R. and Klein, J. (2008). Comparison of failure probabilities in the presence of competing risks. Journal of Statistical Computation and Simulation, 78(10):951-966.
24. Barnett, A., Batra, R., Graves, N., Edgeworth, J., Robotham, J., and Cooper, B. (2009). Using a longitudinal model to estimate the effect of methicillin-resistant staphylococcus aureus infection on length of stay in an intensive care unit. American Journal of Epidemiology, 170(9):1186-1194.
25. Bender, R., Augustin, T., and Blettner, M. (2005). Generating survival times to simulate Cox proportional hazards models. Statistics in Medicine, 24:1713-1723.
26. Bernoulli, D. (1982). Die gesammelten Werke der Mathematiker und Physiker der Familie Bernoulli. Hrsg. von der Naturforschenden Gesellschaft in Basel. Die Werke von Daniel Bernoulli. Band 2: Analysis, Wahrscheinlichkeitsrechnung. Birkhäuser, Basel.
27. Bernoulli, D. and Blower, S. (2004). An attempt at a new analysis of the mortality caused by smallpox and of the advantages of inoculation to prevent it. Reviews in Medical Virology, 14(5):275-288.
28. Beyersmann, J. (2007). A random time interval approach for analysing the impact of a possible intermediate event on a terminal event. Biometrical Journal, 49(5):742-749.
29. Beyersmann, J., Dettenkofer, M., Bertz, H., and Schumacher, M. (2007). A competing risks analysis of bloodstream infection after stem-cell transplantation using subdistribution hazards and cause-specific hazards. Statistics in Medicine, 26(30):5360-5369.
30. Beyersmann, J., Gastmeier, P., Wolkewitz, M., and Schumacher, M. (2008). An easy mathematical proof showed that time-dependent bias inevitably leads to biased effect estimation. Journal of Clinical Epidemiology, 61(12):1216-1221.
31. Beyersmann, J., Latouche, A., Buchholz, A., and Schumacher, M. (2009). Simulating competing risks data in survival analysis. Statistics in Medicine, 28:956-971.
32. Beyersmann, J. and Schumacher, M. (2008). Time-dependent covariates in the proportional subdistribution hazards model for competing risks. Biostatistics, 9:765-776.
33. Beyersmann, J., Wolkewitz, M., Allignol, A., Grambauer, N., and Schumacher, M. (2011). Application of multistate models in hospital epidemiology: advances and challenges. Biometrical Journal, 53:332-350.
34. Beyersmann, J., Wolkewitz, M., and Schumacher, M. (2008). The impact of time-dependent bias in proportional hazards modelling. Statistics in Medicine, 27:6439-6454.
35. Bie, O., Borgan, Ø., and Liestøl, K. (1987). Confidence intervals and confidence bands for the cumulative hazard rate function and their small sample properties. Scandinavian Journal of Statistics, 14:221-233.
36. Billingsley, P. (1968). Convergence of Probability Measures. Wiley, New York.
37. Bradley, L. (1971). Smallpox Inoculation: An Eighteenth Century Mathematical Controversy. Adult Education Department of the University of Nottingham.
38. Braun, T. and Yuan, Z. (2007). Comparing the small sample performance of several variance estimators under competing risks. Statistics in Medicine, 26(5):1170-1180.
39. Breslow, N. (1972). Discussion of the paper by D.R.Cox. Journal of the Royal Statistical Society, Series B, 34:216-217.
40. Burton, A., Altman, D., Royston, P., and Holder, R. (2006). The design of simulation studies in medical statistics. Statistics in Medicine, 25:4279-4292.
41. Cheng, S., Fine, J., and Wei, L. (1998). Prediction of cumulative incidence function under the proportional hazards model. Biometrics, 54:219-228.
42. Claeskens, G. and Hjort, N. (2008). Model Selection and Model Averaging. Cambridge University Press, Cambridge.
43. Clark, T., Altman, D., and De Stavola, B. (2002). Quantification of the completeness of follow-up. The Lancet, 359:1309-1310.
44. Cortese, G. and Andersen, P. (2010). Competing risks and time-dependent covariates. Biometrical Journal, 52(1):138-158.
45. Cox, D. (1972). Regression models and life-tables. Journal of the Royal Statistical Society, Series B: Methodological, 34:187-220.
46. D'Agostino, R., Lee, M., Belanger, A., Cupples, L., Anderson, K., and Kannel, W. (1990). Relation of pooled logistic regression to time dependent Cox regression analysis: the Framingham Heart Study. Statistics in Medicine, 9(12):1501-1515.
47. Dalgaard, P. (2002). Introductory statistics with R. Springer, New York.
48. Datta, S. and Satten, G. A. (2001). Validity of the Aalen-Johansen estimators of stage occupation probabilities and Nelson-Aalen estimators of integrated transition hazards for non-Markov models. Statistics and Probability Letters, 55(4):403-411.
49. de Wreede, L., Fiocco, M., and Putter, H. (2010). The mstate package for estimation and prediction in non- and semi-parametric multi-state and competing risks models. Computer Methods and Programs in Biomedicine, 99:261-274.
50. de Wreede, L. C., Fiocco, M., and Putter, H. (2011). mstate: An R package for the analysis of competing risks and multi-state models. Journal of Statistical Software, 38(7):1-30.
51. Dettenkofer, M., Wenzler-Röttele, S., Babikir, R., Bertz, H., Ebner, W., Meyer, E., Rüden, H., Gastmeier, P., and Daschner, F. (2005). Surveillance of nosocomial sepsis and pneumonia in patients with a bone marrow or peripheral blood stem cell transplant. A multicenter project. Clinical Infectious Diseases, 40:926-931.
52. Dietz, K. and Heesterbeek, J. (2002). Daniel Bernoulli's epidemiological model revisited. Mathematical Biosciences, 180:1-21.
53. Efron, B. (1979). Bootstrap methods: Another look at the jackknife. Annals of Statistics, 7:1-26.
54. Efron, B. (1981). Censored data and the bootstrap. Journal of the American Statistical Association, 76:312-319.
55. Fine, J. (2002). Comparing nonnested Cox models. Biometrika, 89(3):635-648.
56. Fine, J. and Gray, R. (1999). A proportional hazards model for the subdistribution of a competing risk. Journal of the American Statistical Association, 94(446):496-509.
57. Gail, M. (1982). Competing risks. In Banks, D., Read, C., and Kotz, S., editors, Encyclopedia of Statistical Sciences, Volume 2, pages 75-81. Wiley, New York.
58. Gerds, T., Cai, T., and Schumacher, M. (2008). The performance of risk prediction models. Biometrical Journal, 50:457-479.
59. Gerds, T. and Schumacher, M. (2001). On functional misspecification of covariates in the Cox regression model. Biometrika, 88(2):572-580.
60. Geskus, R. (2011). Cause-specific cumulative incidence estimation and the Fine and Gray model under both left truncation and right censoring. Biometrics, 67:39-49.
61. Gill, R. (1984). Understanding Cox's regression model: A martingale approach. Journal of the American Statistical Association, 79:441-447.
62. Gill, R. (1989). Non- and semi-parametric maximum likelihood estimators and the von Mises method (Part 1). Scandinavian Journal of Statistics, 16(2):97-128.
63. Gill, R. (1992). Multivariate survival analysis. Theory of Probability and its Applications, 37(1):18-31.
64. Gill, R. and Johansen, S. (1990). A survey of product-integration with a view towards application in survival analysis. Annals of Statistics, 18(4):1501-1555.
65. Gill, R. and Schumacher, M. (1987). A simple test of the proportional hazards assumption. Biometrika, 74:289-300.
66. Glidden, D. (2002). Robust inference for event probabilities with non-Markov data. Biometrics, 58:361-368.
67. Glynn, R., Rosner, B., and Christen, W. (2009). Evaluation of risk factors for cataract types in a competing risks framework. Ophthalmic Epidemiology, 16(2):98-106.
68. Grambauer, N., Schumacher, M., and Beyersmann, J. (2010). Proportional subdistribution hazards modeling offers a summary analysis, even if misspecified. Statistics in Medicine, 29:875-884.
69. Grambauer, N., Schumacher, M., Dettenkofer, M., and Beyersmann, J. (2010). Incidence densities in a competing events analysis. American Journal of Epidemiology, 172(9):1077-1084.
70. Graw, F., Gerds, T., and Schumacher, M. (2009). On pseudo-values for regression analysis in competing risks models. Lifetime Data Analysis, 15:241-255.
71. Gray, R. (1988). A class of k-sample tests for comparing the cumulative incidence of a competing risk. Annals of Statistics, 16(3):1141-1154.
72. Hjort, N. (1992). On inference in parametric survival data models. International Statistical Review, 60:355-387.
73. Hosmer, D., Lemeshow, S., and May, S. (2008). Applied Survival Analysis. Regression Modeling of Time to Event Data. 2nd ed. Wiley, Hoboken, NJ.
74. Hougaard, P. (2000). Analysis of Multivariate Survival Data. Springer, New York.
75. Jackson, C. (2011). Multi-state models for panel data: the msm package for R. Journal of Statistical Software, 38(8):1-29.
76. Kalbfleisch, J. and Prentice, R. (1980). The Statistical Analysis of Failure Time Data. Wiley, New York.
77. Kalbfleisch, J. and Prentice, R. (2002). The Statistical Analysis of Failure Time Data. 2nd ed. Wiley, Hoboken, NJ.
78. Kay, R. (1982). The analysis of transition times in multistate stochastic processes using proportional hazard regression models. Communications in Statistics-Theory and Methods, 11(15):1743-1756.
79. Keiding, N. and Gill, R. (1990). Random truncation models and Markov processes. The Annals of Statistics, 18:582-602.
80. Klein, J. (1991). Small sample moments of some estimators of the variance of the Kaplan-Meier and Nelson-Aalen estimators. Scandinavian Journal of Statistics, 18:333-340.
81. Klein, J. (2006). Modelling competing risks in cancer studies. Statistics in Medicine, 25:1015-1034.
82. Klein, J., Gerster, M., Andersen, P., Tarima, S., and Perme, M. (2008). SAS and R functions to compute pseudo-values for censored data regression. Computer Methods and Programs in Biomedicine, 89(3):289-300.
83. Klein, J., Keiding, N., Shu, Y., Szydlo, R., and Goldman, J. (2000). Summary curves for patients transplanted for chronic myeloid leukaemia salvaged by a donor lymphocyte infusion: the current leukaemia-free survival curve. British Journal of Haematology, 20:1871-1885.
84. Klein, J. and Moeschberger, M. (2003). Survival Analysis. Techniques for Censored and Truncated Data. 2nd ed. Springer, New York.
85. Koller, M., Stijnen, T., Steyerberg, E., and Lubsen, J. (2008). Meta-analyses of chronic disease trials with competing causes of death may yield biased odds ratios. Journal of Clinical Epidemiology, 61(4):365-372.
86. Latouche, A. (2004). Modele de Ŕegression en Pŕesence de Competition. PhDthesis, Universite Paris 6. http://tel.archives-ouvertes.fr/tel-00129238/fr/.
87. Latouche, A., Allignol, A., Beyersmann, J., Labopin, M., and Fine, J. (2011). Analysing, interpreting and reporting competing risks in stem cell transplantation: a case study in the RIC era. Unpublished manuscript.
88. Latouche, A., Boisson, V., Porcher, R., and Chevret, S. (2007). Misspecified regression model for the subdistribution hazard of a competing risk. Statistics in Medicine, 26(5):965-974.
89. Latouche, A. and Porcher, R. (2007). Sample size calculations in the presence of competing risks. Statistics in Medicine, 26(30):5370-5380.
90. Latouche, A., Porcher, R., and Chevret, S. (2005). A note on including timedependent covariate in regression model for competing risks data. Biometrical Journal, 47(6):807-814.
91. Leisch, F. (2002). Sweave: Dynamic generation of statistical reports using literate data analysis. In Härdle, W. and Rönz, B., editors, Compstat 2002 - Proceedings in Computational Statistics, pages 575-580. Physica Verlag, Heidelberg.
92. Lin, D. (1997). Non-parametric inference for cumulative incidence functions in competing risks studies. Statistics in Medicine, 16:901-910.
93. Lin, D. and Wei, L. (1989). The robust inference for the Cox proportional hazards model. Journal of the American Statistical Association, 84:1074-1078.
94. Lin, D. and Ying, Z. (1994). Semiparametric analysis of the additive risk model. Biometrika, 81:61-71.
95. Lumley, T. (2004). The survival package. R News, 4(1):26-28.
96. Lunn, M. and McNeil, D. (1995). Applying Cox regression to competing risks. Biometrics, 51:524-532.
97. Mackenbach, J., Kunst, A., Lautenbach, H., Oei, Y., and Bijlsma, F. (1999). Gains in life expectancy after elimination of major causes of death: revised estimates taking into account the effect of competing causes. Journal of Epidemiology and Community Health, 53(1):32-37.
98. Mantel, N. and Byar, D. (1974). Evaluation of response-time data involving transient states: An illustration using heart-transplant data. Journal of the American Statistical Association, 69:81-86.
99. Martinussen, T. and Scheike, T. (2006). Dynamic Regression Models for Survival Data. Springer, New York.
100. McKeague, I. and Sasieni, P. (1994). A partly parametric additive risk model. Biometrika, 81:501-514.
101. Meira-Machado, L., de Uña- Alvarez, J., and Cadarso-Súarez, C. (2006). Nonparametric estimation of transition probabilities in a non-Markov illness-death model. Lifetime Data Analysis, 12(3):325-344.
102. Meira-Machado, L. and Pardinas, J. (2011). p3state.msm: Analyzing survival data from an illness-death model. Journal of Statistical Software, 38(3):1-18.
103. Meister, R. and Schaefer, C. (2008). Statistical methods for estimating the probability of spontaneous abortion in observational studies-analyzing pregnancies exposed to coumarin derivatives. Reproductive Toxicology, 26(1):31-35.
104. Meyer, E., Beyersmann, J., Bertz, H., Wenzler-Röttele, S., Babikir, R., Schumacher, M., Daschner, F., Rüden, H., Dettenkofer, M., and the ONKO-KISS study group (2007). Risk factor analysis of blood stream infection and pneumonia in neutropenic patients after peripheral blood stem-cell transplantation. Bone Marrow Transplant, 39(3):173-178.
105. Morgan, B. (1984). Elements of Simulation. Chapman & Hall, London. Pepe, M. and Mori, M. (1993). Kaplan-Meier, marginal or conditional probability curves in summarizing competing risks failure time data? Statistics in Medicine, 12:737-751.
106. Pepe, M. and Mori, M. (1993). Kaplan-Meier, marginal or conditional probability curves in summarizing competing risks failure time data? Statistics in Medicine, 12:737-751.
107. Prentice, R., Kalbfleisch, J., Peterson, A., Flournoy, N., Farewell, V., and Breslow, N. (1978). The analysis of failure times in the presence of competing risks. Biometrics, 34:541-554.
108. Putter, H., Fiocco, M., and Geskus, R. (2007). Tutorial in biostatistics: competing risks and multi-state models. Statistics in Medicine, 26(11):2277-2432.
109. Ripley, B. (1987). Stochastic Simulation. Wiley, New York.
110. Rizzo, M. (2007). Statistical Computing with R. Chapman & Hall, Boca Raton, FL.
111. Robins, J. and Rotnitzky, A. (1992). Recovery of information and adjustment for dependent censoring using surrogate markers. In Jewell, N., Dietz, K., and Farewell, V., editors, AIDS Epidemiology - Methodological Issues, pages 24-33. Birkhäuser, Boston.
112. Rosthøj, S., Andersen, P., and Abildstrom, S. (2004). SAS macros for estimation of the cumulative incidence functions based on a Cox regression model for com peting risks survival data. Computer Methods and Programs in Biomedicine, 74:69-75.
113. Ruan, P. and Gray, R. (2008). Analyses of cumulative incidence functions via nonparametric multiple imputation. Statistics in Medicine, 27(27):5709-5724.
114. Russell, B. (2004). History of Western Philosophy. Reprint of the 1946 ed. Routledge, Oxon.
115. Saha, P. and Heagerty, P. (2010). Time-dependent predictive accuracy in the presence of competing risks. Biometrics, 66:999-1011.
116. Schafer, J. (1997). Analysis of Incomplete Multivariate Data. Chapman & Hall, London.
117. Schaubel, D. and Wei, G. (2007). Fitting the additive hazards model using standard statistical software. Biometrical Journal, 49:719-730.
118. Scheike, T. and Zhang, M.-J. (2007). Direct modelling of regression effects for transition probabilities in multistate models. Scandinavian Journal of Statistics, 34(1):17-32.
119. Scheike, T. and Zhang, M.-J. (2008). Flexible competing risks regression modeling and goodness-of-fit. Lifetime Data Analysis, 14(4):464-483.
120. Scheike, T., Zhang, M.-J., and Gerds, T. (2008). Predicting cumulative incidence probability by direct binomial regression. Biometrika, 95(1):205-220.
121. Schoop, R., Beyersmann, J., Schumacher, M., and Binder, H. (2011). Quantifying the predictive accuracy of time-to-event models in the presence of competing risks. Biometrical Journal, 53:88-112.
122. Schulgen, G., Olschewski, M., Krane, V., Wanner, C., Ruf, G., and Schumacher, M. (2005). Sample sizes for clinical trials with time-to-event endpoints and competing risks. Contemporary Clinical Trials, 26:386-395.
123. Schumacher, M., Wangler, M., Wolkewitz, M., and Beyersmann, J. (2007). Attributable mortality due to nosocomial infections: a simple and useful application of multistate models. Methods of Information in Medicine, 46:595-600.
124. Shiryaev, A. (1995). Probability. 2nd ed. Springer, New York.
125. Struthers, C. and Kalbfleisch, J. (1986). Misspecified proportional hazard models. Biometrika, 73:363-369.
126. Suissa, S. (2008). Immortal time bias in pharmacoepidemiology. American Journal of Epidemiology, 167(4):492-499.
127. Temkin, N. (1978). An analysis for transient states with application to tumor shrinkage. Biometrics, 34(4):571-580.
128. Therneau, T. and Grambsch, P. (2000). Modeling Survival Data: Extending the Cox Model. Springer, New York.
129. Tsai,W. and Crowley, J. (1998). A note on nonparametric estimators of the bivariate survival function under univariate censoring. Biometrika, 85(3):573-580.
130. Tsiatis, A. (1975). A nonidentifiability aspect of the problem of competing risks. Proceedings of the National Academy of Sciences of the USA, 72:20-22.
131. van der Vaart, A. and Wellner, J. A. (1996). Weak Convergence and Empirical Processes. With Applications to Statistics. Springer, New York.
132. van Houwelingen, H. and Putter, H. (2008). Dynamic predicting by landmarking as an alternative for multi-state modeling: an application to acute lymphoid leukemia data. Lifetime Data Analysis, 14:447-463.
133. van Walraven, C., Davis, D., Forster, A., and Wells, G. (2004). Time-dependent bias was common in survival analyses published in leading clinical journals. Journal of Clinical Epidemiology, 57:672-682.
134. Venables, W. and Ripley, B. (2002). Modern Applied Statistics with S. 4th ed. Springer, New York.
135. Wanner, C., Krane, V., März, W., Olschewski, M., Mann, J., Ruf, G., and Ritz, E. (2005). Atorvastatin in patients with type 2 diabetes mellitus undergoing hemodialysis. New England Journal of Medicine, 353(3):238-248.
136. Wolkewitz, M., Vonberg, R., Grundmann, H., Beyersmann, J., Gastmeier, P., Bärwolff, S., Geffers, C., Behnke, M., Rüden, H., and Schumacher, M. (2008). Risk factors for the development of nosocomial pneumonia and mortality on intensive care units: application of competing risks models. Critical Care, 12(2):R44.
137. Zhang, X., Zhang, M.-J., and Fine, J. (2009). A mass redistribution algorithm for right-censored and left-truncated time to event data. Journal of Statistical Planning and Inference, 139(9):3329-3339.
138. Zhang, X., Zhang, M.-J., and Fine, J. (2011). A proportional hazards regression model for the subdistribution with right-censored and left-truncated competing risks data. Statistics in Medicine. DOI: 10.1002/sim.4264.