Weak Convergence of the Wild Bootstrap for the Aalen-Johansen Estimator of the Cumulative Incidence Function of a Competing Risk
We give a rigorous study of weak convergence of the wild bootstrap for non-parametric estimation of the cumulative event probability of a competing risk. The data may be subject to independent left-truncation and right-censoring. Inclusion of left-truncation is motivated by a study on pregnancy outc...
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| Published in | Scandinavian journal of statistics Vol. 40; no. 3; pp. 387 - 402 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Oxford, UK
Blackwell Publishing Ltd
01.09.2013
Wiley Publishing |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0303-6898 1467-9469 |
| DOI | 10.1111/j.1467-9469.2012.00817.x |
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| Abstract | We give a rigorous study of weak convergence of the wild bootstrap for non-parametric estimation of the cumulative event probability of a competing risk. The data may be subject to independent left-truncation and right-censoring. Inclusion of left-truncation is motivated by a study on pregnancy outcomes. The wild bootstrap includes as one case a popular resampling technique, where the limit distribution is approximated by repeatedly generating standard normal variates, while the data are kept fixed. Simulation results and a data example are also presented. |
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| AbstractList | We give a rigorous study of weak convergence of the wild bootstrap for non-parametric estimation of the cumulative event probability of a competing risk. The data may be subject to independent left-truncation and right-censoring. Inclusion of left-truncation is motivated by a study on pregnancy outcomes. The wild bootstrap includes as one case a popular resampling technique, where the limit distribution is approximated by repeatedly generating standard normal variates, while the data are kept fixed. Simulation results and a data example are also presented. . We give a rigorous study of weak convergence of the wild bootstrap for non‐parametric estimation of the cumulative event probability of a competing risk. The data may be subject to independent left‐truncation and right‐censoring. Inclusion of left‐truncation is motivated by a study on pregnancy outcomes. The wild bootstrap includes as one case a popular resampling technique, where the limit distribution is approximated by repeatedly generating standard normal variates, while the data are kept fixed. Simulation results and a data example are also presented. We give a rigorous study of weak convergence of the wild bootstrap for non-parametric estimation of the cumulative event probability of a competing risk. The data may be subject to independent left-truncation and right-censoring. Inclusion of left-truncation is motivated by a study on pregnancy outcomes. The wild bootstrap includes as one case a popular resampling technique, where the limit distribution is approximated by repeatedly generating standard normal variates, while the data are kept fixed. Simulation results and a data example are also presented. [PUBLICATION ABSTRACT] |
| Author | TERMINI, SUSANNA DI BEYERSMANN, JAN PAULY, MARKUS |
| Author_xml | – sequence: 1 givenname: JAN surname: BEYERSMANN fullname: BEYERSMANN, JAN organization: Freiburg Centre for Data Analysis and Modeling, University of Freiburg and Institute of Medical Biometry and Medical Informatics, University Medical Center Freiburg – sequence: 2 givenname: SUSANNA DI surname: TERMINI fullname: TERMINI, SUSANNA DI organization: Freiburg Centre for Data Analysis and Modeling, University of Freiburg and Institute of Medical Biometry and Medical Informatics, University Medical Center Freiburg – sequence: 3 givenname: MARKUS surname: PAULY fullname: PAULY, MARKUS organization: Institute of Mathematics, University of Duesseldorf |
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| Cites_doi | 10.1007/978-0-387-68560-1 10.1093/biomet/asr052 10.1007/s10985-009-9129-1 10.1016/j.reprotox.2008.06.006 10.1002/9780470316962 10.1093/biomet/80.3.557 10.1214/aos/1176349025 10.1002/(SICI)1097-0258(19970430)16:8<901::AID-SIM543>3.0.CO;2-M 10.1007/978-1-4612-2950-6 10.1214/11-EJS596 10.1016/j.csda.2006.05.011 10.2307/2337051 10.1093/biomet/asq012 10.1016/j.jhin.2011.02.003 10.1111/j.0006-341X.2003.00119.x 10.1214/aos/1176350143 10.1016/j.jeconom.2008.08.003 10.1214/aos/1056562462 10.1007/978-1-4614-2035-4 10.1002/bimj.200900039 10.1214/aos/1176350142 10.1007/978-94-015-7983-4_18 10.1214/aos/1176347617 |
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| References | Keiding, N. & Gill, R. (1990). Random truncation models and Markov processes. Ann. Statist.18, 582-602. Aalen, O., Borgan, Ø. & Gjessing, H. (2008). Survival and event history analysis. Springer, New York. Lin, D. Y., Fleming, T. R. & Wei, L. J. (1994). Confidence bands for survival curves under the proportional hazards model. Biometrika81, 73-81. Mammen, E. (1992). When does bootstrap work? Asymptotic results and simulations. Springer, New York, NY. Scheike, T. & Zhang, M. (2003). Extensions and applications of the Cox-Aalen survival model. Biometrics39, 1036-1045. 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. Beyersmann, J., Allignol, A. & Schumacher, M. (2012). Competing risks and multistate models with R. Springer, New York. Elgmati, E., Farewell, D. & Henderson, R. (2010). A martingale residual diagnostic for longitudinal and recurrent event data. Lifetime Data Anal.16, 118-135. Martinussen, T. & Scheike, T. (2006). Dynamic regression models for survival data. Springer, New York, NY. Meister, R. & Schaefer, C. (2008). Statistical methods for estimating the probability of spontaneous abortion in observational studies-analyzing pregnancies exposed to coumarin derivatives. Reprod. Toxicol.26, 31-35. Pauly, M. (2011). Weighted resampling of martingale difference arrays with applications. Electron. J. Stat.5, 41-52. Andersen, P., Borgan, Ø., Gill, R. D. & Keiding, N. (1993). Statistical models based on counting processes, Springer Series in Statistics. Springer, New York, NY. Janssen, A. & Pauls, T. (2003). How do bootstrap and permutation tests work?Ann. Statist.31, 768-806. Davidson, R. & Flachaire, E. (2008). The wild bootstrap, tamed at last. J. Econometrics146, 162-169. Lin, D. Y., Wei, L. J. & Ying, Z. (1993). Checking the Cox model with cumulative sums of martingale-based residuals. Biometrika80, 557-572. Wu, C. (1986). Jackknife, bootstrap and other resampling methods in regression analysis. Ann. Statist.14, 1261-1295. Bajorunaite, R. & Klein, J. P. (2007). Two-sample tests of the equality of two cumulative incidence functions. Comput. Statist. Data Anal.51, 4269-4281. Beran, R. (2000). Discussion: Jackknife, bootstrap and other resampling methods in regression analysis. Ann. Statist.14, 1295-1298. Lin, D. (1997). Non-parametric inference for cumulative incidence functions in competing risks studies. Stat. Med.16, 901-910. Billingsley, P. (1999). Convergence of probability measures. Wiley, New York. Aalen, O. & Johansen, S. (1978). An empirical transition matrix for non-homogeneous Markov chains based on censored observations. Scand. J. Statist.5, 141-150. Hieke, S., Dettenkofer, M., Bertz, H., Schumacher, M. & Beyersmann, J. (2012). Initially fewer bloodstream infections for allogeneic versus autologous stem-cell transplants in neutropenic patients. Epidemiol. Infect. doi: 10.1017/S0950268812000283 (in press). Oza, N. & Russell, S. (2001). Online bagging and boosting. Artif. Intell. Statist.1, 105-112. 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. Mammen, E. (1993). Bootstrap and wild bootstrap for high dimensional linear modelsAnn. Statist.21, 255-285. Lee, H. K. H. & Clyde, M. C. (2004). Lossless online Bayesian bagging. J. Mach. Learn. Res.5, 143-151. Cai, T., Tian, L., Uno, H., Solomon, S. & Wei, L. (2010). Calibrating parametric subject-specific risk estimation. Biometrika. 97, 389-404. Feng, X., He, X. & Hu, J. (2011). Wild bootstrap for quantile regression. Biometrika98, 995-999. 2010; 97 2010; 16 2012 1990; 18 1993; 21 1986; 14 2008 1978; 5 2011; 98 2004; 5 2006 2003; 39 1993 2011; 78 2007; 51 1992 2008; 146 1994; 81 2011; 5 2003; 31 1999 2000; 14 2008; 26 1997; 16 1993; 80 2001; 1 2010; 52 e_1_2_10_23_1 e_1_2_10_24_1 e_1_2_10_21_1 e_1_2_10_22_1 e_1_2_10_20_1 Martinussen T. (e_1_2_10_25_1) 2006 Hieke S. (e_1_2_10_15_1) 2012 Lee H. K. H. (e_1_2_10_19_1) 2004; 5 e_1_2_10_2_1 e_1_2_10_4_1 e_1_2_10_18_1 e_1_2_10_6_1 e_1_2_10_16_1 e_1_2_10_8_1 e_1_2_10_14_1 e_1_2_10_7_1 e_1_2_10_12_1 e_1_2_10_9_1 e_1_2_10_13_1 Andersen P. (e_1_2_10_5_1) 1993 e_1_2_10_10_1 e_1_2_10_11_1 e_1_2_10_30_1 Oza N. (e_1_2_10_27_1) 2001; 1 Aalen O. (e_1_2_10_3_1) 1978; 5 N. Keiding (e_1_2_10_17_1) 1992 e_1_2_10_29_1 e_1_2_10_28_1 e_1_2_10_26_1 |
| References_xml | – reference: Wu, C. (1986). Jackknife, bootstrap and other resampling methods in regression analysis. Ann. Statist.14, 1261-1295. – reference: Andersen, P., Borgan, Ø., Gill, R. D. & Keiding, N. (1993). Statistical models based on counting processes, Springer Series in Statistics. Springer, New York, NY. – reference: 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. – reference: Feng, X., He, X. & Hu, J. (2011). Wild bootstrap for quantile regression. Biometrika98, 995-999. – reference: Mammen, E. (1993). Bootstrap and wild bootstrap for high dimensional linear modelsAnn. Statist.21, 255-285. – reference: Lee, H. K. H. & Clyde, M. C. (2004). Lossless online Bayesian bagging. J. Mach. Learn. Res.5, 143-151. – reference: Oza, N. & Russell, S. (2001). Online bagging and boosting. Artif. Intell. Statist.1, 105-112. – reference: Lin, D. (1997). Non-parametric inference for cumulative incidence functions in competing risks studies. Stat. Med.16, 901-910. – reference: 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. – reference: Janssen, A. & Pauls, T. (2003). How do bootstrap and permutation tests work?Ann. Statist.31, 768-806. – reference: Martinussen, T. & Scheike, T. (2006). Dynamic regression models for survival data. Springer, New York, NY. – reference: Aalen, O., Borgan, Ø. & Gjessing, H. (2008). Survival and event history analysis. Springer, New York. – reference: Lin, D. Y., Wei, L. J. & Ying, Z. (1993). Checking the Cox model with cumulative sums of martingale-based residuals. Biometrika80, 557-572. – reference: Cai, T., Tian, L., Uno, H., Solomon, S. & Wei, L. (2010). Calibrating parametric subject-specific risk estimation. Biometrika. 97, 389-404. – reference: Bajorunaite, R. & Klein, J. P. (2007). Two-sample tests of the equality of two cumulative incidence functions. Comput. Statist. Data Anal.51, 4269-4281. – reference: Pauly, M. (2011). Weighted resampling of martingale difference arrays with applications. Electron. J. Stat.5, 41-52. – reference: Beran, R. (2000). Discussion: Jackknife, bootstrap and other resampling methods in regression analysis. Ann. Statist.14, 1295-1298. – reference: Hieke, S., Dettenkofer, M., Bertz, H., Schumacher, M. & Beyersmann, J. (2012). Initially fewer bloodstream infections for allogeneic versus autologous stem-cell transplants in neutropenic patients. Epidemiol. Infect. doi: 10.1017/S0950268812000283 (in press). – reference: Meister, R. & Schaefer, C. (2008). Statistical methods for estimating the probability of spontaneous abortion in observational studies-analyzing pregnancies exposed to coumarin derivatives. Reprod. Toxicol.26, 31-35. – reference: Elgmati, E., Farewell, D. & Henderson, R. (2010). A martingale residual diagnostic for longitudinal and recurrent event data. Lifetime Data Anal.16, 118-135. – reference: Billingsley, P. (1999). Convergence of probability measures. Wiley, New York. – reference: Keiding, N. & Gill, R. (1990). Random truncation models and Markov processes. Ann. Statist.18, 582-602. – reference: Aalen, O. & Johansen, S. (1978). An empirical transition matrix for non-homogeneous Markov chains based on censored observations. Scand. J. Statist.5, 141-150. – reference: Davidson, R. & Flachaire, E. (2008). The wild bootstrap, tamed at last. J. Econometrics146, 162-169. – reference: Scheike, T. & Zhang, M. (2003). Extensions and applications of the Cox-Aalen survival model. Biometrics39, 1036-1045. – reference: Lin, D. Y., Fleming, T. R. & Wei, L. J. (1994). Confidence bands for survival curves under the proportional hazards model. Biometrika81, 73-81. – reference: Beyersmann, J., Allignol, A. & Schumacher, M. (2012). Competing risks and multistate models with R. Springer, New York. – reference: Mammen, E. (1992). When does bootstrap work? Asymptotic results and simulations. Springer, New York, NY. – year: 2012 article-title: Initially fewer bloodstream infections for allogeneic versus autologous stem‐cell transplants in neutropenic patients publication-title: Epidemiol. Infect. – volume: 81 start-page: 73 year: 1994 end-page: 81 article-title: Confidence bands for survival curves under the proportional hazards model publication-title: Biometrika – volume: 14 start-page: 1295 year: 2000 end-page: 1298 article-title: Discussion: Jackknife, bootstrap and other resampling methods in regression analysis publication-title: Ann. 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| Snippet | We give a rigorous study of weak convergence of the wild bootstrap for non-parametric estimation of the cumulative event probability of a competing risk. The... . We give a rigorous study of weak convergence of the wild bootstrap for non‐parametric estimation of the cumulative event probability of a competing risk. The... We give a rigorous study of weak convergence of the wild bootstrap for non‐parametric estimation of the cumulative event probability of a competing risk. The... |
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| SubjectTerms | abortion Approximation Bootstrap method Clinical outcomes Convergence Estimating techniques Estimators Inclusions left-truncation Pregnancy Probability Public health right-censoring Risk Simulation simultaneous confidence bands Statistical analysis Statistical methods Statistics Studies |
| Title | Weak Convergence of the Wild Bootstrap for the Aalen-Johansen Estimator of the Cumulative Incidence Function of a Competing Risk |
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