Multiple imputation methods for inference on cumulative incidence with missing cause of failure
Analysis of cumulative incidence (sometimes called absolute risk or crude risk) can be difficult if the cause of failure is missing for some subjects. Assuming missingness is random conditional on the observed data, we develop asymptotic theory for multiple imputation methods to estimate cumulative...
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| Published in | Biometrical journal Vol. 53; no. 6; pp. 974 - 993 |
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| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
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Weinheim
WILEY-VCH Verlag
01.11.2011
WILEY‐VCH Verlag Wiley-VCH Wiley - VCH Verlag GmbH & Co. KGaA |
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| Abstract | Analysis of cumulative incidence (sometimes called absolute risk or crude risk) can be difficult if the cause of failure is missing for some subjects. Assuming missingness is random conditional on the observed data, we develop asymptotic theory for multiple imputation methods to estimate cumulative incidence. Covariates affect cause‐specific hazards in our model, and we assume that separate proportional hazards models hold for each cause‐specific hazard. Simulation studies show that procedures based on asymptotic theory have near nominal operating characteristics in cohorts of 200 and 400 subjects, both for cumulative incidence and for prediction error. The methods are illustrated with data on survival after breast cancer, obtained from the National Surgical Adjuvant Breast and Bowel Project (NSABP). |
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| AbstractList | Analysis of cumulative incidence (sometimes called absolute risk or crude risk) can be difficult if the cause of failure is missing for some subjects. Assuming missingness is random conditional on the observed data, we develop asymptotic theory for multiple imputation methods to estimate cumulative incidence. Covariates affect cause‐specific hazards in our model, and we assume that separate proportional hazards models hold for each cause‐specific hazard. Simulation studies show that procedures based on asymptotic theory have near nominal operating characteristics in cohorts of 200 and 400 subjects, both for cumulative incidence and for prediction error. The methods are illustrated with data on survival after breast cancer, obtained from the National Surgical Adjuvant Breast and Bowel Project (NSABP). Analysis of cumulative incidence (sometimes called absolute risk or crude risk) can be difficult if the cause of failure is missing for some subjects. Assuming missingness is random conditional on the observed data, we develop asymptotic theory for multiple imputation methods to estimate cumulative incidence. Covariates affect cause-specific hazards in our model, and we assume that separate proportional hazards models hold for each cause-specific hazard. Simulation studies show that procedures based on asymptotic theory have near nominal operating characteristics in cohorts of 200 and 400 subjects, both for cumulative incidence and for prediction error. The methods are illustrated with data on survival after breast cancer, obtained from the National Surgical Adjuvant Breast and Bowel Project (NSABP).Analysis of cumulative incidence (sometimes called absolute risk or crude risk) can be difficult if the cause of failure is missing for some subjects. Assuming missingness is random conditional on the observed data, we develop asymptotic theory for multiple imputation methods to estimate cumulative incidence. Covariates affect cause-specific hazards in our model, and we assume that separate proportional hazards models hold for each cause-specific hazard. Simulation studies show that procedures based on asymptotic theory have near nominal operating characteristics in cohorts of 200 and 400 subjects, both for cumulative incidence and for prediction error. The methods are illustrated with data on survival after breast cancer, obtained from the National Surgical Adjuvant Breast and Bowel Project (NSABP). |
| Author | Lee, Minjung Gail, Mitchell H. Feuer, Eric J. Cronin, Kathleen A. Dignam, James J. |
| Author_xml | – sequence: 1 givenname: Minjung surname: Lee fullname: Lee, Minjung email: leem5@mail.nih.gov organization: Data Analysis and Interpretation Branch, Division of Cancer Control and Population Studies, National Cancer Institute, Bethesda, MD 20852, USA – sequence: 2 givenname: Kathleen A. surname: Cronin fullname: Cronin, Kathleen A. organization: Data Analysis and Interpretation Branch, Division of Cancer Control and Population Studies, National Cancer Institute, Bethesda, MD 20852, USA – sequence: 3 givenname: Mitchell H. surname: Gail fullname: Gail, Mitchell H. organization: Biostatistics Branch, Division of Cancer Epidemiology and Genetics, National Cancer Institute, Bethesda, MD 20892, USA – sequence: 4 givenname: James J. surname: Dignam fullname: Dignam, James J. organization: Department of Health Studies, University of Chicago, Chicago, IL 60637, USA – sequence: 5 givenname: Eric J. surname: Feuer fullname: Feuer, Eric J. organization: Statistical Methodology and Applications Branch, Division of Cancer Control and Population Studies, National Cancer Institute, Bethesda, MD 20852, USA |
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| Cites_doi | 10.1002/(SICI)1097-0258(19961030)15:20<2191::AID-SIM358>3.0.CO;2-D 10.1093/biomet/92.4.875 10.1002/sim.4133 10.1080/01621459.1998.10474113 10.1111/j.2517-6161.1972.tb00899.x 10.1093/biomet/82.4.821 10.2307/2529620 10.1002/9780470316696 10.1093/biomet/89.1.238 10.1093/biomet/85.4.935 10.2307/2530374 10.1002/sim.3516 10.1200/JCO.1997.15.5.1858 10.2307/2337051 10.1111/j.0006-341X.2001.01191.x 10.1093/biomet/63.3.581 10.1002/bimj.201000073 10.2307/2534009 10.1200/JCO.1999.17.11.3374 10.1080/01621459.1999.10474144 10.1002/cncr.24617 10.1214/aos/1176345976 10.1002/sim.3894 |
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| Copyright | Copyright © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim 2015 INIST-CNRS 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. Copyright Wiley - VCH Verlag GmbH & Co. KGaA Nov 2011 |
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| Keywords | Biometrics Conditional distribution Breast disease Error estimation Missing at random Prediction theory Competing risks Covariate Stochastic process Statistical simulation Survival data Proportional hazards model Hazard function Competing risk Life science Prediction Statistical estimation Breast cancer Statistical method Cause-specific hazard function Counting process Observation data Filtering theory Asymptotic approximation Multiple imputation |
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| References | Andersen, J., Goetghebeur, E. and Ryan, L. ( 1996). Missing cause of death information in the analysis of survival data. Statistics in Medicine 15, 2191-2201. Cox, D. R. ( 1972). Regression models and life-tables (with discussion). Journal of the Royal Statistical Society, Series A 34, 187-220. Fisher, B., Anderson, S., Wickerham, D. L., DeCillis, A., Dimitrov, N., Mamounas, E., Wolmark, N., Pugh, R., Atkins, J. N., Meyers, F. J., Abramson, N., Wolter, J., Bornstein, R. S., Levy, L., Romond, E. H., Caggiano, V., Grimaldi, M., Jochimsen, P. and Deckers, P. ( 1997). Increased intensification and total dose of cyclophosphamide in a doxorubicin-cyclophosphamide regimen for the treatment of primary breast cancer: findings from National Surgical Adjuvant Breast and Bowel Project B-22. Journal of Clinical Oncology 15, 1858-1869. Aalen, O. and Johansen, S. ( 1978). An empirical transition matrix for non-homogeneous Markov chains based on censored observations. Scandinavian Journal of Statistics 5, 141-150. Cheng, S. C., Fine, J. P. and Wei, L. J. ( 1998). Prediction of cumulative incidence function under the proportional hazards model. Biometrics 54, 219-228. Goetghebeur, E. and Ryan, L. ( 1995). Analysis of competing risks survival data when some failure types are missing. Biometrika 82, 821-834. Beyersmann, J., Latouche, A., Buchholz, A. and Schumacher, M. ( 2009). Simulating competing risks data in survival analysis. Statistics in Medicine 8, 956-971. Rubin, D. B. ( 1987). Multiple Imputation for Nonresponse in Surveys. Wiley, New York. van der Vaart, A. W. ( 2000). Asymptotic Statistics. Cambridge University Press, Cambridge. Fine, J. P. and Gray, R. J. ( 1999). A proportional hazards model for the subdistribution of a competing risk. Journal of the American Statistical Association 94, 496-509. Sen, A., Banerjee, M., Li, Y. and Noone, A.-M. ( 2010). A Bayesian approach to competing risks analysis with masked cause of death. Statistics in Medicine 29, 1681-1695. Breslow, N. E. ( 1974). Covariance analysis of censored survival data. Biometrics 30, 89-99. Bakoyannis, G., Siannis, F. and Touloumi, G. ( 2010). Modelling competing risks data with missing cause of failure. Statistics in Medicine 29, 3172-3185. Lu, K. and Tsiatis, A. A. ( 2001). Multiple imputation methods for estimating regression coefficients in the competing risks model with missing cause of failure. Biometrics 57, 1191-1197. Tsiatis, A. A., Davidian, M. and Mcneney, B. ( 2002). Multiple imputation methods for testing treatment differences in survival distributions with missing cause of failure. Biometrika 89, 238-244. Fisher, B., Anderson, S., DeCillis, A., Dimitrov, N., Atkins, J. N., Fehrenbacher, L., Henry, P. H., Romond, E. H., Lanier, K. S., Davila, E., Kardinal, C. G., Laufman, L., Pierce, H. I., Abramson, N., Keller, A. M., Hamm, J. T., Wickerham, D. L., Begovic, M., Tan-Chiu, E., Tian, W. and Wolmark, N. ( 1999). Further evaluation of intensified and increased total dose of cyclophosphamide for the treatment of primary breast cancer: findings from National Surgical Adjuvant Breast and Bowel Project B-25. Journal of Clinical Oncology 17, 13374-3388. Prentice, R. L., Kalbfleisch, J. D., Peterson, A. V., Flournoy, N., Farewell, V. T. and Breslow, N. E. ( 1978). The analysis of failure times in the presence of competing risks. Biometrics 34, 541-554. Andersen, P. K. and Gill, R. D. ( 1982). Cox's regression model for counting processes: a large sample study. Annals of Statistics 10, 1100-1120. Satten, G. A., Datta, S. and Williamson, J. M. ( 1998). Inference based on imputed failure times for the proportional hazards model with interval-censored data. Journal of the American Statistical Association 93, 318-327. 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. Dignam, J. J., Huang, L., Ries, L., Reichman, M., Mariotto, A. and Feuer, E. ( 2009). Estimating breast cancer-specific and other-cause mortality in clinical trial and population-based cancer registry cohorts. Cancer 115, 5272-5283. Rubin, D. B. ( 1976). Inference and missing data. Biometrika 63, 581-592. Gao, G. and Tsiatis, A. A. ( 2005). Semiparametric estimators for the regression coefficients in the linear transformation competing risks model with missing cause of failure. Biometrika 92, 875-891. Lin, D. Y., Fleming, T. R. and Wei, L. J. ( 1994). Confidence bands for survival curves under the proportional hazards model. Biometrika 81, 73-81. Wang, N. and Robins, J. M. ( 1998). Large sample inference in parametric multiple imputation. Biometrika 85, 935-948. Lu, W. and Liang, Y. ( 2008). Analysis of competing risks data with missing cause of failure under additive hazards model. Statistica Sinica 18, 219-234. 1976; 63 1974; 30 1978; 34 2008; 18 1982; 10 2011; 53 1978; 5 1994; 81 1998; 85 1996; 15 2009; 115 1995; 82 2000 2010; 29 1997; 15 1999; 17 2002; 89 1987 2009; 8 2005; 92 1999; 94 1998; 93 1998; 54 1972; 34 2001; 57 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 van der Vaart A. W. (e_1_2_10_26_1) 2000 Aalen O. (e_1_2_10_2_1) 1978; 5 Lu W. (e_1_2_10_18_1) 2008; 18 e_1_2_10_4_1 e_1_2_10_3_1 Cox D. R. (e_1_2_10_9_1) 1972; 34 e_1_2_10_19_1 e_1_2_10_6_1 e_1_2_10_16_1 e_1_2_10_5_1 e_1_2_10_17_1 e_1_2_10_8_1 e_1_2_10_14_1 e_1_2_10_7_1 e_1_2_10_15_1 e_1_2_10_12_1 e_1_2_10_13_1 e_1_2_10_10_1 e_1_2_10_11_1 e_1_2_10_27_1 e_1_2_10_25_1 |
| References_xml | – reference: Prentice, R. L., Kalbfleisch, J. D., Peterson, A. V., Flournoy, N., Farewell, V. T. and Breslow, N. E. ( 1978). The analysis of failure times in the presence of competing risks. Biometrics 34, 541-554. – reference: Aalen, O. and Johansen, S. ( 1978). An empirical transition matrix for non-homogeneous Markov chains based on censored observations. Scandinavian Journal of Statistics 5, 141-150. – reference: Sen, A., Banerjee, M., Li, Y. and Noone, A.-M. ( 2010). A Bayesian approach to competing risks analysis with masked cause of death. Statistics in Medicine 29, 1681-1695. – reference: Rubin, D. B. ( 1976). Inference and missing data. Biometrika 63, 581-592. – reference: Tsiatis, A. A., Davidian, M. and Mcneney, B. ( 2002). Multiple imputation methods for testing treatment differences in survival distributions with missing cause of failure. Biometrika 89, 238-244. – reference: Dignam, J. J., Huang, L., Ries, L., Reichman, M., Mariotto, A. and Feuer, E. ( 2009). Estimating breast cancer-specific and other-cause mortality in clinical trial and population-based cancer registry cohorts. Cancer 115, 5272-5283. – reference: Satten, G. A., Datta, S. and Williamson, J. M. ( 1998). Inference based on imputed failure times for the proportional hazards model with interval-censored data. Journal of the American Statistical Association 93, 318-327. – reference: van der Vaart, A. W. ( 2000). Asymptotic Statistics. Cambridge University Press, Cambridge. – reference: Breslow, N. E. ( 1974). Covariance analysis of censored survival data. Biometrics 30, 89-99. – reference: Gao, G. and Tsiatis, A. A. ( 2005). Semiparametric estimators for the regression coefficients in the linear transformation competing risks model with missing cause of failure. Biometrika 92, 875-891. – reference: Goetghebeur, E. and Ryan, L. ( 1995). Analysis of competing risks survival data when some failure types are missing. Biometrika 82, 821-834. – reference: Lu, W. and Liang, Y. ( 2008). Analysis of competing risks data with missing cause of failure under additive hazards model. Statistica Sinica 18, 219-234. – reference: Cox, D. R. ( 1972). Regression models and life-tables (with discussion). Journal of the Royal Statistical Society, Series A 34, 187-220. – reference: Wang, N. and Robins, J. M. ( 1998). Large sample inference in parametric multiple imputation. Biometrika 85, 935-948. – reference: Andersen, J., Goetghebeur, E. and Ryan, L. ( 1996). Missing cause of death information in the analysis of survival data. Statistics in Medicine 15, 2191-2201. – reference: Cheng, S. C., Fine, J. P. and Wei, L. J. ( 1998). Prediction of cumulative incidence function under the proportional hazards model. Biometrics 54, 219-228. – reference: Rubin, D. B. ( 1987). Multiple Imputation for Nonresponse in Surveys. Wiley, New York. – reference: Fisher, B., Anderson, S., DeCillis, A., Dimitrov, N., Atkins, J. N., Fehrenbacher, L., Henry, P. H., Romond, E. H., Lanier, K. S., Davila, E., Kardinal, C. G., Laufman, L., Pierce, H. I., Abramson, N., Keller, A. M., Hamm, J. T., Wickerham, D. L., Begovic, M., Tan-Chiu, E., Tian, W. and Wolmark, N. ( 1999). Further evaluation of intensified and increased total dose of cyclophosphamide for the treatment of primary breast cancer: findings from National Surgical Adjuvant Breast and Bowel Project B-25. Journal of Clinical Oncology 17, 13374-3388. – reference: Lin, D. Y., Fleming, T. R. and Wei, L. J. ( 1994). Confidence bands for survival curves under the proportional hazards model. Biometrika 81, 73-81. – reference: Andersen, P. K. and Gill, R. D. ( 1982). Cox's regression model for counting processes: a large sample study. Annals of Statistics 10, 1100-1120. – reference: Fisher, B., Anderson, S., Wickerham, D. L., DeCillis, A., Dimitrov, N., Mamounas, E., Wolmark, N., Pugh, R., Atkins, J. N., Meyers, F. J., Abramson, N., Wolter, J., Bornstein, R. S., Levy, L., Romond, E. H., Caggiano, V., Grimaldi, M., Jochimsen, P. and Deckers, P. ( 1997). Increased intensification and total dose of cyclophosphamide in a doxorubicin-cyclophosphamide regimen for the treatment of primary breast cancer: findings from National Surgical Adjuvant Breast and Bowel Project B-22. Journal of Clinical Oncology 15, 1858-1869. – reference: Lu, K. and Tsiatis, A. A. ( 2001). Multiple imputation methods for estimating regression coefficients in the competing risks model with missing cause of failure. Biometrics 57, 1191-1197. – reference: Beyersmann, J., Latouche, A., Buchholz, A. and Schumacher, M. ( 2009). Simulating competing risks data in survival analysis. Statistics in Medicine 8, 956-971. – reference: Fine, J. P. and Gray, R. J. ( 1999). A proportional hazards model for the subdistribution of a competing risk. Journal of the American Statistical Association 94, 496-509. – reference: 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. – reference: Bakoyannis, G., Siannis, F. and Touloumi, G. ( 2010). Modelling competing risks data with missing cause of failure. 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| SubjectTerms | Applications Asymptotic methods Asymptotic properties Biology, psychology, social sciences Biometry - methods Breast cancer Breast Neoplasms - drug therapy Breast Neoplasms - epidemiology Cause-specific hazard function Clinical Trials as Topic Competing risks Counting process Exact sciences and technology Failure analysis Female General topics Hazards Humans Inference from stochastic processes; time series analysis Intestine Mathematics Middle Aged Missing at random Probability and statistics Probability theory and stochastic processes Proportional hazards model Risk Sciences and techniques of general use Statistical models Statistics Stochastic processes Survival Analysis |
| Title | Multiple imputation methods for inference on cumulative incidence with missing cause of failure |
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