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신뢰성응용연구 = Journal of the applied reliability v.18 no.2, 2018년, pp.130 - 142
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### 경쟁적 위험하에서의 회귀분석 Competing Risks Regression Analysis

백재욱   (한국방송통신대학교 정보통계학과UU0001389  );
• #### 초록

Purpose: The purpose of this study is to introduce regression method in the presence of competing risks and to show how you can use the method with hypothetical data. Methods: Survival analysis has been widely used in biostatistics division. But the same method has not been utilized in reliability division. Especially competing risks, where more than a couple of causes of failure occur and the occurrence of one event precludes the occurrence of the other events, are scattered in reliability field. But they are not utilized in the area of reliability or they are analysed in the wrong way. Specifically Kaplan-Meier method is used to calculate the probability of failure in the presence of competing risks, thereby overestimating the real probability of failure. Hence, cumulative incidence function is introduced. In addition, sample competing risks data are analysed using cumulative incidence function along with some graphs. Lastly we compare cumulative incidence functions with regression type analysis briefly. Results: We used cumulative incidence function to calculate the survival probability or failure probability in the presence of competing risks. We also drew some useful graphs depicting the failure trend over the lifetime. Conclusion: This research shows that Kaplan-Meier method is not appropriate for the evaluation of survival or failure over the course of lifetime in the presence of competing risks. Cumulative incidence function is shown to be useful in stead. Some graphs using the cumulative incidence functions are also shown to be informative.

• #### 주제어

Competing Risks .   Cumulative Incidence Function .   Competing Risks Regression .   R Statistical Software.

• #### 참고문헌 (20)

1. Kalbfleisch, J. D. and Prentice, R. L. (2002). "The statistical analysis of failure time data". John Wiley & Sons, New York.
2. Klein, J. P. and Moeschberger, M. L. (2003). "Survival analysis. techniques for censored and truncated data". Springer, New York.
3. Kaplan, E. and Meier, P. (1958). "Nonparametric estimation from incomplete observations". Journal of the American Statistical Association, Vol. 53, pp. 457-481.
4. Porta, N., Gomez, G., and Calle, M. L. (2008). "The Role of survival functions in competing risks". available at http://www.eio.upc.es/nporta, cited on June 20, 2011.
5. Putter, H., Fiocco, M., and Geskus, R. B. (2006). "Tutorial in Biostatistics: Competing risks and multi-state events". Statistics in Medicine, Vol. 26, pp. 2389-2430.
6. Kim, H. (2007). "Cumulative incidence in competing risks data and competing risks regression analysis". Clinical Cancer Research, Vol. 13, pp. 559-565.
7. Scrucca, L., Santucci, A., and Aversa, F. (2007). "Competing risk analysis using R: an easy guide for clinicians". Bone Marrow Transplantation, Vol. 40, pp. 381-387.
8. Chastain, T. M., Young, T. M., Geuss, F. M., and Leon, R. V. (2009). Using reliability tools to characterize wood strand thickness of oriented strand board panels. International Journal of Reliability and Applications, Vol. 10, pp. 89-99.
9. Gooley, T. A., Leisenring, W., Crowley, J., and Storer, B. E. (1999). Estimation of failure probabilities in the presence of competing risks: New representations of old estimators. Statistics in Medicine, Vol. 18, pp. 695-706.
10. Lawless, J. (2003). "Statistical models and methods for lifetime data". John Wiley & Sons, New York.
11. Baik, J. (2016). "Reliability analysis under the competing risks". Journal of Applied Reliability, Vol. 16, pp. 56-63.
12. Furstova, J. and Valenta, Z. (2011). "Statistical analysis of competing risks: overall survival in a group of chronic myeloid leukemia patients". EuroMISE s.r.o., 7, en2-en10.
13. Tsiatis, A. (1975). "A nonidentifiability aspect of the problem of competing risks". Proceedings of the National Academy of Sciences, USA 72, pp. 20-22.
14. Lunn, M. and McNeil D. (1995). "Applying Cox regression to competing risks". Biometrics, Vol. 51, pp. 281-320.
15. Fine, J. and Gray, R. J. (1999). A proportional hazards model for the subpopulation of a competing risk". Journal of American Statistical Society, Vol. 94, pp. 496-509.
16. Klein, J. P. and Anderson, P. K. (2005). "Regression modeling of competing risks". Biometrics, Vol. 61, pp. 223-229.
17. Klein, J. P. and Zhang M. J.(2007). "Survival analysis". Handbook of Statistics, Vol. 27, pp. 281-320.
18. Logan B. R., Zhang, M. J., and Klein, J. P.(2006). "Regression models for hazard rates versus cumulative incidence probabilities in hematopoietic cell transplantation data". Biology of Blood Marrow Transplant, Vol. 12, pp. 107-112.
19. Moeschberger, M. L., Tordoff, K. P., and Kochar, N. (2007). "A Review of Statistical Analyses for Competing Risks". Handbook of Statistics, Vol. 27, pp. 321-341.
20. Kass, R. E. and Raftery, A. E. (1995). "Bayes factors". Journal of American Statistical Association, Vol. 90, pp. 773-795.

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