The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Developing statistical models and constructing clinical systems for analyzing semi-competing risks data produced from medicine, public heath, and epidemiology

의료, 보건, 역학 분야에서 생산되는 준경쟁적 위험자료를 분석하기 위한 통계적 모형의 개발과 임상분석시스템 구축을 위한 연구

  • Kim, Jinheum (Department of Applied Statistics, University of Suwon)
  • Received : 2020.04.06
  • Accepted : 2020.06.10
  • Published : 2020.08.31
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Abstract

A terminal event such as death may censor an intermediate event such as relapse, but not vice versa in semi-competing risks data, which is often seen in medicine, public health, and epidemiology. We propose a Weibull regression model with a normal frailty to analyze semi-competing risks data when all three transition times of the illness-death model are possibly interval-censored. We construct the conditional likelihood separately depending on the types of subjects: still alive with or without the intermediate event, dead with or without the intermediate event, and dead with the intermediate event missing. Optimal parameter estimates are obtained from the iterative quasi-Newton algorithm after the marginalization of the full likelihood using the adaptive importance sampling. We illustrate the proposed method with extensive simulation studies and PAQUID (Personnes Agées Quid) data.

사망과 같은 종말 사건은 중간 사건을 중도절단 시킬 수 있지만 재발과 같은 중간 사건은 종말 사건을 중도절단 시킬 수 없는 자료를 준경쟁위험 자료라고 하는데 의학 및 보건, 역학 분야에서는 이와 같은 자료를 자주 접하게 된다. 본 논문에서는 질병-사망 모형에 포함된 세 가지 전이 시간이 모두 구간중도절단된 준경쟁위험 자료를 분석하기 위해 정규 프레일티를 가진 와이블 회귀모형을 제안하였다. 각 개체는 중간 사건과 종말 사건의 발생 여부에 따라 다섯 가지 유형으로 구분되는데 유형별로 조건부 우도함수를 유도하였다. 조정중요표본추출법을 써서 주변 우도함수를 유도한 후 반복의사뉴톤 알고리즘을 써서 최적 추정량을 얻었다. 제안한 추정 방법의 소표본 성질을 살펴보기 위해 모의실험을 수행하였으며 또한 제안한 추정 방법을 Personnes Agées Quid (PAQUID) 자료에 적용하였다.

Keywords

Acknowledgement

본 논문은 2018학년도 수원대학교 학술진흥연구비 지원에 의한 논문임.

References

  1. Andersen, P. K., Geskus, R. B., de Witte, T., and Putter, H. (2012). Competing risks in epidemiology:possibilities and pitfalls, International Journal of Epidemiology, 41, 861-870. https://doi.org/10.1093/ije/dyr213
  2. Barrett, J. K., Siannis, F., and Farewell, V. T. (2011). A semi-competing risks model for data with intervalcensoring and informative observation: An application to the MRC cognitive function and aging study, Statistics in Medicine, 30, 1-10. https://doi.org/10.1002/sim.4071
  3. Cox, D. R. (1972). Models and life-tables regression, Journal of the Royal Statistical Society, Series B, 34, 187-220.
  4. Cox, D. R. (1975). Partial likelihood, Biometrika, 62, 269-276. https://doi.org/10.1093/biomet/62.2.269
  5. Fine, J. P., Jiang, H., and Chappell, R. (2001). On semi-competing risks data, Biometrika, 88, 907-919. https://doi.org/10.1093/biomet/88.4.907
  6. Frydman, H., Gerds, T., Gron, R., and Keiding, N. (2013). Nonparametric estimation in an "illness-death" model when all transition times are interval censored, Biomedical Journal, 55, 823-843.
  7. Helmer, C., Joly, P., Letenneur, L., Commenges, D., and Dartigues, J. F. (2001). Mortality with dementia:results from a French prospective community-based cohort, American Journal of Epidemiology, 154, 642-648. https://doi.org/10.1093/aje/154.7.642
  8. Joly, P., Commenges, D., Helmer, C., and Letenneur, L. (2002). A penalized likelihood approach for an illness-death model with interval-censored data: application to age-specific incidence of dementia, Biostatistics, 3, 433-443. https://doi.org/10.1093/biostatistics/3.3.433
  9. Kim, J. and Kim, J. (2016). Regression models for interval-censored semi-competing risks data with missing intermediate transition status, The Korean Journal of Applied Statistics, 29, 1311-1327. https://doi.org/10.5351/KJAS.2016.29.7.1311
  10. Kim, J., Kim, J., and Kim, S. W. (2019). Additive-multiplicative hazards regression models for intervalcensored semi-competing risks data with missing intermediate events, BMC Medical Research Methodology, 19, 1-14. https://doi.org/10.1186/s12874-018-0650-3
  11. Lee, K. H., Lee, C., Alvares, D., and Haneuse, S. (2019). Hierarchical models for parametric and semiparametric analyses of semi-competing risks data. Available from: https://CRAN.R-project.org/package=SemiCompRisks
  12. Leffondre, K., Touraine, C., Helmer, C., and Joly, P. (2013). Interval-censored time-to-event and competing risk with death: is the illness-death model more accurate than the Cox model?, International Journal of Epidemiology, 42, 1177-1186. https://doi.org/10.1093/ije/dyt126
  13. Pinheiro, J. C. and Bates, D. M. (1995). Approximations to the log-likelihood function in the nonlinear mixed-effects model, Journal of Computational and Graphical Statistics, 4, 12-35. https://doi.org/10.2307/1390625
  14. Putter, H., Fiocco, M., and Geskus, R. B. (2007). Tutorial in biostatistics: competing risks and multi-state models, Statistics in Medicine, 26, 2389-2430. https://doi.org/10.1002/sim.2712
  15. Siannis, F., Farewell, V. T., and Head, J. (2007). A multi-state model for joint modelling of terminal and non-terminal events with application to Whitehall II, Statistics in Medicine, 26, 426-442. https://doi.org/10.1002/sim.2342
  16. Touraine, C., Gerds, T. A., and Joly, P. (2014). SmoothHazard: An R package for fitting regression models to interval-censored observations of illness-death models, Journal of Statistical Software, 79, 1-22.
  17. Tsiatis, A. A. (2005). Competing risks, Encyclopedia of Biostatistics, 2, 1025-1035.
  18. Wellner, J. A. and Zhan, Y. (1997). A hybrid algorithm for computation of the nonparametric maximum likelihood estimator from censored data, Journal of the American Statistical Association, 92, 945-959. https://doi.org/10.1080/01621459.1997.10474049
  19. Xu, J., Kalbfleisch, J. D., and Tai, B. (2010). Statistical analysis of illness-death processes and semicompeting risks data, Biometrics, 66, 716-725. https://doi.org/10.1111/j.1541-0420.2009.01340.x