The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Regression models for interval-censored semi-competing risks data with missing intermediate transition status

중간 사건이 결측되었거나 구간 중도절단된 준 경쟁 위험 자료에 대한 회귀모형

  • Kim, Jinheum (Department of Applied Statistics, University of Suwon) ;
  • Kim, Jayoun (Research Coordinating Center, Konkuk University Medical Center)
  • 김진흠 (수원대학교 응용통계학과) ;
  • 김자연 (건국대병원 연구지원센터)
  • Received : 2016.08.22
  • Accepted : 2016.11.18
  • Published : 2016.12.31
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Abstract

We propose a multi-state model for analyzing semi-competing risks data with interval-censored or missing intermediate events. This model is an extension of the 'illness-death model', which composes three states, such as 'healthy', 'diseased', and 'dead'. The state of 'diseased' can be considered as an intermediate event. Two more states are added into the illness-death model to describe missing events caused by a loss of follow-up before the end of the study. One of them is a state of 'LTF', representing a lost-to-follow-up, and the other is an unobservable state that represents the intermediate event experienced after LTF occurred. Given covariates, we employ the Cox proportional hazards model with a normal frailty and construct a full likelihood to estimate transition intensities between states in the multi-state model. Marginalization of the full likelihood is completed using the adaptive Gaussian quadrature, and the optimal solution of the regression parameters is achieved through the iterative Newton-Raphson algorithm. Simulation studies are carried out to investigate the finite-sample performance of the proposed estimation procedure in terms of the empirical coverage probability of the true regression parameter. Our proposed method is also illustrated with the dataset adapted from Helmer et al. (2001).

본 논문에서는 종말 사건에 대한 정보는 주어져 있지만 중간 사건이 구간 중도절단되었거나 연구 기간 도중에 추적이 끊겨 중간 사건의 발생 유무를 모르는 준 경쟁 위험 자료에 다중상태모형을 적용하여 모수를 추정하는 방법을 제안하였다. 이를 위해 상태 간 전이 강도는 정규 프레일티를 랜덤효과로 가진 Cox 비례위험모형을 따른다고 가정하였다. 다섯 가지 상태를 가진 다중상태모형에서 가능한 여섯 가지 경로별로 조건부 우도를 정의하였고 주변 우도를 구하기 위해 조정 가우스 구적법을 적용하였으며 뉴튼-랩슨 방법으로 최적 해를 구하였다. 모수의 95% 신뢰구간 포함률을 통해 제안한 방법의 소표본 성질을 살펴보기 위해 모의실험을 수행하였으며, Persones $Ag{\acute{e}}es$ Quid(PAQUID) 자료 (Helmer 등, 2001)에 제안한 모형을 적용하고 그 결과를 해석하였다.

Keywords

References

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