Browse > Article
http://dx.doi.org/10.5351/KJAS.2016.29.7.1311

Regression models for interval-censored semi-competing risks data with missing intermediate transition status  

Kim, Jinheum (Department of Applied Statistics, University of Suwon)
Kim, Jayoun (Research Coordinating Center, Konkuk University Medical Center)
Publication Information
The Korean Journal of Applied Statistics / v.29, no.7, 2016 , pp. 1311-1327 More about this Journal
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).
Keywords
interval-censored intermediate event; lost to follow-up; multi-state model; normal frailty; semi-competing risks data;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Andersen, P. K., Borgan, O., Gill, R. D., and Keiding, N. (1993). Statistical Models based on Counting Processes, Springer, New York.
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 ageing study, Statistics in Medicine, 30, 1-10.   DOI
3 Collett D. (2015). Modeling Survival Data in Medical Research(3rd ed.), CRC Press, Boca Raton.
4 Cox, D. R. (1972). Models and life-tables regression, Journal of the Royal Statistical Society, Series B, 34, 187-220.
5 European Medicines Agency. (2016). Guideline on the Evaluation of Anticancer Medicinal Products in Man, Available from: http://www.ema.europa.eu/docs/en GB/document library/Scientific guideline/2016/03/WC500203320.pdf
6 Food and Drug Administration (FDA) (2007). Guidance for Industry: Clinical Trial Endpoints for the Approval of Cancer Drugs and Biologics, Available from: http://www.fda.gov/downloads/Drugs/Guidances/ucm071590.pdf.
7 Frydman, H. and Szarek, M. (2009). Nonparametric estimation in a Markov "illness-death" process from interval censored observations with missing intermediate transition status, Biometrics, 65, 143-151.   DOI
8 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.   DOI
9 Joly, P., Commenges, D., and Letenneur, L. (1998). A penalized likelihood approach for arbitrarily censored and truncated data: application to age-specific incidence of dementia, Biometrics, 54, 185-194.   DOI
10 Klein, J. P. and Moeschberger, M. L. (2003). Survival Analysis: Techniques for Censored and Truncated Data(2nd Ed.), Springer, New York.
11 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.   DOI
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.   DOI
13 Lindsey, J. C. and Ryan, L. M. (1998). Methods for interval-censored data, Statistics in Medicine, 17, 219-238.   DOI
14 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.
15 Touraine, C., Joly, P., and Gerds, T. A. (2015). Package 'SmoothHazards': fitting illness-death model for interval-censored data (version 1.2.3), Available from: https://cran.r-project.org/web/packages/Smoo thHazard/SmoothHazard.pdf