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JSRI 2020, 16(2): 379-396 Back to browse issues page
A Method for Analyzing Censored Survival Data with Application to Coronary Heart Disease
Azam Rastin, Mohammad Reza Farid Rouhani *1, Davoud Khalili
1- , m_ faridrohani@sbu.ac.ir
Abstract:   (586 Views)

An objective of analyzing survival data via regression is to develop a predictive model given predictors. However, due to the censoring in response variables and the high dimensionality of predictors, information needed for an appropriate model specification is often inadequate. We propose a method for an integrated study of survival time and predictors. At first, variable selection methods are employed for finding the correct subset of predictors with significantly higher probability. This is based on the Lasso approach. Then, the dimension of the predictors is further reduced using sufficient dimension reduction methods. This is based on the Sliced inverse regression for censored data (DSIRII). In particular we use the popular Cox proportional hazards model to build a predictive model for survival data. An application to Coronary heart disease (CHD) data from the Tehran Lipid and Glucose (TGLS) study further illustrates the usefulness of the work.

Keywords: Censored data, sufficient dimension reduction, central subspace, sliced inverse regression, variable selection, corronary heart disease.
Full-Text [PDF 760 kb]   (329 Downloads)    
Type of Study: Research | Subject: General
Received: 2020/01/23 | Accepted: 2021/02/16 | Published: 2021/09/19
1. Kundu, D. and Dey, A.K. (2009). Estimating the Parameters of the Marshall-Olkin Bivariate Weibull Distribution by EM Algorithm. Computational Statistics and Data Analysis, 53, 956-965. [DOI:10.1016/j.csda.2008.11.009]
2. Azizi, F., Rahmani, M., Emami, H.andMadjid, M.(2000).TehranLipidandGlucoseStudy: Rationale and Design. CVD prevention 3, 242-247.
3. Azizi, F., Rahmani, M., Emami, H., Mirmiran, P., Hajipour, R. and Madjid, M. (2002). Cardiovascular Risk Factors in an Iranian Urban Population: Tehran Lipid and Glucose Study (Phase1). Sozial-und pr-ventivmedizin, 476, 408-426. [DOI:10.1007/s000380200008]
4. Barreda, L., Gannoun, A. and Saracco, J. (2007). Some Extensions of Multivariate SIR. Journal of Statistical Computation and Simulation, 77, 1-17. [DOI:10.1080/10629360600687840]
5. Bennett, S. (1983). Analysis of Survival Data by the Proportional Odds Model. Statistics in Medicine, 2, 273-277. [DOI:10.1002/sim.4780020223]
6. Beran, R.Z.(1981).NonparametricRegressionwithRandomlyCensoredSurvivalData. Technical Report, Univ. California, Berkeley.
7. Castelli W.P. (1984). Epidemiology of Coronary Heart Disease: the Framingham Study. American journal of medicine, 76, 4-12. [DOI:10.1016/0002-9343(84)90952-5]
8. Christiansen D.H., Hosking, J.D., Dannenberg, A.L., and Williams, O.D. (1990). Computer Assisted Data Collection in Multicenter Epidemiologic Epidemiologic Research: the Atherosclerosis Risk in Communities (ARIC) Study. Controlled Clinical Trials, 11, 101115. [DOI:10.1016/0197-2456(90)90004-L]
9. Cook, R.D. (1998). Regression Graphics. Wiley, New York. [DOI:10.1002/9780470316931]
10. Cook, R.D. (1996). Graphics for Regressions with a Binary Response. Wiley, New York. [DOI:10.1080/01621459.1996.10476968]
11. Cox, D.R.(1972).Regression Models and Life Tables(withDiscussion). Journal of the Royal Statistical Society, Series B 34, 187-220 . [DOI:10.1111/j.2517-6161.1972.tb00899.x]
12. Cox, D.R., and Oakes, D. (1984). Analysis of Survival Data. Chapman and Hall, New York.
13. Efroymson, M. (1960). Multiple Regression Analysis. In Mathematical Methods for Digital Computers (eds A. Ralston and H. Wilf). Wiley, New York.
14. Bagherzadeh-Khiabani,F.,Ramezankhani,A.,Azizi,F.,Hadaegh,F.,Steyerberg,E.W.,and Khalili, D. (2015). A Tutorial on Variable Selection for Clinical Prediction Models: Feature Selection Methods in Data Mining Could Improve the Results. Journal of Clinical Epidemiology, 71, 76-85. [DOI:10.1016/j.jclinepi.2015.10.002]
15. Liu,H.,andYu,L.(2005).TowardIntegratingFeatureSelectionAlgorithmsforClassification and Clustering. IEEE Trans Knowl Data Eng, 17, 491-502. [DOI:10.1109/TKDE.2005.66]
16. Saeys, Y., Inza, I., and Larra naga, P.A. (2007). Toward Integrating Feature Selection Algorithms for Classification and Clustering. Bioinformatics, 23, 2507-2517. [DOI:10.1093/bioinformatics/btm344]
17. Keil, U. (2005). Das Weltweite WHO-MONICAProjekt: Ergebnisse und Ausblic [The Worldwide WHO MONICA Project: Results and Perspectives]. Gesundheitswesen, 67, S38-45. [DOI:10.1055/s-2005-858240]
18. Li, K.C. (1991). Sliced Inverse Regression for Dimension Reduction (with Discussion). Journal of the American Statistical Association, 86, 316-327. [DOI:10.1080/01621459.1991.10475035]
19. Li, L. (2007). Sparse Sufficient Dimension Reduction. Biometrika, 94, 603-613. [DOI:10.1093/biomet/asm044]
20. Li, K.C., Wang, J.L., and Chen, C.H. (1999). Dimension Reduction for Censored Regression Data. The Annals of Statistics, 27, 1-23. [DOI:10.1214/aos/1018031097]
21. Li, L., and Li, H. (2004). Dimension Reduction Methods for Microarrays with Application to Censored Survival Data. Bioinformatics, 20, 3406-3412. [DOI:10.1093/bioinformatics/bth415]
22. Li, L., Simonoff, J.S., and Tsai, C.L. (2007). Tobit Model Estimation and Sliced Inverse Regression. Statistical Modelling, 7, 107-123. [DOI:10.1177/1471082X0700700201]
23. Lue, H.H. (2009). Sliced Inverse Regression for Multivariate Response Regression. J. Statist. Plann. Inference, 139, 2656-2664. [DOI:10.1016/j.jspi.2008.12.006]
24. Lu, W., and Li, L. (2011). Sufficient Dimension Reduction for Censored Regressions. Journal of the International Biometric society, 67, 513-523. [DOI:10.1111/j.1541-0420.2010.01490.x]
25. Li, L., and Lu, W. (2008). Sufficient Dimension Reduction with Missing Predictors. Journal of the American Statistical Association, 03(482), 822-831. [DOI:10.1198/016214508000000283]
26. Nabipour, I., Amiri, M., Imami, S.R., Jahfari, S.M., Shafeiae, E., Nosrati, A., Iranpour, D., and Soltanian, A.R. (2007). The Metabolic Syndrome and Nonfatal Ischemic Heart Disease; a Population-Based Study. International Journal of Cardiology, 118, 48-53 . [DOI:10.1016/j.ijcard.2006.06.017]
27. Nadkarni, N.V., Zhao, Y., and Kosorok, M. (2011). Inverse Regression Estimation for Censored Data. Journal of the American Statistical Association, 106, 178-190. [DOI:10.1198/jasa.2011.tm08250]
28. Reddy K.S., and Yusuf, S. (1998). Emerging Epidemic of Cardiovascular Disease in Developing Countries. Circulation, 97, 596-601. [DOI:10.1161/01.CIR.97.6.596]
29. Rastin,A.,andFaridrohani,M.(2020).ModificationofSlicedInverseRegressiontoCensored Survival Data. J. of Stat. Sci., 13, 427-440. [DOI:10.29252/jss.13.2.427]
30. Rastin, A., Faridrohani, M., Momenan, A., Eskandari, F., and Khalili, D. (2019). Analysis of Censored Survival Data with Dimension Reduction Methods: Tehran Lipid and Glucose Study. And ishe, 23, 17-25.
31. Saracco,J.(2005).AsymptoticsforPooledMarginalSlicingEstimatorBasedonSIRα. Journal of Multivariate Analysis, 96, 117-135. [DOI:10.1016/j.jmva.2004.10.003]
32. Shao, Y., Cook, R.D., and Weisberg, S. (2009). Partial Central Subspace and Sliced Average Variance Estimation. J. Statist. Plann. Inference, 139, 952-961. [DOI:10.1016/j.jspi.2008.06.002]
33. Thom, T.J. et al. (1998). Incidence, Prevalence and Mortality of Cardiovascular Disease in the United States. Hurst's the heart, 9th ed. McGraw-Hill, New York.
34. Tibshirani, R.(1997).The Lasso Method for Variable Selection in the Cox Model. Stat. Med, 16, 385-395. https://doi.org/10.1002/(SICI)1097-0258(19970228)16:4<385::AID-SIM380>3.0.CO;2-3 [DOI:10.1002/(SICI)1097-0258(19970228)16:43.0.CO;2-3]
35. World Health Organization, Eastern Mediterranean Regional Office (1995). Prevention and control of cardiovascular diseases. Alexandria: WHO-EMRO: 24.
36. Yoo, J.K.(2016a).Tutorial: Dimension Reduction in Regression with a Notion of Sufficiency. Communications for Statistical Applications and Methods, 23, 93-103. [DOI:10.5351/CSAM.2016.23.2.093]
37. Yoo, J.K. (2016b). Tutorial: Methodologies for sufficient dimension reduction in regression. Communications for Statistical Applications and Methods 23, 105-117. [DOI:10.5351/CSAM.2016.23.2.105]

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