An additive Cox model for coronary heart disease study

References

• P.K. Andersen and R.D. Gill, Cox's regression model for counting processes: A large sample study, Ann. Stat. 10 (1982), pp. 1100–1120. doi: 10.1214/aos/1176345976
   Web of Science ®Google Scholar
• R. Andraws, J.S. Berger, and D.L. Brown, Effects of antibiotic therapy on outcomes of patients with coronary artery disease: A meta-analysis of randomized controlled trials, JAMA 293 (2005), pp. 2641–2647. doi: 10.1001/jama.293.21.2641
   PubMed Web of Science ®Google Scholar
• J.L. Andreassi, Psychophysiology: Human Behavior and Physiological Response, L Erlbaum, Mahwah, NJ, 2000, p. 287.
   Google Scholar
• A. Antoniadis and J. Fan, Regularization of wavelet approximations (with discussion), J. Am. Stat. Assoc. 96 (2001), pp. 939–967. doi: 10.1198/016214501753208942
   Web of Science ®Google Scholar
• J.M. Begun, W.J. Hall, W.-M. Huang, and J.A. Wellner, Information and asymptotic efficiency in parametric-nonparametric models, Ann. Stat. 11 (1983), pp. 432–452. doi: 10.1214/aos/1176346151
   Web of Science ®Google Scholar
• R. Bender, T. Augustin, and M. Blettner, Generating survival times to simulate Cox proportional hazards models, Stat. Med. 34 (2005), pp. 207–228.
   Google Scholar
• J. Bradic and R. Song, Gaussian Oracle inequalities for structured selection in non-parametric Cox model, preprint (2012). Available at: arXiv:1207.4510.
   Google Scholar
• N. Breslow, Contribution to the discussion paper by D.R. Cox, J. R. Stat. Soc. B 34 (1972), pp. 187–220.
   Google Scholar
• N. Breslow, Covariance analysis of censored survival data, Biometrics 30 (1974), pp. 89–99. doi: 10.2307/2529620
   PubMed Web of Science ®Google Scholar
• D.R. Cox, Regression models and life tables (with discussion), J. R. Stat. Soc. B 34 (1972), pp. 187–220.
   Google Scholar
• A. Chatterjee and S.N. Lahiri, Bootstrapping LASSO estimators, J. Amer. Statist. Assoc. 106 (2011), pp. 608–625. doi: 10.1198/jasa.2011.tm10159
   Web of Science ®Google Scholar
• K. Chen, H. Lin, and Y. Zhou, Efficient estimation for the Cox model with varying coefficients, Biometrika 2 (2012), pp. 379–392. doi: 10.1093/biomet/asr081
   Web of Science ®Google Scholar
• C. de Boor, A Practical Guide to Splines, Revised ed., Springer, New York, 2001.
   Google Scholar
• D.L. Donoho and I.M. Johnston, Ideal spatial adaptation by wavelet shrinkage, Biometrika 81 (1994), pp. 425–455. doi: 10.1093/biomet/81.3.425
   Web of Science ®Google Scholar
• J. Fan, Comment on “Wavelets in statistics: A review” by A. Antoniadis, J. Ital. Statist. Assoc. 6 (1997), pp. 131–138. doi: 10.1007/BF03178906
   Google Scholar
• J. Fan and I. Gijbels, Local Polynomial Modeling and Its Applications, Chapman & Hall, London, 1996.
   Google Scholar
• J. Fan and R. Li, Variable selection via non-concave penalized likelihood and its oracle properties, J. Amer. Statist. Assoc. 96 (2001), pp. 1348–1360. doi: 10.1198/016214501753382273
   Web of Science ®Google Scholar
• J. Fan and R. Li, Variable selection for Cox's proportional hazards model and frailty model, Ann. Statist. 96 (2002), pp. 1348–1360.
   Google Scholar
• J. Fan, I. Gijbels, and M. King, Local likelihood and local partial likelihood in hazard regression, Ann. Statist. 25 (1997), pp. 1661–1690. doi: 10.1214/aos/1031594736
   Web of Science ®Google Scholar
• J. Fan, H. Lin, and Y. Zhou, Local partial-likelihood estimation for lifetime data, Ann. Statist. 34 (2006), pp. 290–325. doi: 10.1214/009053605000000796
   Web of Science ®Google Scholar
• J.A. Finegold, P. Asaria, and D.P. Francis, Mortality from ischaemic heart disease by country, region, and age: Statistics from World Health Organization and United Nations, Int. J. Cardiol. 168 (2012), pp. 934–945. doi: 10.1016/j.ijcard.2012.10.046
   PubMed Web of Science ®Google Scholar
• D. Gamerman, Markov chain Monte Carlo for dynamic generalised linear models, Biometrika 85 (1991), pp. 215–227. doi: 10.1093/biomet/85.1.215
   Web of Science ®Google Scholar
• R. Gentleman and J. Crowley, Local full likelihood estimation for the proportional hazards model, Biometrics 47 (1991), pp. 1283–1296. doi: 10.2307/2532386
   PubMed Web of Science ®Google Scholar
• T. Gorgens, Average derivatives for hazard functions, Econom. Theory 20 (2004), pp. 437–463. doi: 10.1017/S0266466604203012
   Web of Science ®Google Scholar
• R.J. Gray, Flexible methods for analyzing survival data using splines, with applications to breast cancer prognosis, J. Amer. Statist. Assoc. 87 (1992), pp. 942–951. doi: 10.1080/01621459.1992.10476248
   Web of Science ®Google Scholar
• C. Gu, Penalized likelihood hazard estimation: A general procedure, Statist. Sin. 6 (1996), pp. 861–876.
   Web of Science ®Google Scholar
• C. Gu, Smoothing Spline ANOVA Models, Springer, New York, 2002.
   Google Scholar
• J. Huang and L. Liu, Polynomial spline estimation and inference of proportional hazards regression models with flexible relative risk form, Biometrika 62 (2006), pp. 269–276.
   Google Scholar
• S. Johansen, An extension of Cox's regression model, Int. Statist. Rev. 51 (1983), pp. 165–174. doi: 10.2307/1402746
   Web of Science ®Google Scholar
• M. Kivimäki, S.T. Nyberg, G.D. Batty, E.I. Fransson, K. Heikkilä, L. Alfredsson, J.B. Bjorner, M. Borritz, H. Burr, A. Casini, E. Clays, D. De Bacquer, N. Dragano, J.E. Ferrie, G.A. Geuskens, M. Goldberg, M. Hamer, W.E. Hooftman, I.L. Houtman, M. Joensuu, M. Jokela, F. Kittel, A. Knutsson, M. Koskenvuo, A. Koskinen, A. Kouvonen, M. Kumari, I.E. Madsen, M.G. Marmot, M.L. Nielsen, M. Nordin, T. Oksanen, J. Pentti, R. Rugulies, P. Salo, J. Siegrist, A. Singh-Manoux, S.B. Suominen, A. Väänänen, J. Vahtera, M. Virtanen, P.J. Westerholm, H. Westerlund, M. Zins, A. Steptoe, and T. Theorell, Job strain as a risk factor for coronary heart disease: a collaborative meta-analysis of individual participant data, Lancet 380 (2012), pp. 1491–1497. doi: 10.1016/S0140-6736(12)60994-5.
   PubMed Web of Science ®Google Scholar
• K. Knight and W. Fu, Asymptotics for LASSO-type estimators, Ann. Statist. 28 (2000), pp. 1356–1378. doi: 10.1214/aos/1015957397
   Web of Science ®Google Scholar
• S. Kong and B. Nan, Non-asymptotic oracle inequalities for the high-dimensional Cox regression via LASSO, Statist. Sin. 24 (2014), pp. 25–42.
   PubMed Web of Science ®Google Scholar
• E.T. Lee, B.V. Howard, W. Wang, T.K. Welty, J.M. Galloway, L.G. Best, R.R. Fabsitz, Y. Zhang, J. Yeh, and R.B. Devereux, Prediction of coronary heart disease in a population with high prevalence of diabetes and albuminuria: The Strong Heart Study, Circulation 113 (2006), pp. 2897–2905. doi: 10.1161/CIRCULATIONAHA.105.593178
   PubMed Web of Science ®Google Scholar
• I.-M. Lee, E.J. Shiroma, F. Lobelo, P. Puska, S.N. Blair, and P.T. Katzmarzyk, Effect of physical inactivity on major non-communicable diseases worldwide: An analysis of burden of disease and life expectancy, Lancet 380 (2012), pp. 219–229. doi: 10.1016/S0140-6736(12)61031-9.
   PubMed Web of Science ®Google Scholar
• J. Li and R. Zhang, Partially varying coefficient single index proportional hazards regression models, Comput. Statist. Data Anal. 55 (2011), pp. 389–400. doi: 10.1016/j.csda.2010.05.007
   Web of Science ®Google Scholar
• H. Lin, M. Tan, and Y. Li, A semiparametrically efficient estimator of single-index varying coefficient Cox proportional model, Statist. Sin. (2016). doi: 10.5705/ss.202015.0062.
   PubMed Web of Science ®Google Scholar
• R. Lockhart, J. Taylor, R.J. Tibshirani, and R. Tibshirani, A significance test for the LASSO, Ann. Statist. 42 (2014), pp. 413–468. doi: 10.1214/13-AOS1175
   PubMed Web of Science ®Google Scholar
• X. Lu, G. Chen, X.-K. Song, and R.S. Singh, A class of partially linear single-index survival models, Can. J. Statist. 34 (2006), pp. 97–112. doi: 10.1002/cjs.5550340108
   Web of Science ®Google Scholar
• T. Martinussen, T.H. Scheike, and I.M. Skovgaard, Efficient estimation of fixed and time-varying covariates effects in multiplicative intensity models, Scand. J. Stat. 29 (2000), pp. 57–74.
   Google Scholar
• L. Marzec and P. Marzec, A partly parametric additive risk model, Biometrika 81 (1994), pp. 901–908.
   Web of Science ®Google Scholar
• Mayo Foundation for Medical Education and Research. (2012). Causes, Coronary artery disease, 29 June 2012. DS00064.
   Google Scholar
• S.J.H. McCann, The precocity–longevity hypothesis: Earlier peaks in career achievement predict shorter lives, Pers. Soc. Psychol. Bull. 27 (2001), pp. 1429–1439. doi: 10.1177/01461672012711004
   Web of Science ®Google Scholar
• Mount Sinai Hospital, New York. Heart attack/coronary heart disease.
   Google Scholar
• S.A. Murphy and P.K. Sen, Time-dependent coefficients in a Cox-type regression model, Stoch. Process. Appl. 39 (1991), pp. 153–180. doi: 10.1016/0304-4149(91)90039-F
   Web of Science ®Google Scholar
• J.P. Nielsen, O.B. Linton, and P.J. Bickel, On a semiparametric survival model with flexible covariate effect, Ann. Statist. 26 (1998), pp. 215–241. doi: 10.1214/aos/1030563983
   Web of Science ®Google Scholar
• F. O'Sullivan, Nonparametric estimation in the Cox model, Ann. Statist. 21 (1993), pp. 124–145. doi: 10.1214/aos/1176349018
   Web of Science ®Google Scholar
• P. Saikku, M. Leinonen, L. Tenkanen, E. Linnanmäki, M.R. Ekman, V. Manninen, M. Mänttäri, M.H. Frick, and J.K. Huttunen, Chronic Chlamydia pneumoniae infection as a risk factor for coronary heart disease in the Helsinki Heart Study, Ann. Intern. Med. 116 (1992), pp. 273–278. doi: 10.7326/0003-4819-116-4-273
   PubMed Web of Science ®Google Scholar
• L. Schumaker, Spline Functions: Basic Theory, 3rd ed., Cambridge University Press, Cambridge, UK, 2007.
   Google Scholar
• N.M. Shara, H. Wang, E. Valaitis, M. Pehlivanova, E.A. Carter, H.E. Resnick, W. Wang, J.G. Umans, E.T. Lee, B.V. Howard, R.B. Devereux, and P.W.F. Wilson, Comparison of estimated glomerular filtration rates and albuminuria in predicting risk of coronary heart disease in a population with high prevalence of diabetes mellitus and renal disease, Amer. J. Cardiol. 107 (2011), pp. 399–405. doi: 10.1016/j.amjcard.2010.09.036
   PubMed Web of Science ®Google Scholar
• L.A. Sleeper and D.P. Harrington, Regression splines in the Cox model with application to covariate effects in liver disease, J. Amer. Statist. Assoc. 85 (1990), pp. 941–949. doi: 10.1080/01621459.1990.10474965
   Web of Science ®Google Scholar
• J. Sun, K.A. Kopciuk, and X. Lu, Polynomial spline estimation of partially linear single-index proportional hazards regression models, Comput. Statist. Data Anal. 53 (2008), pp. 176–188. doi: 10.1016/j.csda.2008.07.003
   Web of Science ®Google Scholar
• L. Tian, D. Zucker, and L.J. Wei, On the Cox model with time-varying regression coefficients, J. Amer. Statist. Assoc. 100 (2005), pp. 172–183. doi: 10.1198/016214504000000845
   Web of Science ®Google Scholar
• R. Tibshirani and T. Hastie, Local likelihood estimation, J. Amer. Statist. Assoc. 82 (1987), pp. 559–567. doi: 10.1080/01621459.1987.10478466
   Web of Science ®Google Scholar
• R. Tibshirani, Regression shrinkage and selection via the LASSO, J. R. Statist. Soc. B 58 (1996), pp. 267–288.
   Google Scholar
• R. Tibshirani, The LASSO method for variable selection in the Cox model, Statist. Med. 16 (1997), pp. 385–395. doi: 10.1002/(SICI)1097-0258(19970228)16:4<385::AID-SIM380>3.0.CO;2-3
   PubMed Web of Science ®Google Scholar
• A.A. Tsaitis, A large sample study of Cox's regression model, Ann. Statist. 9 (1981), pp. 93–108. doi: 10.1214/aos/1176345335
   Web of Science ®Google Scholar
• M.G. Valsecchi, D. Silvestri, and P. Sasieni, Evaluation of long-term survival: Use of diagnostics and robust estimator with Cox's proportional hazards model, Statist. Med. 15 (1996), pp. 2763–2780. doi: 10.1002/(SICI)1097-0258(19961230)15:24<2763::AID-SIM319>3.0.CO;2-O
   PubMed Web of Science ®Google Scholar
• G. Wahba, Spline Models for Observational Data, SIAM, Philadelphia, 1990.
   Google Scholar
• W. Wang, Proportional hazards regression model with unknown link function and time-dependent covariates, Statist. Sin. 14 (2004), pp. 885–905.
   Web of Science ®Google Scholar
• H.-X. Wang, C. Leineweber, R. Kirkeeide, B. Svane, K. Schenck-Gustafsson, T. Theorell, and K. Orth-Gomér, Psychosocial stress and atherosclerosis: Family and work stress accelerate progression of coronary disease in women. The Stockholm Female Coronary Angiography Study, J. Intern. Med. 261 (2007), pp. 245–254. doi: 10.1111/j.1365-2796.2006.01759.x
   PubMed Web of Science ®Google Scholar
• P.W.F. Wilson, R.B. D'Agostino, D. Levy, A.M. Belanger, H. Silbershatz, and W.B. Kannel, Prediction of coronary heart disease using risk factor categories, Circulation 97 (1998), pp. 1837–1847. doi: 10.1161/01.CIR.97.18.1837
   PubMed Web of Science ®Google Scholar
• World Health Organization Department of Health Statistics and Informatics in the Information, Evidence and Research Cluster, The global burden of disease 2004 update, Geneva, WHO, 2004. ISBN 92-4-156371-0.
   Google Scholar
• T. Yoshida and K. Naito, Asymptotics for penalized additive B-spline regression, J. Japan Statist. 42 (2012), pp. 81–107. doi: 10.14490/jjss.42.81
   Google Scholar
• H.H. Zhang and W. Lu, Adaptive LASSO for Cox's proportional hazards model, Biometrika 94 (2007), pp. 691–703. doi: 10.1093/biomet/asm037
   Web of Science ®Google Scholar
• D.M. Zucker and A.F. Karr, Nonparametric survival analysis with time-dependent covariates: A penalized partial likelihood approach, Ann. Statist. 18 (1990), pp. 329–353. doi: 10.1214/aos/1176347503
   Web of Science ®Google Scholar