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A class of weighted estimators for additive hazards model in case-cohort studies. (English) Zbl 1305.62344

Summary: Case-cohort sampling is a commonly used and efficient method for studying large cohorts. In many situations, some covariates are easily measured on all cohort subjects, and surrogate measurements of the expensive covariates also may be observed. In this paper, to make full use of the covariate data collected outside the case-cohort sample, we propose a class of weighted estimators with general time-varying weights for the additive hazards model, and the estimators are shown to be consistent and asymptotically normal. We also identify the estimator within this class that maximizes efficiency, and simulation studies show that the efficiency gains of the proposed estimator over the existing ones can be substantial in practical situations. A real example is provided.

MSC:

62N02 Estimation in survival analysis and censored data
62N01 Censored data models
62G05 Nonparametric estimation
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[1] Barlow, W.E. Robust variance estimation for the case-cohort design. Biometrics, 50: 1064-1072 (1994) · Zbl 0825.62794 · doi:10.2307/2533444
[2] Bickel, P.J., Klaassen, C.A.J., Ritov, Y., Wellner, J.A. Efficient and Adaptive Inference in Semiparametric Models. Johns Hopkins University Press, Baltimore, 1993 · Zbl 0786.62001
[3] Borgan, O., Langholz, B., Samuelsen, S.O., Goldstein, L., Pogoda, J. Exposure stratified case-cohort designs. Lifetime Data Analysis, 6: 39-58 (2000) · Zbl 0948.62069 · doi:10.1023/A:1009661900674
[4] Breslow, N,E., Wellner, J.A. Weighted Likelihood for semiparametric models and two-phase stratified samples, with application to Cox regression. Scandinavian Journal of Statistics, 34: 86-102 (2007) · Zbl 1142.62014 · doi:10.1111/j.1467-9469.2006.00523.x
[5] Chen, H.Y. Weighted semiparametric likelihood method for fitting a proportional odds regression model to data from the case-cohort design. Journal of the American Statistical Association, 96: 1446-1457 (2001) · Zbl 1073.62525 · doi:10.1198/016214501753382354
[6] Chen, H.Y. Fitting semiparametric transformation regression models to data from a modified case-cohort design. Biometrika, 88: 255-268 (2001) · Zbl 0979.62088 · doi:10.1093/biomet/88.1.255
[7] Chen, Y.H., Zucker, D.M. Case-cohort analysis with semiparametric transformation models. Journal of Statistical Planning and Inference, 139: 3706-3717 (2009) · Zbl 1168.62088 · doi:10.1016/j.jspi.2009.04.023
[8] Chen, K. Generalized case-cohort sampling. Journal of the Royal Statistical Society (Ser. B), 63: 791-809 (2001) · Zbl 0988.62063 · doi:10.1111/1467-9868.00313
[9] Chen, K., Lo, S.H. Case-cohort and case-control analysis with Cox’s model. Biometrika, 86: 755-764 (1999) · Zbl 0940.62108 · doi:10.1093/biomet/86.4.755
[10] Cox, D.R. Regression models and life tables (with discussion). Journal of Royal Statistical Society B, 34: 187-220 (1972) · Zbl 0243.62041
[11] D’Angio, G.J., Breslow, N., Beckwith, J.B., et al. Treaatment of Wilms tumor: Results of the third National Wilms Tumor Study. Cancer, 64: 349-360 (1989) · doi:10.1002/1097-0142(19890715)64:2<349::AID-CNCR2820640202>3.0.CO;2-Q
[12] Folsom, A.R., Aleksic, N., Catellier, D., Juneja, H.S., Wu, K.K. C-reactive protein and incident coronary heart disease in the Atherosclerosis Risk in Communities (ARIC) study. American Heart Journal, 144: 233-238 (2002) · doi:10.1067/mhj.2002.124054
[13] Green, D.M., Breslow, N.E., Beckwith, J.B., et al. Comparison between single-dose and divided-dose administration of dactinomycin and doxorubicin for patients with Wilms’ tumor: a report from the National Wilms’ Tumor Study Group. Journal of Clinical Oncology, 16: 237-245 (1998)
[14] Kong, L., Cai, J., Sen, P.K. Weighted estimating equations for semiparametric transformation models with censored data from a case-cohort design. Biometrika, 91: 305-319 (2004) · Zbl 1081.62096 · doi:10.1093/biomet/91.2.305
[15] Kulich, M., Lin, D.Y. Additive hazards regression for case-cohort studies. Biometrika, 87: 73-87 (2000) · Zbl 0974.62104 · doi:10.1093/biomet/87.1.73
[16] Kulich, M., Lin, D.Y. Improving the efficiency of relative-risk estimation in case-cohort studies. Journal of the American Statistical Association, 99: 832-844 (2004) · Zbl 1117.62373 · doi:10.1198/016214504000000584
[17] Lin, D.Y., Ying Z. Cox regression with incomplete covariate measurements. Journal of the American Statistical Association, 88, 1341-1349 (1993) · Zbl 0794.62073 · doi:10.1080/01621459.1993.10476416
[18] Lin, D.Y., Ying Z. Semiparametric analysis of the additive risk model. Biometrika, 81: 61-71 (1994) · Zbl 0796.62099 · doi:10.1093/biomet/81.1.61
[19] Lu, W., Tsiatis, A.A. Semiparametric transformation models for the case-cohort study. Biometrika, 93: 207-214 (2006) · Zbl 1152.62084 · doi:10.1093/biomet/93.1.207
[20] Nokta, M.A., Holland, F., De Gruttola, V., et al. Cytomegalovirus (CMV) polymerase chain reaction profiles in individuals with advanced human immunodeficiency virus infection: Relationship to CMV disease. The Journal of Infectious Diseases, 185: 1717-1722 (2002) · doi:10.1086/340651
[21] Pollard, D. Empirical Processes: Theory and Applications. Hayward, CA: Institute of Mathematical Statistics, 1990 · Zbl 0741.60001
[22] Prentice, R.L. A case-cohort design for epidemiologic cohort studies and disease prevention trials. Biometrika, 73: 1-11 (1986) · Zbl 0595.62111 · doi:10.1093/biomet/73.1.1
[23] Qi, L., Wang, C.Y., Prentice, R.L. Weighted estimators for proportional hazards regression with missing covariates. Journal of the American Statistical Association, 100: 1250-1263 (2005) · Zbl 1117.62413 · doi:10.1198/016214505000000295
[24] Rasmussen, M.L., Folsom, A.R., Catellier, D.J., Tsai, M.Y., Garg, U., Eckfeldt, J.H. A prospective study of coronary heart disease and the hemochromatosis gene (HFE) C282Y mutation: The Atherosclerosis Risk in Communities (ARIC) study. Atherosclerosis, 154: 739-746 (2001) · doi:10.1016/S0021-9150(00)00623-7
[25] Robins, J.M., Rotnitzky, A., Zhao, L.P. Estimation of regression coefficients when some regressors are not always observed. Journal of the American Statistical Association, 89: 846-866 (1994) · Zbl 0815.62043 · doi:10.1080/01621459.1994.10476818
[26] Self, S.G., Prentice, R.L. Asymptotic distribution theory and efficiency results for case-cohort studies. Annals of Statistics, 16: 64-81 (1988) · Zbl 0666.62108 · doi:10.1214/aos/1176350691
[27] Samuelsen, S.O., Anestad, H., Skrondal, A. Stratified case-cohort analysis of general cohort sampling designs. Scandinavian Journal of Statistics, 34: 103-119 (1997) · Zbl 1142.62082 · doi:10.1111/j.1467-9469.2006.00552.x
[28] Tsiatis, A.A. Semiparametric Theory and Missing Data. Springer-Verlag, New York, 2006 · Zbl 1105.62002
[29] Zeegers, M.P.A., Goldbohm, R.A., van den Brandt, P.A. Are retinol, vitamin C, vitamin E, folate and carotenoids intake associated with bladder cancer risks? Results from the Netherlands Cohort Study. British Journal of Cancer, 85: 977-983 (2001) · doi:10.1054/bjoc.2001.1968
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