Case-cohort analysis with general additive-multiplicative hazard models
Tóm tắt
The case-cohort design is widely used in large epidemiological studies and prevention trials for cost reduction. In such a design, covariates are assembled only for a subcohort which is a random subset of the entire cohort and any additional cases outside the subcohort. In this paper, we discuss the case-cohort analysis with a class of general additive-multiplicative hazard models which includes the commonly used Cox model and additive hazard model as special cases. Two sampling schemes for the subcohort, Bernoulli sampling with arbitrary selection probabilities and stratified simple random sampling with fixed subcohort sizes, are discussed. In each setting, an estimating function is constructed to estimate the regression parameters. The resulting estimator is shown to be consistent and asymptotically normally distributed. The limiting variance-covariance matrix can be consistently estimated by the case-cohort data. A simulation study is conducted to assess the finite sample performances of the proposed method and a real example is provided.
Tài liệu tham khảo
Anderson, P.K., Gill, R.D. Cox’s regression model for counting processes: A large sample study. The Annals of Statistics, 10: 1100–1120 (1982)
Chen, K. Generalized case-cohort sampling. Journal of the Royal Statistical Society B. Statistical Methodology, 63: 791–809 (2001)
Chen, K., Lo, S.H. Case-cohort and case-control analysis with Cox’s model. Biometrika, 86: 755–764 (1999)
Chen, Y.H. Weighted semiparametric likelihood method for fitting a proportional odds regression model to data from case-cohort design. Journal of the American Statistical Association, 96: 1446–1458 (2001)
Chen, Y.H., Zucker, D.M. Case-cohort analysis with semiparametric transformation models. Journal of Statistical Planning and Inference, 139: 3706–3717 (2009)
Cox, D.R. Regression models and life tables (with discussion). Journal of the Royal Statistical Society B. Statistical Methodology, 34: 187–220 (1972)
Cox, D.R., Oakes, D. Analysis of Survival Data. Chapman and Hall, London, 1984
D’Angio, G.J., Breslow, N.E., Beckwith, J.B. Treatment of Wilms tumor: Results of the third National Wilms Tumor Study. Cancer, 64: 349–360 (1989)
Green, D.M., Breslow, N.E., Beckwith, J.B. 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)
Kong, L., Cai, J. Case-cohort analysis with accelerated failure time model. Biometrics, 65: 135–142 (2009)
Kulich, M., Lin, D.Y. Additive hazards regression for case-cohort studies. Biometrika, 87: 73–87 (2000)
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)
Lin, D.Y., Ying, Z. Cox regression with incomplete covariate measurements. Journal of the American Statistical Association, 88: 1341–1349 (1993)
Lin, D.Y., Ying, Z. Semiparametric analysis of the additive risk model. Biometrika, 81: 61–71 (1994)
Lin D.Y., Ying, Z. Semiparametric analysis of general additive-multiplicative hazard models for counting processes. The Annals of Statistics, 23: 1712–1734 (1995)
Lu, W., Tsiatis, A.A. Semiparametric transformation models for the case-cohort study. Biometrika, 93: 207–214 (2006)
Nan, B., Yu, M., Kalbfleisch, J.D. Censored linear regression for case-cohort studies. Biometrika, 93: 747–762 (2006)
Prentice, R.L. A case-cohort design for epidemiologic cohort studies and disease prevention trials. Biometrika, 73: 1–11 (1986)
Self, S.G., Prentice, R.L. Asymptotic distribution theory and efficiency results for case-cohort studies. The Annals of Statistics, 16: 64–81 (1988)
van der Vaart, A.W., Wellner, J.A. Weak Convergence and Empirical Processes. Springer-Verlag, New York, 1996