×

Statistical inference for the accelerated failure time model under two-stage generalized case-cohort design. (English) Zbl 07529908

Summary: In this article, we propose a two-stage generalized case-cohort design and develop an efficient inference procedure for the data collected with this design. In the first-stage, we observe the failure time, censoring indicator and covariates which are easy or cheap to measure, and in the second-stage, select a subcohort by simple random sampling and a subset of failures in remaining subjects from the first-stage subjects to observe their exposures which are different or expensive to measure. We derive estimators for regression parameters in the accelerated failure time model under the two-stage generalized case-cohort design through the estimated augmented estimating equation and the kernel function method. The resulting estimators are shown to be consistent and asymptotically normal. The finite sample performance of the proposed method is evaluated through the simulation studies. The proposed method is applied to a real data set from the National Wilm’s Tumor Study Group.

MSC:

62D05 Sampling theory, sample surveys
62N01 Censored data models
62J99 Linear inference, regression
62-XX Statistics
Full Text: DOI

References:

[1] Andersen, P. K.; Gill, R. D., Cox’s regression model for counting processes: a large sample study, The Annals of Statistics, 10, 4, 1100-20 (1982) · Zbl 0526.62026
[2] Breslow, N. E.; Cain, K. C., Logistic regression for two-stage case-control data, Biometrika, 75, 1, 11-20 (1988) · Zbl 0635.62110
[3] Brown, B. M.; Wang, Y. G., Induced smoothing for rank regression with censored survival times, Statistics in Medicine, 26, 4, 828-36 (2007)
[4] Cao, Y.; Yang, Q.; Yu, J., Optimal generalized case-cohort analysis with accelerated failure time model, Journal of the Korean Statistical Society, 46, 2, 298-307 (2017) · Zbl 1362.62187
[5] Chatterjee, N.; Chen, Y.; Breslow, N., A pseudo-score estimator for regression problems with two-phase sampling, Journal of the American Statistical Association, 98, 461, 158-68 (2003) · Zbl 1047.62031
[6] Chen, K., Generalized case-cohort sampling, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 63, 4, 791-809 (2001) · Zbl 0988.62063
[7] Chen, K.; Lo, S. H., Case-cohort and case-control analysis with cox’s model, Biometrika, 86, 4, 755-64 (1999) · Zbl 0940.62108
[8] Eubank, R. L., Smoothing spline and nonparametric regression (1988), New York: Dekker, New York · Zbl 0702.62036
[9] Green, D. M.; Breslow, N. E.; Beckwith, J. B.; Finklestein, J. Z.; Grundy, P. E.; Thomas, P. R.; Kim, T.; Shochat, S. J.; Haase, G. M.; Ritchey, M. L., 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, Journal of Clinical Oncology, 16, 1, 237-45 (1998)
[10] Johnson, L.; Strawderman, R., Induced smoothing for the semiparametric accelerated failure time model: asymptotics and extensions to clustered data, Biometrika, 96, 3, 577-90 (2009) · Zbl 1170.62069
[11] Kang, S.; Cai, J., Marginal hazards model for case-cohort studies with multiple disease outcomes, Biometrika, 96, 4, 887-901 (2009) · Zbl 1179.62140
[12] Kang, S.; Cai, J.; Chambless, L., Marginal additive hazards model for case-cohort studies with multiple disease outcomes: An application to the atherosclerosis risk in communities (ARIC) study, Biostatistics, 14, 1, 28-41 (2013)
[13] Kim, S.; Cai, J.; Lu, W., More efficient estimators for case-cohort studies, Biometrika, 100, 3, 695-708 (2013) · Zbl 1284.62660
[14] Kong, L.; Cai, J., Case-cohort analysis with accelerated failure time model, Biometrics, 65, 1, 135-42 (2009) · Zbl 1159.62076
[15] Kong, L.; Cai, J.; Sen, P. K., Weighted estimating equations for semiparametric transformation models with censored data from a case-cohort design, Biometrika, 91, 2, 305-19 (2004) · Zbl 1081.62096
[16] Kosorok, M. R., Introduction to empirical processes and semiparametric inference (2008), New York: Springer, New York · Zbl 1180.62137
[17] Kulich, M.; Lin, D. Y., Additive hazards regression with covariate measurement error, Journal of the American Statistical Association, 95, 449, 238-48 (2000) · Zbl 0996.62038
[18] Lin, D. Y.; Wei, L. J.; Yang, I.; Ying, Z., Semiparametric regression for the mean and rate functions of recurrent events, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 62, 4, 711-30 (2000) · Zbl 1074.62510
[19] Liu, Y. Y.; Zhou, H. B.; Cai, J., Estimated pseudopartial-likelihood method for correlated failure time data with auxiliary covariates, Biometrics, 65, 4, 1184-93 (2009) · Zbl 1180.62177
[20] Liu, Y. Y.; Wu, Y. S.; Zhou, H., Multivariate failure times regression with a continuous auxiliary covariate, Journal of Multivariate Analysis, 101, 3, 679-91 (2010) · Zbl 1181.62159
[21] Lu, W. B.; Tsiatis, A. A., Semiparametric transformation models for the case-cohort study, Biometrika, 93, 1, 207-14 (2006) · Zbl 1152.62084
[22] Nan, B.; Yu, M.; Kalbfleisch, J. D., Censored linear regression for case-cohort studies, Biometrika, 93, 4, 747-62 (2006) · Zbl 1436.62460
[23] Neyman, J., Contribution to the theory of sampling from human populations, Journal of the American Statistical Association, 33, 201, 101-16 (1938) · JFM 64.1224.02
[24] Pollard, D., Empirical processes: Theory and applications (1990), Hayward: Institute of Mathematical Statistics, Hayward · Zbl 0741.60001
[25] Prentice, R. L., A case-cohort design for epidemiologic cohort studies and disease prevention trials, Biometrika, 73, 1, 1-11 (1986) · Zbl 0595.62111
[26] Self, S. G.; Prentice, R. L., Asymptotic distribution theory and efficiency results for case-cohort studies, The Annals of Statistics, 16, 1, 64-81 (1988) · Zbl 0666.62108
[27] Shi, X. P.; Liu, Y. Y.; Wu, Y. S., Continuous auxiliary covariate in additive hazards regression for survival data, Journal of Systems Science and Complexity, 27, 6, 1247-62 (2014) · Zbl 1310.62087
[28] Sun, Y.; Qian, X.; Shou, Q.; Gilbert, P., Analysis of two-phase sampling data with semiparametric additive hazards models, Lifetime Data Analysis, 23, 3, 377-99 (2017) · Zbl 1402.62292
[29] Yin, G.; Li, H.; Zeng, D., Partially linear additive hazards regression with varying coefficients, Journal of the American Statistical Association, 103, 483, 1200-13 (2008) · Zbl 1205.62047
[30] Ying, Z., A large sample study of rank estimation for censored regression data, The Annals of Statistics, 21, 1, 76-99 (1993) · Zbl 0773.62048
[31] Yu, J.; Liu, Y.; Sandler, D. P.; Zhou, H., Statistical inference for the additive hazards model under outcome-dependent sampling, Canadian Journal of Statistics, 43, 3, 436-53 (2015) · Zbl 1321.62013
[32] Yu, J.; Liu, Y.; Cai, J.; Sandler, D. P.; Zhou, H., Outcome-dependent sampling design and inference for cox’s proportional hazards model, Journal of Statistical Planning and Inference, 178, 24-36 (2016) · Zbl 1353.62110
[33] Zeng, D.; Lin, D. Y., Efficient estimation of semiparametric transformation models for two-phase cohort studies, Journal of the American Statistical Association, 109, 505, 371-83 (2014) · Zbl 1367.62099
[34] Zhou, H.; Xu, W.; Zeng, D.; Cai, J., Semiparametric inference for data with a continuous outcome from a two-phase probability-dependent sampling scheme, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 76, 1, 197-215 (2014) · Zbl 1411.62090
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.