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A new approach for regression analysis of multivariate current status data with informative censoring. (English) Zbl 1530.62029

Summary: Regression analysis of interval-censored failure time data has recently attracted a great deal of attention partly due to their increasing occurrences in many fields. In this paper, we discuss a type of such data, multivariate current status data, where in addition to the complex interval data structure, one also faces dependent or informative censoring. For inference, a sieve maximum likelihood estimation procedure is developed and the proposed estimators of regression parameters are shown to be asymptotically consistent and efficient. For the implementation of the method, an EM algorithm is provided, and the results from an extensive simulation study demonstrate the validity and good performance of the proposed inference procedure. For an illustration, the proposed approach is applied to a tumorigenicity experiment.

MSC:

62N02 Estimation in survival analysis and censored data
62N01 Censored data models
62P10 Applications of statistics to biology and medical sciences; meta analysis
Full Text: DOI

References:

[1] Chang, I.S., Wen, C.C., Wu, Y.J.: A profile likelihood theory for the correlated gamma-frailty model with current status family data. Statistica Sinica 17, 1023-1046(2007) · Zbl 1133.62021
[2] Chen, CM; Lu, TFC; Chen, MH; Hsu, CM, Semiparametric transformation models for current status data with informative censoring, Biom. J., 19, 641-656 (2012) · Zbl 1400.62061 · doi:10.1002/bimj.201100131
[3] Chen, CM; Wei, JC; Hsu, CM; Lee, MY, Regression analysis of multivariate current status data with dependent censoring: application to ankylosing spondylitis data, Stat. Med., 33, 772-785 (2014) · doi:10.1002/sim.5985
[4] Chen, MH; Tong, XW; Sun, J., The proportional odds model for multivariate interval-censored failure time data, Stat. Med., 26, 5147-5161 (2007) · doi:10.1002/sim.2907
[5] Cox, DR, Regression analysis and life tables (with discussion), J. R. Stat. Soc. B, 34, 187-220 (1972) · Zbl 0243.62041
[6] Dunson, DB; Dinse, GE, Bayesian models for multivariate current status data with informative censoring, Biometrics, 58, 79-88 (2002) · Zbl 1209.62031 · doi:10.1111/j.0006-341X.2002.00079.x
[7] Efron, B., Censored data and the bootstrap, J. Am. Stat. Assoc., 76, 312-319 (1981) · Zbl 0461.62039 · doi:10.1080/01621459.1981.10477650
[8] Finkelstein, DM, A proportional hazards model for interval-censored failure time data, Biometrics, 42, 845-854 (1986) · Zbl 0618.62097 · doi:10.2307/2530698
[9] Goggins, WB; Finkelstein, DM, A proportional hazards model for multivariate interval-censored failure time data, Biometrics, 56, 940-943 (2000) · Zbl 1060.62617 · doi:10.1111/j.0006-341X.2000.00940.x
[10] Guo, G.; Rodriguez, G., Estimating a multivariate proportional hazards model for clustered data using the EM algorithm, with an application to child survival in Guatemala, J. Am. Stat. Assoc., 87, 969-976 (1992) · doi:10.1080/01621459.1992.10476251
[11] Hu, T.; Zhou, Q.; Sun, J., Regression analysis of bivariate current status data under the proportional hazards model, Can. J. Stat., 45, 410-424 (2017) · Zbl 1474.62341 · doi:10.1002/cjs.11344
[12] Jewell, NP; van der Laan, MJ; Lei, X., Bivariate current status data with univariate monitoring times, Biometrika, 92, 847-862 (2005) · Zbl 1160.62353 · doi:10.1093/biomet/92.4.847
[13] Kalbfleisch, JD; Prentice, RL, The Statistical Analysis of Failure Time Data (2002), New York: Wiley, New York · Zbl 1012.62104 · doi:10.1002/9781118032985
[14] Li, SW; Hu, T.; Wang, PJ; Sun, J., Regression analysis of current status data in the presence of dependent censoring with applications to tumorigenicity experiments, Comput. Stat. Data Anal., 110, 75-86 (2017) · Zbl 1466.62144 · doi:10.1016/j.csda.2016.12.011
[15] Lin, DY; Oakes, D.; Ying, Z., Additive hazards regression with current status data, Biometrika, 85, 289-298 (1998) · Zbl 0938.62121 · doi:10.1093/biomet/85.2.289
[16] Liu, YQ; Hu, T.; Sun, J., Regression analysis of current status data in the presence of a cured subgroup and dependent censoring, Lifetime Data Anal., 23, 626-650 (2017) · Zbl 1468.62392 · doi:10.1007/s10985-016-9382-z
[17] Lu, M.; Zhang, Y.; Huang, J., Estimation of the mean function with panel count data using monotone polymial splines, Biometrika, 94, 705-706 (2007) · Zbl 1135.62069 · doi:10.1093/biomet/asm057
[18] Ma, L.; Hu, T.; Sun, J., Sieve maximum likelihood regression analysis of dependent current status data, Biometrika, 85, 649-658 (2015) · Zbl 1452.62832
[19] National Toxicology Program: Toxicology and carcinogenesis studies of chloroprene (case no. 126-99-8) in \(F344/N\) rats and \(B6C3F_1\) mice (inhalation studies). Technical Report 467. U.S. Department of Health and Human Services, Public Health Service, National Institutes of Health, Bethesda, MD (1998)
[20] Pakes, A.; Pollard, D., simulation and the asymptotic of optimization estimators, Econometrica, 57, 1027-1057 (1989) · Zbl 0698.62031 · doi:10.2307/1913622
[21] Ramsay, JO, Monotone regression splines in action, Stat. Sci., 3, 425-441 (1988)
[22] Shen, X.; Wrong, W., Convergence rate of sieve estimates, Ann. Stat., 57, 580-615 (1994) · Zbl 0805.62008
[23] Su, YR; Wang, JL, Semiparametric efficient estimation for shared-frailty models with doubly-censored clustered data, Ann. Stat., 44, 1298-1331 (2016) · Zbl 1341.62285 · doi:10.1214/15-AOS1406
[24] Sun, J., The Statistical Analysis of Interval-Censored Failure Time Data (2006), New York: Springer, New York · Zbl 1127.62090
[25] Van Der Vaart, AW, Asymptotic Statistics (1998), New York: Cambridge University Press, New York · Zbl 0910.62001 · doi:10.1017/CBO9780511802256
[26] Van Der Vaart, AW; Wellner, JA, Weak Convergence and Empirical Processes (1996), New York: Springer, New York · Zbl 0862.60002 · doi:10.1007/978-1-4757-2545-2
[27] Wang, N.; Wang, L.; McMahan, CS, Regression analysis of bivariate current status data under the Gamma-frailty proportional hazards model using the EM algorithm, Comput. Stat. Data Anal., 83, 140-150 (2015) · Zbl 1507.62178 · doi:10.1016/j.csda.2014.10.013
[28] Wen, CC; Chen, YH, Nonparametric maximum likelihood analysis of clustered current status data with the gamma-frailty Cox model, Comput. Stat. Data Anal., 83, 140-150 (2011) · Zbl 1284.62067
[29] Wei, LJ; Lin, DY; Weissfeld, L., Regression analysis of multivariate incomplete failure time data by modeling marginal distributions, J. Am. Stat. Assoc., 84, 1065-1073 (1989) · doi:10.1080/01621459.1989.10478873
[30] Zhang, Z.; Sun, J.; Sun, L., Statistical analysis of current data with informative observation times, Stat. Med., 24, 1399-1407 (2005) · doi:10.1002/sim.2001
[31] Zhao, S.; Hu, T.; Ma, L.; Wang, P.; Sun, J., Regression analysis of informative current status data with the additive hazards model, Lifetime Data Anal., 21, 241-258 (2015) · Zbl 1322.62296 · doi:10.1007/s10985-014-9303-y
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