A New Approach for Regression Analysis of Multivariate Current Status Data with Informative Censoring

Abstract

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.

Keywords

Additive hazards model / Current status data / Informative censoring

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)

[2] Chen CM, Lu TFC, Chen MH, Hsu CM. Semiparametric transformation models for current status data with informative censoring. Biom. J.. 2012, 19 641-656

[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.. 2014, 33 772-785

[4] Chen MH, Tong XW, Sun J. The proportional odds model for multivariate interval-censored failure time data. Stat. Med.. 2007, 26 5147-5161

[5] Cox DR. Regression analysis and life tables (with discussion). J. R. Stat. Soc. B. 1972, 34 187-220

[6] Dunson DB, Dinse GE. Bayesian models for multivariate current status data with informative censoring. Biometrics. 2002, 58 79-88

[7] Efron B. Censored data and the bootstrap. J. Am. Stat. Assoc.. 1981, 76 312-319

[8] Finkelstein DM. A proportional hazards model for interval-censored failure time data. Biometrics. 1986, 42 845-854

[9] Goggins WB, Finkelstein DM. A proportional hazards model for multivariate interval-censored failure time data. Biometrics. 2000, 56 940-943

[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.. 1992, 87 969-976

[11] Hu T, Zhou Q, Sun J. Regression analysis of bivariate current status data under the proportional hazards model. Can. J. Stat.. 2017, 45 410-424

[12] Jewell NP, van der Laan MJ, Lei X. Bivariate current status data with univariate monitoring times. Biometrika. 2005, 92 847-862

[13] Kalbfleisch JD, Prentice RL. The Statistical Analysis of Failure Time Data. 2002 2 New York: Wiley

[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.. 2017, 110 75-86

[15] Lin DY, Oakes D, Ying Z. Additive hazards regression with current status data. Biometrika. 1998, 85 289-298

[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.. 2017, 23 626-650

[17] Lu M, Zhang Y, Huang J. Estimation of the mean function with panel count data using monotone polymial splines. Biometrika. 2007, 94 705-706

[18] Ma L, Hu T, Sun J. Sieve maximum likelihood regression analysis of dependent current status data. Biometrika. 2015, 85 649-658

[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. 1989, 57 1027-1057

[21] Ramsay JO. Monotone regression splines in action. Stat. Sci.. 1988, 3 425-441

[22] Shen X, Wrong W. Convergence rate of sieve estimates. Ann. Stat.. 1994, 57 580-615

[23] Su YR, Wang JL. Semiparametric efficient estimation for shared-frailty models with doubly-censored clustered data. Ann. Stat.. 2016, 44 1298-1331

[24] Sun J. The Statistical Analysis of Interval-Censored Failure Time Data. 2006 New York: Springer

[25] Van Der Vaart AW. Asymptotic Statistics. 1998 New York: Cambridge University Press

[26] Van Der Vaart AW, Wellner JA. Weak Convergence and Empirical Processes. 1996 New York: Springer

[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.. 2015, 83 140-150

[28] Wen CC, Chen YH. Nonparametric maximum likelihood analysis of clustered current status data with the gamma-frailty Cox model. Comput. Stat. Data Anal.. 2011, 83 140-150

[29] Wei LJ, Lin DY, Weissfeld L. Regression analysis of multivariate incomplete failure time data by modeling marginal distributions. J. Am. Stat. Assoc.. 1989, 84 1065-1073

[30] Zhang Z, Sun J, Sun L. Statistical analysis of current data with informative observation times. Stat. Med.. 2005, 24 1399-1407

[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.. 2015, 21 241-258