Additive Hazards Regression for Misclassified Current Status Data

Abstract

We discuss regression analysis of current status data with the additive hazards model when the failure status may suffer misclassification. Such data occur commonly in many scientific fields involving the diagnosis test with imperfect sensitivity and specificity. In particular, we consider the situation where the sensitivity and specificity are known and propose a nonparametric maximum likelihood approach. For the implementation of the method, a novel EM algorithm is developed, and the asymptotic properties of the resulting estimators are established. Furthermore, the estimated regression parameters are shown to be semiparametrically efficient. We demonstrate the empirical performance of the proposed methodology in a simulation study and show its substantial advantages over the naive method. Also an application to a motivated study on chlamydia is provided.

Keywords

EM algorithm / Maximum likelihood estimation / Misclassification / Regression analysis

References

[1] Aranda-OrdazFJ. An extension of the proportional-hazards model for grouped data. Biometrics, 1983, 39: 109-117

[2] BertrandA, LegrandC, CarrollRJ, De MeesterC, van KeilegomI. Inference in a survival cure model with mismeasured covariates using a simulation-extrapolation approach. Biometrika, 2017, 104: 31-50

[3] BuckleyJD. Additive and multiplicative models for relative survival rates. Biometrics, 1984, 40: 51-62

[4] ChenCM, LuTFC, ChenMH, HsuCM. Semiparametric transformation models for current status data with informative censoring. Biom. J., 2012, 19: 641-656

[5] ChenZ, YiGY, WuC. Marginal methods for correlated binary data with misclassified responses. Biometrika, 2011, 98: 647-662

[6] CoxDR. Regression models and life-tables. J. Roy. Stat. Soc. B, 1972, 34: 187-220

[7] DunsonDB, DinseGE. Bayesian models for multivariate current status data with informative censoring. Biometrics, 2002, 58: 79-88

[8] García-ZatteraMJ, JaraA, KomárekA. A flexible AFT model for misclassified clustered interval-censored data. Biometrics, 2016, 72: 473-483

[9] GhoshD. Goodness-of-fit methods for additive-risk models in tumorigenicity experiments. Biometrics, 2003, 59: 721-726

[10] GuX, MaY, BalasubramanianR. Semiparametric time to event models in the presence of error-prone, self-reported outcomes with application to the women’s health initiative. Ann. Appl. Stat., 2015, 9: 714-730

[11] HuangJ. Efficient estimation for the Cox model with interval censoring. Ann. Stat., 1996, 24: 540-568

[12] JamshidianM, JennrichRI. Standard errors for EM estimation. J. Roy. Stat. Soc. B, 2000, 62: 257-270

[13] Jewell, N.P., van der Laan, M.J.: Current Status Data: Review, Recent Developments and Open Problems. Advances in Survival Analysis, pp. 625–642. Ellsevier, Amsterdam (2004)

[14] JewellNP, van der LaanM, HennemanT. Nonparametric estimation from current status data with competing risks. Biometrika, 2003, 90: 183-197

[15] LiL, JaraA, García-ZatteraMJ, HansonTE. Marginal Bayesian semiparametric modeling of mismeasured multivariate interval-censored data. J. Am. Stat. Assoc., 2019, 114: 129-145

[16] LiS, HuT, SunJ. Regression analysis of misclassified current status data. J. Nonparametric Stat., 2020, 32: 1-19

[17] LiS, HuT, WangP, SunJ. 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

[18] LinDY, OakesD, YingZ. Additive hazards regression with current status data. Biometrika, 1998, 85: 289-298

[19] LinDY, YingZ. Semiparametric analysis of the additive risk model. Biometrika, 1994, 81: 61-71

[20] MaL, HuT, SunJ. Sieve maximum likelihood regression analysis of dependent current status data. Biometrika, 2015, 102: 731-738

[21] MartinussenJ, ScheikeTH. Efficient estimation in additive hazards regression with current status data. Biometrika, 2002, 89: 649-658

[22] McKeownK, JewellNP. Misclassification of current status data. Lifetime Data Anal., 2010, 16: 215-230

[23] PanD, HeH, SongX, SunL. Regression analysis of additive hazards model with latent variables. J. Am. Stat. Assoc., 2015, 511: 1148-1159

[24] PetitoLC, JewellNP. Misclassified group-tested current status data. Biometrika, 2016, 103: 801-815

[25] RossiniAJ, TsiatisAA. A semiparametric proportional odds regression model for the analysis of current status data. J. Am. Stat. Assoc., 1996, 91: 713-721

[26] Sal y Rosas, V. G., and Hughes, J. P.: Nonparametric and semiparametric analysis of current status data subject to outcome misclassification. Stat. Commun. Infect. Dis., Article no. 364 (2010)

[27] SunJThe Statistical Analysis of Interval-Censored Failure Time Data, 2006New YorkSpringer

[28] TitmanAC. Non-parametric maximum likelihood estimation of interval-censored failure time data subject to misclassification. Stat. Comput., 2016.

[29] van der VaartAWAsymptotic Statistics, 1998New YorkCambridge University Press

[30] van der VaartAW, WellnerJAWeak Convergence and Empirical Processes, 1996New YorkSpringer

[31] WangD, McMahanCS, GallagherCM. Semiparametric group testing regression models. Biometrika, 2014, 101: 587-598

[32] XuC, BainesPD, WangJ-L. Standard error estimation using the EM algorithm for the joint modeling of survival and longitudinal data. Biostatistics, 2014, 15: 731-744

[33] YanY, YiGY. A class of functional methods for error-contaminated survival data under additive hazards models with replicate measurements. J. Am. Stat. Assoc., 2016, 514: 684-695

[34] YoungJG, JewellNP, SamuelsSJ. Regression analysis of a disease onset distribution using diagnosis data. Biometrics, 2008, 64: 24-28

[35] ZengD, MaoL, LinDY. Maximum likelihood estimation for semiparametric transformation models with interval-censored data. Biometrika, 2016, 103: 253-271

Funding

National Natural Science Foundation of China(11901128)

RIGHTS & PERMISSIONS

School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature