Publication: Modified Cox regression with current status data
Full text at PDC
Advisors (or tutors)
In survival analysis, the lifetime under study is not always observed. In certain applications, for some individuals, the value of the lifetime is only known to be smaller or larger than some random duration. This framework represent an exten sion of standard situations where the lifetime is only left or only right randomly censored. We consider the case where the independent observation units include also some covariates, and we propose two semiparametric regression models. The new models extend the standard Cox proportional hazard model to the situation of a more complex censoring mechanism. However, like in Cox’s model, in both models the nonparametric baseline hazard function still could be expressed as an explicit functional of the distribution of the observations. This allows to define the estimator of the finite-dimensional parameters as the maximum of a likelihood-type criterion which is an explicit function of the data. Given an estimate of the finite dimensional parameter, the estimation of the baseline cumulative hazard function is straightforward.
 Braekers, R. & Grouwels, Y. (2015). A semi-parametric Cox’s regression model for zero-inflated left-censored time to event data. Communications in Statistics – The�ory and Methods 45(7), 1969–1988.  Cox, D.R. (1972). Regression models and life tables (with discussion). J. Roy. Statist. Soc. Ser. B 34, 187–220.  Cox, D.R. (1975). Partial likelihood. Biometrika 62, 269–276.  Fang, H.B., Li, G., & Sun, J. (2005). Maximum likelihood estimation in a semi�parametric Logistic/proportional-hazards mixture model. Scand. J. Statist. 32, 59–75.  Gill, R.D. (1994). Lectures on survival analysis. Lectures on probability theory: Ecole d’t de probabilits de Saint-Flour XXII. Lecture notes in mathematics 1581. Springer.  Gill, R.D., Johansen, S. (1990). A Survey of Product-Integration with a View Toward Application in Survival Analysis. Ann. Statist. 18(4), 1501–1555.  Huang, J. (1999). Asymptotic properties of nonparametric estimation based on partly interval-censored data. Statistica Sinica 9, 501–519.  Kim, J.S. (2003). Maximum likelihood estimation for the proportional hazards models with partly interval-censored data. J. Royal Stat. Soc. B 65, 489–502.  Kim, Y., Kim, B., Jang, W. (2010). Asymptotic properties of the maximum like�lihood estimator for the proportional hazards model with doubly censored data. J. Multivar. Anal. 101, 1339–1351.  Kosorok, M.D. (2008). Introduction to empirical process and semiparametric in�ference. Springer Series in Statistics, Springer: New-York.  Link, C.L. (1984). Confidence intervals for the survival function using Cox’s proportional-hazard model with covariates. Biometrics 40, 601–609.  Murphy, S. A., & A. W. van der Vaart (2000). On profile likelihood. J. Amer. Statist. Assoc. 95(450), 449–465.  Patilea, V., & Rolin, J.-M. (2006a). Product-limit estimators of the survival function for two modified forms of current-status data. Bernoulli 12, 801–819.  Patilea, V., & Rolin, J.-M. (2006b). Product-limit estimators of the survival function with twice censored data. Ann. Statist. 34, 925–938.  Turnbull, B.W. (1974). Nonparametric estimation of a survivorship function with doubly censored data. J. Amer. Statist. Assoc. 69, 169–173.  van der Vaart, A.D. (1998). Asymptotic Statistics. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, Cambridge.  van der Vaart, A.D., & Wellner, J.A. (1996). Weak convergence and empirical processes. Springer Series in Statistics. Springer-Verlag, New-York.  van der Vaart, A.D., & Wellner, J.A. (2007). Empirical processes indexed by estimated functions. In Asymptotics: Particles, Processes and Inverse Problems, IMS Lecture NotesMonograph Series, Vol. 55 (2007) 234–252.  Zheng, D., Yin, G. & Ibrahim, J.G. (2006). Semiparametric Transformation Models for Survival Data With a Cure Fraction. J. Amer. Statist. Assoc. 101(474), 670–684.