Semiparametric additive risks model for interval-censored data

Interval-censored event time data often arise in medical and public health studies. In such a setting, the exact time of the event of interest cannot be observed and is only known to fall between two monitoring times. Our interest focuses on the estimation of the eect of risk factors on interval-censored data under the semiparametric additive hazards model. A nonparametric step-function is used to characterize the baseline hazard function. The covariate coecien ts are estimated by maximizing the observed likelihood function, and their variances are obtained using the prole likelihood approach. We show that the proposed estimates are con- sistent and have asymptotic normal distributions. We also show that the estimator obtained for the covariate coecien t is the most ecien t estimator. Simulation studies are conducted to assess the performance of the estimate. The method is illustrated through application to a data set from an HIV study.

[1]  David R. Cox,et al.  Regression models and life tables (with discussion , 1972 .

[2]  S. Geer.  Hellinger-Consistency of Certain Nonparametric Maximum Likelihood Estimators , 1993 .

[3]  Somnath Datta,et al.  Inference Based on Imputed Failure Times for the Proportional Hazards Model with Interval-Censored Data , 1998 .

[4]  Zhiliang Ying,et al.  Additive hazards regression with current status data , 1998 .

[5]  Zhiliang Ying,et al.  Semiparametric analysis of the additive risk model , 1994 .

[6]  B. Turnbull.  The Empirical Distribution Function with Arbitrarily Grouped, Censored, and Truncated Data , 1976 .

[7]  S. Cheng,et al.  Confidence Bands for Cumulative Incidence Curves Under the Additive Risk Model , 1999, Biometrics.

[8]  W. Liu,et al.  A nonparametric two‐sample test of the failure function with interval censoring case 2 , 2001 .

[9]  Ian W. McKeague,et al.  A partly parametric additive risk model , 1994 .

[10]  A. W. van der Vaart,et al.  On Profile Likelihood , 2000 .

[11]  D. Finkelstein,et al.  A proportional hazards model for interval-censored failure time data. , 1986, Biometrics.

[12]  J. Klein,et al.  Statistical Models Based On Counting Process , 1994 .

[13]  Efficiency Considerations in the Additive Hazards Model with Current Status Data , 2001 .

[14]  Susan A. Murphy,et al.  Rejoinder to discussion of ``On Profile Likelihood''. , 2000 .

[15]  Jon A. Wellner,et al.  Weak Convergence and Empirical Processes: With Applications to Statistics , 1996 .

[16]  Jian Huang,et al.  Efficient estimation for the proportional hazards model with interval censoring , 1996 .

[17]  J Sun,et al.  A non-parametric test for interval-censored failure time data with application to AIDS studies. , 1996, Statistics in medicine.

[18]  A. J. Rossini,et al.  A Semiparametric Proportional Odds Regression Model for the Analysis of Current Status Data , 1996 .

[19]  Anastasios A. Tsiatis,et al.  Regression with interval-censored data , 1995 .

[20]  Jon A. Wellner,et al.  Two estimators of the mean of a counting process with panel count data , 2000 .