A semiparametric probit model for case 2 interval‐censored failure time data

Interval-censored data occur naturally in many fields and the main feature is that the failure time of interest is not observed exactly, but is known to fall within some interval. In this paper, we propose a semiparametric probit model for analyzing case 2 interval-censored data as an alternative to the existing semiparametric models in the literature. Specifically, we propose to approximate the unknown nonparametric nondecreasing function in the probit model with a linear combination of monotone splines, leading to only a finite number of parameters to estimate. Both the maximum likelihood and the Bayesian estimation methods are proposed. For each method, regression parameters and the baseline survival function are estimated jointly. The proposed methods make no assumptions about the observation process and can be applicable to any interval-censored data with easy implementation. The methods are evaluated by simulation studies and are illustrated by two real-life interval-censored data applications.

[1]  W. Johnson,et al.  A Bayesian Semiparametric AFT Model for Interval-Censored Data , 2004 .

[2]  Donglin Zeng,et al.  Semiparametric additive risks model for interval-censored data , 2006 .

[3]  Xingwei Tong,et al.  REGRESSION ANALYSIS OF CASE II INTERVAL-CENSORED FAILURE TIME DATA WITH THE ADDITIVE HAZARDS MODEL. , 2010, Statistica Sinica.

[4]  J J Goedert,et al.  HIV-1 infection incidence among persons with hemophilia in the United States and western Europe, 1978-1990. Multicenter Hemophilia Cohort Study. , 1994, Journal of acquired immune deficiency syndromes.

[5]  Zhiliang Ying,et al.  Semiparametric analysis of transformation models with censored data , 2002 .

[6]  Donglin Zeng,et al.  Maximum likelihood estimation in semiparametric regression models with censored data , 2007, Statistica Sinica.

[7]  Jian Huang,et al.  Interval Censored Survival Data: A Review of Recent Progress , 1997 .

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

[9]  J. Kalbfleisch,et al.  The Statistical Analysis of Failure Time Data: Kalbfleisch/The Statistical , 2002 .

[10]  Xiaotong Shen,et al.  Proportional odds regression and sieve maximum likelihood estimation , 1998 .

[11]  Tianxi Cai,et al.  On the Accelerated Failure Time Model for Current Status and Interval Censored Data , 2006 .

[12]  Xiao Wang,et al.  Bayesian Free-Knot Monotone Cubic Spline Regression , 2008 .

[13]  G. Satten.  Rank-based inference in the proportional hazards model for interval censored data , 1996 .

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

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

[16]  John D. Kalbfleisch,et al.  The Statistical Analysis of Failure Data , 1986, IEEE Transactions on Reliability.

[17]  Donglin Zeng,et al.  Efficient Algorithm for Computing Maximum Likelihood Estimates in Linear Transformation Models , 2006 .

[18]  D. F. Andrews,et al.  Scale Mixtures of Normal Distributions , 1974 .

[19]  Liang Zhu,et al.  A transformation approach for the analysis of interval-censored failure time data , 2008, Lifetime data analysis.

[20]  T. Cai,et al.  Hazard Regression for Interval‐Censored Data with Penalized Spline , 2003, Biometrics.

[21]  L. Devroye.  Non-Uniform Random Variate Generation , 1986 .

[22]  Anastasios A. Tsiatis,et al.  Computationally simple accelerated failure time regression for interval censored data , 2001 .

[23]  Jian Huang,et al.  Sieve Estimation for the Proportional-Odds Failure-Time Regression Model with Interval Censoring , 1997 .

[24]  J. Ramsay.  Monotone Regression Splines in Action , 1988 .

[25]  A M Zaslavsky,et al.  A Markov chain Monte Carlo EM algorithm for analyzing interval-censored data under the Cox proportional hazards model. , 1998, Biometrics.

[26]  Hongqi Xue,et al.  Semi‐parametric accelerated failure time regression analysis with application to interval‐censored HIV/AIDS data , 2006, Statistics in medicine.

[27]  C. Holmes,et al.  Bayesian auxiliary variable models for binary and multinomial regression , 2006 .

[28]  Emmanuel Lesaffre,et al.  BAYESIAN ACCELERATED FAILURE TIME MODEL FOR CORRELATED INTERVAL-CENSORED DATA WITH A NORMAL MIXTURE AS ERROR DISTRIBUTION , 2007 .

[29]  Naji Younes,et al.  LINK-BASED MODELS FOR SURVIVAL DATA WITH INTERVAL AND CONTINUOUS TIME CENSORING , 1997 .

[30]  Linxiong Li,et al.  Regression models with arbitrarily interval-censored observations , 1999 .

[31]  R A Betensky,et al.  Using Conditional Logistic Regression to Fit Proportional Odds Models to Interval Censored Data , 2000, Biometrics.

[32]  Zhigang Zhang,et al.  Regression analysis of interval‐censored failure time data with linear transformation models , 2005 .

[33]  Michael R. Kosorok,et al.  Penalized log-likelihood estimation for partly linear transformation models with current status data , 2005 .

[34]  P. Rosenberg,et al.  Hazard function estimation using B-splines. , 1995, Biometrics.

[35]  P. Green.  Reversible jump Markov chain Monte Carlo computation and Bayesian model determination , 1995 .

[36]  David B Dunson,et al.  Semiparametric bayes' proportional odds models for current status data with underreporting. , 2011, Biometrics.

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

[38]  R. Wolfe,et al.  A semiparametric model for regression analysis of interval-censored failure time data. , 1985, Biometrics.

[39]  D Sinha,et al.  Bayesian Analysis and Model Selection for Interval‐Censored Survival Data , 1999, Biometrics.