Accelerated failure time models for counting processes

SUMMARY We present a natural extension of the conventional accelerated failure time model for survival data to formulate the effects of covariates on the mean function of the counting process for recurrent events. A class of consistent and asymptotically normal rank estimators is developed for estimating the regression parameters of the proposed model. In addition, a Nelson-Aalen-type estimator for the mean function of the counting process is constructed, which is consistent and, properly normalised, converges weakly to a zeromean Gaussian process. We assess the finite-sample properties of the proposed estimators and the associated inference procedures through Monte Carlo simulation and provide an application to a well-known bladder cancer study.

[1]  E. Gumbel.  Bivariate Exponential Distributions , 1960 .

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

[3]  R. Prentice.  Linear rank tests with right censored data , 1978 .

[4]  I. James,et al.  Linear regression with censored data , 1979 .

[5]  R. Gill,et al.  Cox's regression model for counting processes: a large sample study : (preprint) , 1982 .

[6]  J. Kalbfleisch,et al.  The Statistical Analysis of Failure Time Data , 1980 .

[7]  D. Cox,et al.  Analysis of Survival Data. , 1985 .

[8]  J. Wellner,et al.  Empirical Processes with Applications to Statistics , 2009 .

[9]  L. J. Wei,et al.  Regression analysis of multivariate incomplete failure time data by modeling marginal distributions , 1989 .

[10]  A. Tsiatis.  Estimating Regression Parameters Using Linear Rank Tests for Censored Data , 1990 .

[11]  D. Pollard.  Empirical Processes: Theory and Applications , 1990 .

[12]  Zhiliang Ying,et al.  Linear regression analysis of censored survival data based on rank tests , 1990 .

[13]  Ya'acov Ritov,et al.  Estimation in a Linear Regression Model with Censored Data , 1990 .

[14]  Danyu Lin,et al.  Goodness-of-Fit Analysis for the Cox Regression Model Based on a Class of Parameter Estimators , 1991 .

[15]  Zhiliang Ying,et al.  Large Sample Theory of a Modified Buckley-James Estimator for Regression Analysis with Censored Data , 1991 .

[16]  Zhiliang Ying,et al.  Rank Regression Methods for Left-Truncated and Right-Censored Data , 1991 .

[17]  D. Harrington,et al.  Counting Processes and Survival Analysis , 1991 .

[18]  Charles J. Geyer,et al.  Computational Methods for Semiparametric Linear Regression with Censored Data , 1992 .

[19]  James M. Robins,et al.  Semiparametric estimation of an accelerated failure time model with time-dependent covariates , 1992 .

[20]  Zhiliang Ying,et al.  A Large Sample Study of Rank Estimation for Censored Regression Data , 1993 .

[21]  Jianwen Cai,et al.  Some Graphical Displays and Marginal Regression Analyses for Recurrent Failure Times and Time Dependent Covariates , 1993 .

[22]  Lee-Jen Wei,et al.  Confidence bands for survival curves under the proportional , 1994 .

[23]  Nancy Reid,et al.  On “A conversation with Sir David Cox” , 1994, Issue 5.2, Spring 2023.

[24]  Z. Ying,et al.  A resampling method based on pivotal estimating functions , 1994 .

[25]  Zhiliang Ying,et al.  Semiparametric inference for the accelerated life model with time-dependent covariates , 1995 .

[26]  Jerald F. Lawless,et al.  Some Simple Robust Methods for the Analysis of Recurrent Events , 1995 .

[27]  Zhiliang Ying,et al.  Towards a general asymptotic theory for Cox model with staggered entry , 1997 .

[28]  Analysis of Mean and Rate Functions for Recurrent Events , 1997 .