Estimation for an accelerated failure time model with intermediate states as auxiliary information

The accelerated failure time (AFT) model is a common method for estimating the effect of a covariate directly on a patient’s survival time. In some cases, death is the final (absorbing) state of a progressive multi-state process, however when the survival time for a subject is censored, traditional AFT models ignore the intermediate information from the subject’s most recent disease state despite its relevance to the mortality process. We propose a method to estimate an AFT model for survival time to the absorbing state that uses the additional data on intermediate state transition times as auxiliary information when a patient is right censored. The method extends the Gehan AFT estimating equation by conditioning on each patient’s censoring time and their disease state at their censoring time. With simulation studies, we demonstrate that the estimator is empirically unbiased, and can improve efficiency over commonly used estimators that ignore the intermediate states.

[1]  Y. Ritov,et al.  Monotone Estimating Equations for Censored Data , 1994 .

[2]  Anastasios A. Tsiatis,et al.  Improving the efficiency of the log-rank test using auxiliary covariates , 2008 .

[3]  Jun Yan,et al.  Marginal semiparametric multivariate accelerated failure time model with generalized estimating equations , 2012, Lifetime data analysis.

[4]  O. Aalen,et al.  Survival and Event History Analysis: A Process Point of View , 2008 .

[5]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[6]  James D. Berry,et al.  Design and Initial Results of a Multi-Phase Randomized Trial of Ceftriaxone in Amyotrophic Lateral Sclerosis , 2013, PloS one.

[7]  D. Cox.  Regression Models and Life-Tables , 1972 .

[8]  R. Strawderman,et al.  Induced smoothing for the semiparametric accelerated failure time model: asymptotics and extensions to clustered data. , 2009, Biometrika.

[9]  Martin Schumacher,et al.  Empirical Transition Matrix of Multi-State Models: The etm Package , 2011 .

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

[11]  Lee-Jen Wei,et al.  Linear Regression Analysis for Multivariate Failure Time Observations , 1992 .

[12]  Luís Meira-Machado,et al.  Nonparametric estimation of transition probabilities in the non‐Markov illness‐death model: A comparative study , 2015, Biometrics.

[13]  B. M. Brown,et al.  Induced smoothing for rank regression with censored survival times , 2007, Statistics in medicine.

[14]  Yijian Huang,et al.  Censored regression with the multistate accelerated sojourn times model , 2002 .

[15]  D. Schoenfeld,et al.  A model‐informed rank test for right‐censored data with intermediate states , 2015, Statistics in medicine.

[16]  Z. Ying,et al.  Rank-based inference for the accelerated failure time model , 2003 .

[17]  Glenn Heller.  Smoothed Rank Regression With Censored Data , 2007 .

[18]  Carmen Cadarso-Suárez,et al.  Nonparametric estimation of transition probabilities in a non-Markov illness–death model , 2006, Lifetime data analysis.

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

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

[21]  E. Gehan.  A GENERALIZED WILCOXON TEST FOR COMPARING ARBITRARILY SINGLY-CENSORED SAMPLES. , 1965, Biometrika.

[22]  N. Mantel.  Evaluation of survival data and two new rank order statistics arising in its consideration. , 1966, Cancer chemotherapy reports.

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

[24]  Ren Johansen.  An Empirical Transition Matrix for Non-homogeneous Markov Chains Based on Censored Observations , 1978 .

[25]  Z. Ying,et al.  A Monte Carlo method for variance estimation for estimators based on induced smoothing. , 2015, Biostatistics.

[26]  J. Cedarbaum,et al.  The ALSFRS-R: a revised ALS functional rating scale that incorporates assessments of respiratory function , 1999, Journal of the Neurological Sciences.

[27]  J. Peto,et al.  Asymptotically Efficient Rank Invariant Test Procedures , 1972 .