Semiparametric Accelerated Failure Time Research Articles

Rank Regression Analysis of Multivariate Failure Time Data Based on Marginal Linear Models

Abstract. Multivariate failure time data arises when each study subject can potentially ex-perience several types of failures or recurrences of a certain phenomenon, or when failure times are sampled in clusters. We formulate the marginal distributions of such multivariate data with semiparametric accelerated failure time models (i.e. linear regression models for log-transformed failure times with arbitrary error distributions) while leaving the dependence structures for related failure times completely unspecified. We develop rank-based monotone estimating functions for the regression parameters of these marginal models based on right-censored observations. The estimating equations can be easily solved via linear programming. The resultant estimators are consistent and asymptotically normal. The limiting covariance matrices can be readily estimated by a novel resampling approach, which does not involve non-parametric density estimation or evaluation of numerical derivatives. The proposed estimators represent consistent roots to the potentially non-monotone estimating equations based on weighted log-rank statistics. Simulation studies show that the new inference procedures perform well in small samples. Illustrations with real medical data are provided.

Two-sample statistics for testing the equality of survival functions against improper semi-parametric accelerated failure time alternatives: an application to the analysis of a breast cancer clinical trial.

This paper presents two-sample statistics suited for testing equality of survival functions against improper semi-parametric accelerated failure time alternatives. These tests are designed for comparing either the short- or the long-term effect of a prognostic factor, or both. These statistics are obtained as partial likelihood score statistics from a time-dependent Cox model. As a consequence, the proposed tests can be very easily implemented using widely available software. A breast cancer clinical trial is presented as an example to demonstrate the utility of the proposed tests.

Bayesian Semiparametric Regression for Median Residual Life

Abstract. With survival data there is often interest not only in the survival time distribution but also in the residual survival time distribution. In fact, regression models to explain residual survival time might be desired. Building upon recent work of Kottas & Gelfand [J. Amer. Statist. Assoc. 96 (2001) 1458], we formulate a semiparametric median residual life regression model induced by a semiparametric accelerated failure time regression model. We utilize a Bayesian approach which allows full and exact inference. Classical work essentially ignores covariates and is either based upon parametric assumptions or is limited to asymptotic inference in non‐parametric settings. No regression modelling of median residual life appears to exist. The Bayesian modelling is developed through Dirichlet process mixing. The models are fitted using Gibbs sampling. Residual life inference is implemented extending the approach of Gelfand & Kottas [J. Comput. Graph. Statist. 11 (2002) 289]. Finally, we present a fairly detailed analysis of a set of survival times with moderate censoring for patients with small cell lung cancer.

Estimating subject-specific survival functions under the accelerated failure time model

SUMMARY We use the semiparametric accelerated failure time model to predict the survival function and its related quantities for future subjects with a given set of covariates. We derive the large-sample distribution for the subject-specific cumulative hazard function estimate. We then propose a simple resampling technique for constructing pointwise confidence intervals and simultaneous bands for the corresponding survival function and its quantile function over a properly selected time interval. The new proposals are illustrated with the Mayo primary biliary cirrhosis data.

Rank-based inference for the accelerated failure time model

A broad class of rank‐based monotone estimating functions is developed for the semiparametric accelerated failure time model with censored observations. The corresponding estimators can be obtained via linear programming, and are shown to be consistent and asymptotically normal. The limiting covariance matrices can be estimated by a resampling technique, which does not involve nonparametric density estimation or numerical derivatives. The new estimators represent consistent roots of the non‐monotone estimating equations based on the familiar weighted log‐rank statistics. Simulation studies demonstrate that the proposed methods perform well in practical settings. Two real examples are provided.

Semiparametric estimation of an accelerated failure time model with time-dependent covariates

SUMMARY A class of semiparametric accelerated failure time models is introduced that are useful for modelling the relationship of survival distributions to time dependent covariates. A class of semiparametric rank estimators is derived for the parameters in this model when the survival data are right censored. These estimates are shown to be consistent, and asymptotically normal with variances that can be consistently estimated. It is also shown that estimators within this class achieve the semiparametric efficiency bound. We consider an accelerated failure time model for time-to-event data in which the survival distribution is scaled by a factor which may be a function of time-dependent covariates. These models directly model the effect of covariates on the length of survival. This is in contrast to the more commonly-used proportional hazards model which models the hazard rate itself. In some applications it may be easier to visualize the concept that a treatment intervention or exposure to an environmental contaminant increases or decreases the length of survival by a certain proportion, as compared to the concept that the hazard rate is changed. For time independent covariates, say, Z = (Z1,.. , Zp)', the class of accelerated failure time models assumes that the survival distribution at time t, given a set of covariates Z = z, is given by F(t I z) = F0{ h (z) t}. The proportionality constant h (z) can be interpreted as the scale factor by which lifetime is decreased as a function of the covariates z. Often h(z) is taken to be log linear or h(z) = exp (,B'z). In such cases, if z = 0, we can interpret Fo(t) as the 'baseline' survival distribution or the survival distribution for individuals with covariates all equal to zero. A useful way of envisioning this model is to consider a hypothetical random variable, U, that corresponds to an individual's survival time if that individual had covariate values all equal to zero. This baseline failure time, U, would be modified for values of the covariate different than zero. For example, if we denote the actual survival time by T, then for an individual with covariate value Z we have T =- e'ZU. The parameters, ,B, in this model have a direct interpretation in terms of the increase or decrease in lifespan as a function of the covariates. The assumption that U is independent of Z in this hypothetical construct, induces the probabilistic model

Semiparametric accelerated failure time modeling for multivariate failure times under multivariate outcome-dependent sampling designs

Semiparametric accelerated failure time modeling for multivariate failure times under multivariate outcome-dependent sampling designs