Journal ArticleDOI
The asymptotic information in censored survival data
TLDR
In this paper, various procedures are considered for fitting a regression model to censored survival data in continuous time with time-dependent covariate functions, including maximum likelihood with the underlying hazard function known completely and known up to a multiplicative constant, and the maximization of Cox's partial likelihood.Abstract:
Various procedures are considered for fitting a regression model to censored survival data in continuous time with time-dependent covariate functions. These include maximum likelihood with the underlying hazard function known completely and known up to a multiplicative constant, and the maximization of Cox's partial likelihood. Explicit formulae for the asymptotic variances of the estimators are derived informally and compared. It is shown how sample second derivatives may be used to estimate the amount of information lost through lack of knowledge of the underlying hazard function. Corresponding results for a more general parameterization which includes the Weibull hazard function are indicated.read more
Citations
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Journal ArticleDOI
Linear regression with censored data
Jonathan Buckley,Ian R. James +1 more
TL;DR: In this paper, a method of estimating parameters in the linear regression model which allows the dependent variable to be censored and the residual distribution to be unspecified is presented, which appears to overcome the inconsistency problems in Miller's approach.
Journal ArticleDOI
Covariate measurement errors and parameter estimation in a failure time regression model
TL;DR: In this paper, a hazard function model is induced for the failure rate given the measured covariate and a partial likelihood function is derived for the relative risk parameters, which may involve the baseline hazard function as well as the regression parameter.
Journal ArticleDOI
Multiplicative Models and Cohort Analysis
TL;DR: In this paper, three methods of cohort analysis are presented for a statistical model wherein the explanatory or exposure variables act multiplicatively on age × calendar year specific death rates, and all three approaches yield roughly equivalent estimates of the relative risk associated with arsenic exposure.
Journal ArticleDOI
Chi-squared goodness-of-fit tests for the proportional hazards regression model
TL;DR: In this article, a class of omnibus chi-squared goodness-of-fit tests is presented for the model, relating failure time to covariate values, proposed by Cox (1972), which are based on the expected and observed frequency that a data point, representing a failure with associated covariates, falls into one of L mutually exclusive categories.
Journal ArticleDOI
Analyzing Duration Times in Marketing: Evidence for the Effectiveness of Hazard Rate Models
TL;DR: The findings indicate the superiority of proportional hazard regression methods vis-i-vis common procedures in terms of stability and face validity of the estimates and in predictive accuracy.
References
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Book ChapterDOI
Regression Models and Life-Tables
TL;DR: The analysis of censored failure times is considered in this paper, where the hazard function is taken to be a function of the explanatory variables and unknown regression coefficients multiplied by an arbitrary and unknown function of time.
Journal ArticleDOI
The Efficiency of Cox's Likelihood Function for Censored Data
TL;DR: In this paper, the authors show that Cox's method has full asymptotic efficiency under conditions which are likely to be satisfied in many realistic situations, and the connection of Cox's methods with the Kaplan-Meier estimator of a survival curve is made explicit.
Journal ArticleDOI
Exponential survivals with censoring and explanatory variables
TL;DR: In this article, the analysis of survival times, censored and uncensored, arising from a hazard function that varies exponentially with covariates and is otherwise constant is given, and the results are extended to include a Weibull component in the hazard.
Journal ArticleDOI
Some effciency calculations for survival distributions
TL;DR: In this article, the relative efficiency of the rank analysis arising out of Cox's regression and life model versus the analogous analysis in the exponential case is examined, and it is found to compare favourably with the more model-dependent analysis in most cases of practical importance.