Parameter estimation in regression for long-term survival rate from censored data

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Abstract

In recent years, regression models have been shown to be useful for predicting the long-term survival probabilities of patients in clinical trials. The importance of a regression model is that once the regression parameters are estimated information about the regressed quantity is immediate. A simple estimator is proposed for the regression parameters in a model for the long-term survival rate. The proposed estimator is seen to arise from an estimating function that has the missing information principle underlying its construction. When the covariate takes values in a finite set, the proposed estimating function is equivalent to an ad hoc estimating function proposed in the literature. However, in general, the two estimating functions lead to different estimators of the regression parameter. For discrete covariates, the asymptotic covariance matrix of the proposed estimator is simple to calculate using standard techniques involving the predictable covariation process of martingale transforms. An ad hoc extension to the case of a one-dimensional continuous covariate is proposed. Simplicity and generalizability are two attractive features of the proposed approach. The last mentioned feature is not enjoyed by the other estimator.

Original languageEnglish (US)
Pages (from-to)211-222
Number of pages12
JournalJournal of Statistical Planning and Inference
Volume99
Issue number2
DOIs
StatePublished - Dec 1 2001
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

Keywords

  • 62N02
  • Conditional Kaplan-Meier estimator
  • Counting process
  • Cox proportional hazards
  • Cumulative hazard function
  • Martingale
  • Newton-Raphson method
  • Primary 62N01
  • Secondary 62E20

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