Statistics for the Two-Sample Survival Analysis Problem Based on Product Limit Estimators of the Survival Functions.

Abstract

A class of statistics for the two-sample survival analysis problem is introduced. The SW-statistic may be written as the integral of a weighted difference in the estimated survival functions, the integral being with respect to Lebesgue measure on time. Since the integral is with respect to real-time the statistics are not generalized rank-statistics. However, with an appropriate choice of weight function they are non-parametric in the sense that weak convergence is guaranteed for any underlying configuration of survival and censoring distributions. Asymptotic distribution theory under the null is derived. Consistency under a fixed alternative is shown. Efficacy expressions under natural sequences of local alternatives are given and an expression for the most efficient weight function is developed. The asymptotic efficiencies of some specific SW-statistic under the proportional hazards alternative are examined. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1986
Accession Number
ADA176956

Entities

People

  • Margaret O'sullivan
  • Thomas R. Fleming

Organizations

  • University of North Carolina at Chapel Hill

Tags

Communities of Interest

  • Energy and Power Technologies
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Consistency
  • Convergence
  • Data Science
  • Distribution Theory
  • Efficiency
  • Estimators
  • Gaussian Processes
  • Information Science
  • Integrals
  • Intervals
  • North Carolina
  • Probability
  • Random Variables
  • Statistics
  • Stochastic Processes
  • Two Dimensional
  • Weak Convergence

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Regression Analysis.