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On large sample sequential analysis with applications to survivorship data

Published online by Cambridge University Press:  14 July 2016

Norman Breslow
Norman Breslow*
Affiliation:
University of Washington, Seattle
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Extract

Although his work on the application of invariance concepts to the sequential testing of composite hypotheses is better known, Cox (1963) has also outlined a large sample approach to the same problem. His method is based on Bartlett's (1946) recognition that the sequence of maximum likelihood estimates (MLE) of the parameter of interest, calculated from an increasing number of observations, resembles asymptotically a random walk of normally distributed variables. However, the large sample theory needed to justify this approach rigorously is left largely implicit. At the end of his paper, Cox suggests that these methods may be extended to yield a sequential comparison of survival curves (Armitage (1959)), a suggestion which has been reiterated as a research problem in the monograph of Wetherill (1966).

Type
Research Papers
Information
Journal of Applied Probability , Volume 6 , Issue 2 , August 1969 , pp. 261 - 274
Copyright
Copyright © Sheffield: Applied Probability Trust 

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