Hostname: page-component-77c89778f8-9q27g Total loading time: 0 Render date: 2024-07-17T06:28:32.020Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Armitage, P. (1959) The comparison of survival curves. J. R. Statist. Soc. A 122, 279–300.Google Scholar
Armitage, P. (1960) Sequential Medical Trials. Blackwell Scientific Publications, Oxford.Google Scholar
Bartlett, M. S. (1946). The large sample theory of sequential tests. Proc. Camb. Phil. Soc. 42, 239–244.Google Scholar
Billingsley, P. (1968) Convergence of Probability Measures. Wiley, New York.Google Scholar
Chase, G. (1968) On the efficiency of matched pairs in Bernouilli trials. Biometrika 55, 365–369.Google Scholar
Cox, D. R. (1963) Large sample sequential tests for composite hypotheses. Sankya 25, 5–12.Google Scholar
Hájek, J. and Sidák, Z. (1967) Theory of Rank Tests. Academic Press, New York.Google Scholar
Parthasarathy, K. R. (1967) Probability Measures on Metric Spaces. Acadmic Press, New York.Google Scholar
Skorohod, A. V. (1956) Limit theorems for stochastic processes. Theor. Probability Appl. 1, 188–192.Google Scholar
Skorohod, A. V. (1957) Limit theorems for stochastic processes with independent increments. Theor. Probability Appl. 2, 138–171.CrossRefGoogle Scholar
Wald, A. (1947) Sequential Analysis. Wiley, New York.Google Scholar
Wetherill, G. B. (1966) Sequential Methods in Statistics. Methuen, London.Google Scholar
Ylvisaker, D. (1968) A note on the absence of tangencies in Gaussian sample paths. Ann. Math. Statist. 39, 261–263.Google Scholar