Estimation Of Odds Ratio Function With Censored Data
Jae-Kee, Song
Kyungpook National University, Department of Statistics
#1370, Sankyuk-dong, Puk-gu
Taegu City, 702-701, Korea (Rep.)
jksong@kyungpook.ac.kr
Jung-Suk, Kim
Taegu Polytechnic College, Department of Computer Science
#395, Manchon-dong, Susung-gu
Taegu City, 706-711, Korea (Rep.)
Z941095@rose0.kyungpook.ac.kr
Dong-Myung, Jeong
National Statistical Office, Statistical Information & Data Management Bureau
Government Complex Taejon, #920, Dunsan-dong, So-gu
Taejon City, 302-701, Korea (Rep.)
dmjeong@nso.go.kr
1. Introduction and Summary
Odds ratio is often used for comparing the odds that a subject will survive among subjects
who have been exposed to a risk factor to the odds that a subject will survive in subjects who have
not been exposed. Since odds ratio provides a kind of snapshot analysis at a particular time point, a
single odds ratio alone does not show the whole picture. Therefore it is natural for odds ratio to be
extended in order to see trend over the entire time span.
In this paper we define odds ratio function, provide three estimators, and compare them when
there is censoring. The first one is a nonparametric estimator based on the Nelson-Aalen estimator
of the cumulative hazard function, and the others are obtained using the concept of the usual odds
ratio estimate.
Asymptotics are also investigated and confidence intervals for odds ratio function are
constructed. The performances of the proposed estimators finally are compared and the results are
illustrated using real data.
REFERENCES
Andersen, P. K., Borgan, ∅., Gill, R. D. and Keiding, N. (1993). Statistical Models Based on
Counting Processes, Springer-Verlag, New York.
Breslow, N. E. (1996). Statistics in Epidemiology : The Case-Control Study, Journal of the
American Statistical Association 91, 14-28.
Pearce, Neil. (1993). What does the odds ratio estimate in a case-control study? International
Journal of Epidemiology 22, 1189-1192.
RÉSUMÉ
Le ratio de différence seul ne montre pas tous ce qui concerne la mesure de la risque relative
des deux groupes. Dans ce papier, donc, on définit la fonction du ratio de différence qui peut en
étiduer le cours sur toute l'étendu du temps. Trois estimateurs sont étudiés et comparés, et le résultat
est illustré avec le data réel.