An easy approach to the Robins-Breslow-Greenland variance estimator
Tóm tắt
The Mantel-Haenszel estimate for the odds ratio (and its logarithm) in stratified case control studies lacked a generally acceptable variance estimate for many years. The Robins-Breslow-Greenland estimate has met this need, but standard textbooks still do not provide an explanation of how it is derived. This article provides an accessible derivation which demonstrates the link between the Robins-Breslow-Greenland estimate and the familiar Woolf estimate for the variance of the log odds ratio, and which could easily be included in Masters level courses in epidemiology. The relationships to the unconditional and conditional maximum likelihood estimates are also reviewed.
Tài liệu tham khảo
Mantel N, Haenszel W: Statistical aspects of the analysis of data from retrospective studies of disease. JNCI 1959, 22:719–748.
Breslow NE, Day NE: Statistical methods in cancer research, Volume 1 – the analysis of case-control studies Lyons: International Agency for Research on Cancer 1980.
Robins J, Breslow N, Greenland S: Estimators of the Mantel-Haenszel variance consistent in both sparse data and large-strata limiting models. Biometrics 1986, 42:311–323.
Kuritz SJ, Landis JR, Koch GG: A general overview of Mantel-Haenszel methods: applications and recent developments. Ann Rev Public Health 1988, 9:123–160.
Phillips A, Holland PW: Estimators of the variance of the Mantel-Haenszel log-odds-ratio estimate. Biometrics 1987, 43:425–431.
Armitage P, Berry G, Matthews JNS: Statistical methods in medical research 4 Edition Oxford: Blackwell Science 2002.
Fleiss JL, Levin B, Paik MC: Statistical Methods for Rates & Proportions Chichester: John Wiley 2003.
Clayton D, Hills M: Statistical methods in epidemiology Oxford: Oxford University Press 1995.
Hauck WW: The large-sample variance of the Mantel-Haenszel estimator of a common odds ratio. Biometrics 1979, 35:817–819.
Flanders WD: A new variance estimator for the Mantel-Haenszel odds ratio. Biometrics 1985, 41:637–642.
Sato T: Confidence limits for the Common Odds Ratio Based on the Asymptotic Distribution of the Mantel-Haenszel Estimator. Biometrics 1990, 46:71–80.
Woolf B: On estimating the relationship between blood group and disease. Human Genet 1955, 19:251–253.
Ury HK: Hauck's approximate large-sample variance of the Mantel-Haenszel estimator [letter]. Biometrics 1982, 38:1094–1095.