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Estimation of a Common Effect Parameter from Sparse Follow-Up Data

Sander Greenland and James M. Robins
Biometrics
Vol. 41, No. 1 (Mar., 1985), pp. 55-68
DOI: 10.2307/2530643
Stable URL: http://www.jstor.org/stable/2530643
Page Count: 14
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Estimation of a Common Effect Parameter from Sparse Follow-Up Data
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Abstract

Breslow (1981, Biometrika 68, 73-84) has shown that the Mantel-Haenszel odds ratio is a consistent estimator of a common odds ratio in sparse stratifications. For cohort studies, however, estimation of a common risk ratio or risk difference can be of greater interest. Under a binomial sparse-data model, the Mantel-Haenszel risk ratio and risk difference estimators are consistent in sparse stratifications, while the maximum likelihood and weighted least squares estimators are biased. Under Poisson sparse-data models, the Mantel-Haenszel and maximum likelihood rate ratio estimators have equal asymptotic variances under the null hypothesis and are consistent, while the weighted least squares estimators are again biased; similarly, of the common rate difference estimators the weighted least squares estimators are biased, while the estimator employing "Mantel-Haenszel" weights is consistent in sparse data. Variance estimators that are consistent in both sparse data and large strata can be derived for all the Mantel-Haenszel estimators.

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