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Simultaneous Confidence Intervals for Comparing Binomial Parameters

Alan Agresti, Matilde Bini, Bruno Bertaccini and Euijung Ryu
Biometrics
Vol. 64, No. 4 (Dec., 2008), pp. 1270-1275
Stable URL: http://www.jstor.org/stable/25502211
Page Count: 6
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Simultaneous Confidence Intervals for Comparing Binomial Parameters
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Abstract

To compare proportions with several independent binomial samples, we recommend a method of constructing simultaneous confidence intervals that uses the studentized range distribution with a score statistic. It applies to a variety of measures, including the difference of proportions, odds ratio, and relative risk. For the odds ratio, a simulation study suggests that the method has coverage probability closer to the nominal value than ad hoc approaches such as the Bonferroni implementation of Wald or "exact" small-sample pairwise intervals. It performs well even for the problematic but practically common case in which the binomial parameters are relatively small. For the difference of proportions, the proposed method has performance comparable to a method proposed by Piegorsch (1991, Biometrics 47, 45-52). /// Pour comparer des proportions avec plusieurs échantillons binomiaux indépendants, nous recommandons une méthode construisant des intervalles de confiance simultanés qui utilisent la distribution de l'étendue studentisée avec une statistique du score. Elle s'applique à une grande variété de mesures, dont la différence de proportions, les rapports de chance (odds-ratios), et le risque relatif. Pour les odds-ratios, une étude de simulation suggère que la méthode a un taux de couverture de probabilité plus proche de la valeur nominale que les approches ad hoc telles l'implémentation de Bonferroni de Wald, ou les intervalles appariés exacts pour petits échantillons. Elle a un bon comportement même dans le cas délicat, mais en fait commun, de paramètres binomiaux relativement petits. Pour la différence de proportions, la performance de la méthode proposée est comparable à celle d'une méthode proposée par Piegorsch (1991).

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