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A BAYESIAN METHOD FOR THE CHOICE OF THE SAMPLE SIZE IN EQUIVALENCE TRIALS
Author(s) -
Gubbiotti Stefania,
De Santis Fulvio
Publication year - 2011
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/j.1467-842x.2011.00643.x
Subject(s) - mathematics , equivalence (formal languages) , sample size determination , statistics , bayesian probability , confidence interval , interval (graph theory) , coverage probability , prior probability , combinatorics , discrete mathematics
Summary In this paper we consider a Bayesian predictive approach to sample size determination in equivalence trials. Equivalence experiments are conducted to show that the unknown difference between two parameters is small. For instance, in clinical practice this kind of experiment aims to determine whether the effects of two medical interventions are therapeutically similar. We declare an experiment successful if an interval estimate of the effects‐difference is included in a set of values of the parameter of interest indicating a negligible difference between treatment effects (equivalence interval). We derive two alternative criteria for the selection of the optimal sample size, one based on the predictive expectation of the interval limits and the other based on the predictive probability that these limits fall in the equivalence interval. Moreover, for both criteria we derive a robust version with respect to the choice of the prior distribution. Numerical results are provided and an application is illustrated when the normal model with conjugate prior distributions is assumed.