Efficient interval estimation of a ratio of marginal probabilities in matched‐pair data: Non‐iterative method

Matched‐pair designs have been commonly employed in diagnostic, epidemiologic and laboratory studies. For estimation of a ratio of two marginal probabilities in matched‐pair data, a Wald‐type logarithmic method is computationally simple, but an actual coverage rate is known to be smaller than a nominal one and a length of the confidence interval is shorter than it should be. The Fieller‐type method based on constrained maximum likelihood (CML) estimators possesses asymptotically optimum statistical properties and a coverage rate is close to a nominal one. However, hitherto the limits have been obtained by numerical iterations. In this paper, we derive the efficient confidence limits based on CML as analytical solutions of a quartic equation and present the confidence limits in a closed form. Published in 2009 by John Wiley & Sons, Ltd.