Estimation of rate ratio and relative difference in matched-pairs under inverse sampling

To increase the efficiency of a study and to eliminate the effects of some nuisance confounders, we may consider employing a matched-pair design. Under the commonly assumed quadrinomial sampling, in which the total number of matched-pairs is fixed, we note that the maximum likelihood estimator (MLE) of rate ratio (RR) has an infinitely large bias and no finite variance, and so does the MLE of relative difference (RD). To avoid this theoretical concern, this paper suggests use of an inverse sampling and notes that the MLEs of these parameters, which are actually of the same forms as those under the quadrinomial sampling, are also the uniformly minimum variance estimators (UMVUEs) under the proposed samplings. This paper further derives the exact variances of these MLEs and the corresponding UMVUEs of these variances. Finally, this paper includes a discussion on interval estimation of the RR and RD using these results as well. Copyright (C) 2001 John Wiley & Sons, Ltd.