Statistics and Its Interface

Volume 15 (2022)

Number 1

Further study on testing the equality of response rates under Dallal’s model

Pages: 115 – 126



Yafei Chen (College of Mathematics and System Science, Xinjiang University, Urumqi, China)

Zhiming Li (College of Mathematics and System Science, Xinjiang University, Urumqi, China)

Changxing Ma (Department of Biostatistics, University at Buffalo, New York, U.S.A.)


Paired binary data naturally arises when paired body parts are investigated in clinical trials. In this paper, we will further study whether the response rates of $g (g \geq 2)$ groups are equal under Dallal’s model and propose eight test statistics ($T^a_L$, $T^a_W$, $T^a_{SC}$, $T^a_R$, $T^b_L$, $T^b_W$, $T^b_{SC}$ and $T^b_R$). Some expressions of these tests are derived. The simulation results show that likelihood ratio and Wald-type tests are not robust with respect to empirical type I error rates (TIEs). The score and Ronser-type tests can produce satisfactory TIEs and power, and therefore are recommended. A real example is given to illustrate the proposed methods.


paired binary data, Dallal’s model, likelihood ratio test, Wald-type test, score test, Ronser-type test

This research is funded by the National Natural Science Foundation of China (Grant Nos. 12061070, 11661076), and by the Science and Technology Department of Xinjiang Uygur Autonomous Region (Grant No. 2018Q011).

Received 8 January 2021

Accepted 1 June 2021

Published 11 August 2021