sizes are denoted by $m_{+1}$ for the treatment group and $m_{+0}$ for the control group and these are assumed fixed by design. Hence, $(m_{0i}, m_{1i},
m_{2i})$ follows the trinomial distribution with total number of trials $m_{+i}$ and probability parameter vector $(p_{0i}, p_{1i}, p_{2i})$ for $i=0,1$ such as $$p_{0i} = 1 - (1+\gamma)\lambda_i, \;\;
p_{1i} = 2\gamma\lambda_i, \;\; \mbox{and} \;\;
p_{2i} = (1-\gamma)\lambda_i.$$ Dallal’s model also implies that the correlation coefficients between the $Z_{ijk}$ variables take the form: $$\begin{aligned}
\rho_i = {\mathbf{Corr}}\big(Z_{ijk}, Z_{ij(3-k)}\big) = 1- \dfrac{\gamma
}{1-\lambda_i},\qquad i=0,1.\label{eq1sec2}\end{aligned}$$ In fact, the conditional probability assumption in Dallal’s model can be replaced by the statement in about the correlation coefficient. The correlation coefficient, $\rho_i$, takes both positive and negative values over the entire range $(-1,1)$. The excess risk is defined as $$\delta_i = P(Z_{ijk}=1 \mid Z_{ij(3-k)}=1) - P(Z_{ijk}=1 ) = 1-\gamma-
\lambda_i$$ for $i=0,1$.

The main parameter of interest in this investigation is the risk difference, $\Delta=\lambda_1 - \lambda_0$, and, therefore, $\gamma$ can be viewed as a nuisance parameter. The risk ratio, $R =\dfrac{\lambda_1}{\lambda_0}$ and the odds ratio, $\psi= \dfrac{\lambda_1(1-\lambda_0)}{(1-\lambda
_1)\lambda_0}$ can also be of interest. Another parameter of interest is the difference of excess risks in both the treatment and the control 