-- -- ----------------------
                                              
  Numbers of                                  
  cured organs   Treatment                    Control
  0              $m_{01} \; (p_{01})$         $m_{00} \; (p_{00})$
  1              $m_{11} \; (p_{11})$         $m_{10} \; (p_{10})$
  2              $m_{21} \; (p_{21})$         $m_{20} \;(p_{20})$
  Total          $m_{+1}$                     $m_{+0}$
  -------------- ---------------------- -- -- ----------------------

  : Data structure for bilateral data along with their corresponding trinomial probabilities. $p_{00}+p_{10}+p_{20}=1=p_{01}+p_{11}+p_{21}$, $m_{00}+m_{10}+m_{20}=m_{+0}$ and $m_{01}+m_{11}+m_{21}=m_{+1}$ are fixed by design.[]{data-label="tab1sec1"}

The main parameter in bilateral models is the difference between the proportion of body parts $(\lambda_0,\lambda_1)$ with the characteristic of interest in the two groups, $\Delta=\lambda_1-\lambda_0$. However, the dependency between paired observations cannot be ignored. @Rosner1982, @Morris1993, and @TangTangRosner2006 discuss the consequences of ignoring this dependency.

Five models have been proposed for bilateral data: Rosner’s model, Dallal’s model, the equal correlation model, the independence model, and the full or saturated model. Of these five models, the most extensively studied is Rosner’s model. @TangTangQiu2008 present several test statistics for the equality of $\lambda_0$ and $\lambda_1$ under Rosner’s model. @QiuTangTang2009 consider the problem of sample size calculations under Rosner’s model. @TangQiuTangPei2011 discuss various techniques to construct asymptotic confidence intervals for $\Delta$ under Rosner’s model and evaluate the performance of these via empirical studies. @TangPeiWongLi2010 is perhaps the only paper that discusses all five models simultaneously 