The appendix of the paper of [McPherson et al (1982)][1] contains a derivation of the *systematic component variation SCV*. I understand the derivation with exception of the first step. Here are the **premisses**:  

$O_i$: observed cases in region i    
$E_i$: expected cases in region i   
$\lambda_i$: *multiplicative factor associated with region i* (I suppose it means $O_i=\lambda_i*E_i$)    

Now the following **assumptions** have been done:  
  
$O_i$ is approximately Poisson distributed with mean $\lambda_iE_i$    
$\lambda_i$ is considered as a random variable with expected value $1$ and variance $\sigma^2$.    

From these the following **formula** is concluded:   

var($O_i$) = $E_i^2\sigma^2$ + $E_i$      


I tried to find out how to get the formula by the given premisses and assumptions and didn't succeed. Any idea? Thanks for help.

  [1]: http://www.nejm.org/doi/pdf/10.1056/NEJM198211183072104