The appendix of the paper of [McPherson et al (1982) 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

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