How to express a Poisson regression equation as a quasi-Poisson I was reading this paper: http://www.researchgate.net/publication/13878515_A_simple_non-linear_model_in_incidence_prediction
and was wondering whether the equations 1 and 3 presented in the paper to represent modeling of cancer incidence using a Poisson distribution could be converted into a quasi-Poission model. Is this possible? How would the formulae below look if they follow a quasi-Poisson model instead?
$ln(EM_{it}) = \alpha_i + \beta t$
$EM_{it} = \alpha_i(1 + \beta t)$
where $i$ is age group and $t$ period, $EM_{it}$ is the expected incidence rate, $\beta$ is a drift parameter and $\alpha_i$ is the baseline incidence rate.
NOTE: the journal requires a subscription but is not necessary to access since I have put the two relevant equations above.
 A: The difference between a Poisson and quasi-Poisson regression affects nothing but the standard errors. The form of the mean model remains unchanged, as do the point estimates for the coefficients. The difference is that the quasi-Poisson model has a mean-variance relationship of $\sigma^2=\delta\mu$, where $\mu$ is the mean, $\sigma^2$ is the variance, and $\delta$ is a free parameter known as the dispersion parameter. The Poisson model forces $\delta=1$. 
Don't expect to get reliable standard errors with a Poisson regression. For example, in a regression with only intercept, the maximum likelihood estimate of the variance under a Poisson model is the sample mean. If the data are actually not Poisson but Gaussian with mean 10000 and standard deviation 10 (variance 100), the estimated variance will converge to 10000, and not to the true value of 100. The standard errors will be $\sqrt{100} = 10$ times too big. This makes Poisson regression heavily dependent on the true distribution of the response. Quasi-poisson is much more accommodating: it will set the dispersion parameter to 1/100 so that the standard errors are more or less correct.
