Independence in Poisson regression when used for rates estimation I'm interested in using Poisson regression for estimating mortality rates. I've observations for a rather long period, and have to face the fact that covariates often vary over time. This is especially the case when the age of the people comes into play and the observation period exceeds a few months.
In this case, here is my way to deal with this issue : the observation period is divided into intervals where the covariates are constant. Each observation then becomes a set of observations and the exposures are calculated for each interval. However, the log-likelihood in Poisson regression models assume independence between the observations.
But, as I have, say for a person named Jack, a period where he is forty and another one where he is forty one, I will have for Jack two observations in my model, and I can't really say that those two observations are independent.
Can I just assume that the death rates are independent anyway, or are there specific methods to deal with this issue in a better way?
EDIT
In this lesson, at the paragrah 7.4.3 The Equivalent Poisson Model there is something that could let think my approach is not invalid. Nevertheless, as far as I'am aggregating data in each bunch of pseudo-observation (and not as in the text , one for each combination of individual and interval) I wonder if it still stand.
EDIT
About grouping data :
I have a set of thousands of observations. Each one relate to an individual, and for each one I have the date of entry in the study, the date of exit, the date of death, an indicator for smoking or not, the birth date, the gender (and a few other one but that don't matter here).
I cut the whole interval of time covered form the first entry to the last at each time something happen (someone entre or leave the study, or a covariate changes).
For each interval of time, and for each set of similar age and other covaraiates, I compute the total exposition, and the number of deaths. And I this way I get "pseudo-observations" with a number of death, an exposition, and covariates.
Then I fit a Poisson Regression (generalised linear model, with expostion as offset).

If you want to divide the observation period for each subject into epochs you can use generalized estimating equations (GEE) to model this as a quasi-Poisson process while accounting for the correlation between subject measurements across epochs.  I don't think this is standard practice, though.  It might be more appropriate to adjust a cross-sectional Poisson model for baseline age or other factors to investigate if the mortality rate differs across groups.  In either model I recommend including an additional scale parameter or using the empirical sandwich covariance estimator when estimating standard errors.
