Robust error poisson regression for relative risk

[Luke Masha]

A variant of a Poisson regression called the "robust-error-variance Poisson regression" is an approach adapted for binary data, specially as an alternative to the logistic regression. This is something I am interested in for a cohort study I am working on as I want to report multivariate estimates of relative risk as opposed to odds ratios. I tried a log binomial glm model and ran into convergence issues.

My question is this. What are the conditions of validity that are needed to apply a "robust error variance Poisson regression" to a cohort study? Am I correct in assuming that in the application of this regression model to cohort studies, the outcome in question need not necessarily strictly follow a poisson distribution as the robust error variance treats the SD using a normal distribution?

[Maarten Buis]

It helps if you told us exactly what you typed in Stata. I am guessing (but I should not have to do so) that you typed something like glm y x1 i.x2, link(log) family(binomial) vce(robust). I think that this is what you did, as you reported convergence problems and this model tends to lead to convergence problems when many predicted outcomes are larger than 1.

However, this does not exactly estimate the model you are after. Instead you should have typed: glm y x1 i.x2, link(log) family(poisson) vce(robust), or just poisson y x1 i.x2, vce(robust).

Beware, however, that if you had the convergence problems because of many implausible predicted outcomes, you may still get convergence in this model, but the results may not be meaningful.

As to your question: no, not quite.

[Luke Masha]

My stata code was as you stated. The model I am running had convergence issues with a logbinomal regression but worked fine with a poisson regression with robust error variance.
Thank you for the response but I don't need assistance with running the regressions in stata.

What I would appreciate is a little teaching/explanation of the basic assumptions that need to be met in order to consider running a poisson regression with robust error variance for a cohort study. Is there anything in my data I should check or consider which if present may invalidate the results of this regression? Normality assumptions? Assumptions about the variance of the predictors? Etc. Reading what I see in the literature it appears that using the robust error variance options allows for the relaxation of a lot of issues with poisson regression. For reference, the outcome in the model is a binary outcome and the predictors are a mix of categorical and continuous variables.

[Maarten Buis]

Given that the logbinomial model did not converge I am very worried about your predicted values. I suspect that a fair number of those will exceed 1, and if that happens often enough then you should worry about the validity of your model. To check that, just type predict muhat, mu after your glm model. This will create a new variable muhat, that will contain the predicted values. So you can type sum muhat, detail to see if there are predicted values larger than 1. If that is the case you can try to fix that by allowing for non-linearity in the effect of continuous variables. I like linear splines (see help mkspline), but tastes differ.

For a complete and accessible discussion of what to test for and how to do so in Stata see Hardin & Hilbe (2012) Generalized Linear Models and Extensions, third edition. College Station, TX: Stata Press. http://www.stata-press.com/books/gen...nd-extensions/