If you assume piecewise constant hazard rates, then the likelihood function (as a function of parameteres) has same form as if the number of events had been poisson distributed. Therefore, you can use poisson regression on time to event data where you have counts on left side in the model statement. If you chop the timeaxis into finer and finer pieces, then the model will be equivalent to a cox-regression, and in that case the difference is only that the parameter of the time-effect is non-parametric in the cox-regression while it will be estimated together with other parametes in the Poisson regression model.   Be aware, there is no assumption that the counts actually are poisson distributed - and they are obviously not since the count are limited by the number of subjects in the trial, whereas if it was poisson distributed then there would not be an upper limit. Still, it is called poisson regression because of the similarity of the likelihood functions. Since data are not poisson distributed, it will not give meaning to apply model check that rely on the poison distribution ("variance = mean" does not give sense here). ... View more

Hello, you are doing some mistakes. 1) it doesnt give meaing to multiply the character variable sex with time. That should be replaced with something that can intepretate and translate characters into numeric. Try this    timeXsex=time*(sex='Male');   2) This is the most important! It doesnt give meaing to make the interaction terms between covariates and the time variable in the dataset. These interaction terms should be made inside phreg. The reason for this is that interaction should based on the time at each riskset, and not the time for event at each observation. it will be something like this (simplified)  proc phreg data=simulation; class sex; timeXsex=time*(sex='Male'); model time=exposure sex timeXsex; run;   3) Unless you have very low statistical power, I dont see any reason for why you have all covariates in the model line, and none in the strata statement. Have the covariates in the strata statement gives a more robust model, and you will then then only need to check the proportional hazard assumption on the covariate of interest which should be in the model line.  ... View more

I agree with @Ksharp . It will be impossible to do with glimmix, because this procedure will estimate a parameter for each family.  It should be possible to estimate with generelized estimation equations (genmod+repeated) or GEE, because this method works in a non-parametric way. I will though not use type=un, but rather type=cs, as cs assume same correlation between any two individuals within a familiy. ... View more

My suggestion is to use the poisson regression model - no matter whether you see overdisperson or not. The reason for that that overdispersion is something that measure variance relative to mean for count-data. But here the data was time-to-event, which has been summarized by number of events and person-time. It can be analyzed with poisson regression assuming piecewice constant incidence rates, because the likelihood function for will be similar to what you would have if you assumed the count-data was poisson distributed. As you dont need the assumption of distribution it you also dont need to check for overdispersion.   It quite easy to simulate time to event data with some incidence rate, and estimate the incidencerate with confidence interval correctly, even that you may have a big over dispersion. The dispersion will depend on how much you have aggreated (for example 5 agegroup instead of 10), which can be completely arbitrary and irrelevant for the rate estimate and it std error. So, just use proc genmod with the dist=poisson, and remember the offset=logtime. ... View more