Older ages will be undersampled giving these people highly influential values, possibly skewing analyses. A random sample of 100 people 65 and over will be result in very precise estimate of trends in people close to age 65 because of the distribution of age. That is why a stratified sample can improve power. In general, the greater the variability of the covariates, the more power you have.
![poisson regression stata poisson regression stata](https://www.researchgate.net/profile/David-Lindstrom/publication/236761981/figure/tbl2/AS:671521240535041@1537114548435/Parameter-Estimates-for-Multilevel-Poisson-Regression-Model.png)
It is more apparent when you calculate power using simulation, which is effectively the same thing as using MCMC integration to calculate quantiles of non-central distributions according to critical values for null hypothesis significance testing.
![poisson regression stata poisson regression stata](https://blog.uvm.edu/tbplante/files/2021/05/image-2.png)
The latter is the point of performing a power analysis: to make a minimum number of reasonable assumptions to illustrate the feasibility of an analysis. You do not need to make assumptions about the distribution of covariates in order perform regression, but you do need to make assumptions about the distribution of covariates in order to simulate results of regression modeling. I will not repeat the arguments in that case. So, if you are able to influence data collection, it is better to plan for well spread out values of $x$.Īll of the above (except the concrete formulas) will be valid for Poisson regression. On that page, they state, "The variance [ of the regression parameter estimate $\hat$ depends on the empirical variance of $x$. On page 870-2 of that document, they give a formula for sample size calculations. I was rather confused by this, since regression models don't make assumptions about the distribution of the covariates, so I checked the online documentation ( here). However, I noticed that in the "Poisson Regression" menu for PASS, one of the options is specifying the distribution of the PREDICTOR variable (X).
![poisson regression stata poisson regression stata](https://data.library.virginia.edu/files/nb_fig_1.png)
#Poisson regression stata software
For quick and simple calculations of this nature, I often use PASS, a statistical software package dedicated to power/sample size calculations. Recently, I was tasked with a sample size calculation for a study in which the outcome is to be modeled using a Poisson regression (i.e.