Comparing different poisson distributions with very variable sample sizes I have data on around 50 different roads: The number of accidents and the volume of traffic on each. 
I'd like to compare these and estimate which is the most dangerous/safest, but the volumes (and therefore also the number of accidents) are highly variable. Some roads have such low traffic volumes that they have only 0 or 1 accident (Some have hundreds). 
As you would expect, comparing the rates at face value shows that highest and lowest accident rates are both on low volume roads. Should the estimated rates be pulled towards the overall rate in proportion to the sample size?
Is there a way to account for this sample size variation when comparing the accident rates, so that I can come up with a better estimate of the true risk on each road? 
Thank you.
 A: Consider that we have noisy estimates; where the exposure is very low, the rate is very unreliable, so it's impossible to reliably construct an ordering that includes them. 
You may be able to do some pooling (pulling toward the overall rate) that improves the mean square error, but at the expense of some bias. This is a common tool in actuarial work, where they call it credibility. Done optimally, it's essentially a Bayesian idea, and that's the way it's often presented these days. 
[However, I am not certain that necessarily helps you in finding the 'safest' or 'most dangerous' roads, because the resulting regularized rates may still tend to have the low volume rates at the extremes. I'd have to check that. Still, it might be worth investigating such methods in order to get more stable - and generally more realistic - estimates.]
One thing you could do is construct upper and lower limits (from confidence intervals) for the rate. Then when identifying the safest roads, pick the roads with the lowest upper limit on the rate (ones almost sure to be safe). These will tend to be the safest of the larger-exposure roads, but medium ones that do very well can get in there.
When identifying the most dangerous roads, it's a little trickier, since it depends on whether you're more interested in what might be dangerous or what we can be pretty sure is dangerous. Assuming the latter, you would pick the ones with the highest lower limit as the most dangerous (i.e. ones you're pretty sure are dangerous).
