Analyzing treatment effect with possibly flawed control data I've got some rather messy data from a natural experiment.  A number of subjects were measured (the measurements were  hopefully-Poisson distributed counts and associated offsets), placed on a treatment at time T, and then measured again sometime afterward.  However, there is some reason to suspect that the dependent variable has been changing over time, so we found a control dataset and measured those subjects before and after T as well.  Unfortunately, I don't know which of the subjects in the control dataset were on the treatment - all I know is the ones who were on stayed on and the ones who were off stayed off.  I can obtain this information, but it is rather time-consuming/expensive.  
There are two questions I would like to answer:   


*

*Does the treatment have an overall effect? 

*Does the treatment affect the majority of subjects?


I don't really know how to answer 2 (some variant of McNemar's test?) so I would appreciate some advice there, but for 1 I've been setting up the problem something like this:
glm(counts ~ as.factor(subject.id) + before + offset(log(observation.time)),family=quasipoisson)

where before is coded 0 or 1.  So I have two rows per subject.  I've done that regression for both the control and test datasets, and the respective confidence intervals of before don't intersect, so I've been mildly optimistic.  What is the best way to combine the two datasets in a single analysis, though?  If I knew which of the control dataset had the treatment and which didn't, it seems fairly easy, but like I said, I don't know that.  
 A: There is a growing econometric literature on the misclassification of treatment status.
A standard difference-in-difference approach would be a natural starting point here - see e.g. http://www.nber.org/WNE/lect_10_diffindiffs.pdf p.17 mentioning Poisson case. The problem with misclassification for a general conditional mean function is described here: https://www2.bc.edu/~lewbel/mistreanote2.pdf If it applies to your set up, then you may be confident of a significant effect finding as the bias is said to be towards zero.
A: I'd suggest looking into multiple imputation or other missing data approaches for dealing with your control data. You can build a vast array of different possible combinations of whether or not a given control was on or off treatment, and see how they effect your results. 
When it comes down to it, yes, you can combine the two data sets, and using something like a multiple imputation method will allow you to handle your missing data problem, though of course you'll likely have wider confidence intervals and the approach is somewhat less elegant, and this harder to explain.
