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I need to test data on patients in a pre/post setting. I have data on the counts of seizures in a starting interval, and then another count of seizures after the patient was treated for the same time interval.

I'd like to test the reduction (if it exists) offered by the treatment. I have no other adjustment variables and am not sensitive to the timing of the data (time doesn't matter its just paired differences).

Data looks something like:

ID PreMedSeizures OnMedSeizures
1  20             10
2  150            60
3  30             40
4  200            120
5  1000           500
...

My initial thought was a simple test of location (t-test, Wilcox, whatever) dealing with all of the non-normalities, perhaps trimming outliers (most of the data looks like lines 1-3, there are a few that resemble 5) but on second blush this seems insufficient. Raw numbers of seizures does not capture the magnitude of improvement--or worsening--for each patient. For example, ID 1 had a 50% improvement, and ID 5 did as well..but if you test for location you're looking at raw numbers of seizures and that magnitude gets buried.

So, I went the real complicated route and thought about poisson and hierarchical models but I'm concerned this is way over-complicating the problem. There should be something simpler.

Perhaps the simple answer is to work with the proportions (Om/Pm), but I'm not sure what test that would be either. Seems heretical. Maybe I just need to transform the paired-differences before testing? I need some help. Thanks.

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  • $\begingroup$ See stats.stackexchange.com/a/166513/17230. But why are the counts all multiples of ten? $\endgroup$ – Scortchi Nov 10 '15 at 14:57
  • $\begingroup$ They're not. Its still early in the morning here, the point was more that counts range from 3 to 1000 in either variable. $\endgroup$ – intra Nov 10 '15 at 15:31
  • $\begingroup$ So you're right to have qualms about simple location tests, but a drop of say 1000 to 500 counts should surely have more import than one of 20 to 10 even though the ratios are the same. $\endgroup$ – Scortchi Nov 10 '15 at 16:40
  • $\begingroup$ Perhaps. That is more of an expert decision, not a data one because not all types of seizures are the same for every person. At a minimum, I have to be able to vouch for both views (e.g. represent a proportional drop, or an absolute one). $\endgroup$ – intra Nov 10 '15 at 16:47
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    $\begingroup$ Have you looked at a scatterplot of the data on linear and logarithmic scales? It might be instructive. $\endgroup$ – tristan Nov 10 '15 at 18:22
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This question was posed several years ago now, but the paper below published this month (September, 2018), is a helpful discussion around comparing paired counts for those who may come across this question as I just did. In the simulations conducted in the below, over a range of sample sizes, the authors note that the paired samples t-test performed quite well (showing small downward bias, particularly in small samples), though it is not really a valid test for this situation. Signed-rank test, GLMM (NB) and GEE, showed small upward bias in small samples and bias diminished as sample size increased as expected.

Proudfoot, J. A., Lin, T., Wang, B., & Tu, X. M. (2018). Tests for paired count outcomes. Gen Psych, 31(1), e100004. Retrieved from: https://gpsych.bmj.com/content/31/1/e100004

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