Couldn't you use PROC GLIMMIX in SAS?
Set the data up in a longitudinal form, i.e. two observations per person, one with the the pre measurement and one with the post measurement and a time indicator (1 for pre, 2 for post) and then run code similar to the following:
proc glimmix data=long;
model score = time / solution dist=poisson link=log;
random intercept_ / id=subject;
run;
quit;
If you do this with "normally" distributed data and a type=cs correlation structure you have the traditional paired t-test. So, Shahidul gets his "paired t-test" that the investigators are familiar with as well as the Poisson distribution he is after.
I may be totally off base and I could easily be missing the point, so take anything I say with a grain of salt.
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Leroy Thacker
Assistant Professor
Virginia Commonwealth University
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Original Message:
Sent: 10-26-2011 11:55
From: Margot Tollefson
Subject: Paired Count Data
Shahidul,
This is some old fashioned statistics, but, for matched pairs, the variance of the differences between the pairs is estimated by finding the sample variance of the differences. The test statistic is then the mean of the differences divided by the square root of the quantity (the sample variance of the differences divided by the sample size). If you can consider the sample as being a random sample from a very large population, and if the sample size is large enough, the test statistic is distributed approximately normal with mean = 0 and variance = 1. If the population from which the sample is drawn is small relative to the sample size, the sample variance should be adjusted by the finite correction factor. The variance to use in the test statisitic is then the sample variance multipied by the quantity ( 1/n - 1/N), where n is the sample size and N is the population size.
Hope this is helpful.
Margot
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Margot Tollefson
Owner
Vanward Statistical Consulting
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Original Message:
Sent: 10-26-2011 10:36
From: Shahidul Islam
Subject: Paired Count Data
Thanks Michael for your suggestion but I am interested in looking at the differences and not the effect.
From reading through articles, I am thinking of calculating the following test statistic then a p-value:
Test Statistic= ?pre- ?post /Var(?pre- ?post)
Where Var(?pre- ?post)=V(?pre) + V(?post) - 2 Cov(?pre, ?post)
Since ?pre and ?post are not independent, we will need to estimate the covariance as follows:
Cov (?pre ,?post)=E[?pre ].E[?post] - E[?pre .?post]
Now we can get a p-value based on the above test statistic. Thoughts anyone??
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Shahidul Islam, MPH
Biostatistician
Winthrop University Hospital
Mineola, NY 11590
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Original Message:
Sent: 10-26-2011 08:07
From: Michael Chernick
Subject: Paired Count Data
Now I hope everyone sees that the context of the problem is very important. Given this detailed explanation I would say that Colleen Kelly"s recommendation is the best so far. I think you could make post surgery count the response variable and use the baseline pre surgery count as a covariate rather than look at the difference in counts. since crossing the lower boundary is suppose to be a rare event perhaps the Poisson model is a good one. The use of the covariate allows you to see how closely the two counts relate to each other on a patient by patient basis. I would test the regression coefficient for statistical significance.
This type of analysis is far better in my opinion than a signed rank test. There may be a better approach but I don't know what it would be off hand.
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Michael Chernick
Director of Biostatistical Services
Lankenau Institute for Medical Research
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Original Message:
Sent: 10-25-2011 23:08
From: Shahidul Islam
Subject: Paired Count Data
Thanks to all for taking the time to response to my request.
To answer Michael's valuable questions:
Patients are pretty similar as they share some common characteristics.
Outcome variable is "number of times blood glucose levels drop below a cutoff point" (a rare event for my patient population) during a standardized glucose monitoring period.
We want to measure this prior to a surgery then post surgery at several times (at least 5 time points)
For repeated measure data, I can use proc genmod for poisson distribution. However, I am interested in comparing the pre-measure with each of the post measures separately. I thought of using signed rank test but wondered if there is a different test to compare differences for rare count data.
Thanks again for your help.
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Shahidul Islam, MPH
Biostatistician
Winthrop University Hospital
Mineola, NY 11590
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