Is calculating Incidence Rate Difference/Ratio appropriate for single case experimental design? (This is part-2 of my long question, you can have a look at part-1 here)
I am going to do a quasi-experiment, with measuring the base line of a sample (actually not quite a sample, but a ward, with high patient turn-over rate), and then we do a intervention, and measure the variables (i.e. infection rate) again.
I googled a bit and found that this is something called a single case experiment, and it was said that single case experiment doesn't have very solid statistics because you don't have the control, you can't conclude on the causality in a solid manner.
I have googled a bit again and found that I can compare the incidence rate (or call it infection rate), but doing something like "incidence rate difference" (IRD) or "incidence rate ratio" (IRR). (I found it from here)
What is the difference between IRD and t-test? And is there any statistical test complementary for IRR?
But mostly importantly, is it appropriate for me to use this test (does it have a name?) for single case experiment? Because the patients in the ward keep changing, this is what I worried about.
 A: If you cannot collect data on a different ward where you don't do the intervention, your conclusions will be weak, because you cannot rule out other causes that act simultaneously (change in weather, season, epidemic of something, etc, etc). However if you observe a large effect, your study would still contribute an interesting piece of evidence.
The rest of your questions are a bit confused. If your outcome is binary: infection yes/no in a bunch of patients (probably adjusted for length of stay so it becomes a rate?), then you could not even do a t-test, so there is no point in discussing its appropriateness. But in the sense that it looks at differences it is similar to a t-test when you have continuous outcomes.
There is a test loosely called "ratio t-test", which is a t-test conducted on log-transformed data that concentrates on ratios instead of differences. So it is in some sense the counterpart of IRR, however I don't think you could actually perform it, because you don't have a continuous outcome variable.
So pick either the IRD or IRR. The difference is usually more important from a public health point of view, while ratios tend to be more impressive especially for rare events.
A: First, a discussion of the "incidence rate" - this is a measure that is simply the number of events / the time the study subjects are at risk of the outcome. The incidence rate difference is typically:
Incidence Rate in the Exposed - Incidence Rate in the Unexposed
Similarly, the Incidence Rate Ratio is:
Incidence Rate in the Exposed / Incidence Rate in the Unexposed
That has...nothing to do with a t-test, and honestly, at this point, you should abandon all hope of attempting to use a t-test. It's a tool, with a particular purpose, and that purpose is not this type of data. As has been noted, your question is a bit confused from there, so I'm going to make some suggestions:
You have a wards worth of data. That's not just a single sample, that's all the data for a ward. Pharmacoepidemiology has developed some pretty sophisticated methods for dealing with questions like yours - what happens when you change something mid-stream for a rare outcome. I'd start with combing through Epidemiology and The American Journal of Epidemiology for "case-crossover" studies.
