# Paired binary data with a zero cell

How do you analyse and obtain a p-value from a 2*2 table examining a binary outcome that is paired, when one cell has zero events?

To clarify, I was looking at the success rate of obtaining an adequate image, using two different ultrasound windows, in the same participant. Then we repeated this experiment for 30 different participants.

So each participant had the two views attempted, and the success rates of obtaining a good view for each attempt was recorded. So the data is paired, and our results are in the first picture:

.

My understanding is that I cannot run a Fisher’s exact test as the data is not independent and it will not run anyways with a zero value cell.

So I tried rearranging the data and running a McNemar test.

But the McNemar would not run because of the zero value in cell c.

I needed a p-value for these results and I’m at a loss as to what to do! I use SAS for analysis. Any pointers would be much appreciated.

The outcome data is binary and paired. This can be analyzed using a McNemar test. The data therefore needs to be arranged appropriately for that test. Given the problem at hand (in the comments), the data would look like this:

The sum of the discordant cells (b +c) however, is low. When the sum of discordant cells b +c is < 25, an exact McNemar test is more appropriate.

You notice cell c, is a zero cell. SAS will not recognize zero cells, for the purpose of this calculation, unless the zeros statement is made. To run an exact Mcnemar test you also need to specify the exact mcnem statement.

SAS Code:

data viewcomp;
input view1 $view2$ count;
cards:
success success 26
success failure 4
failure success 0
failure failure 0
;
run;

proc freq data = viewcomp;
weight count / zeros;
tables view1*view2 / agree;
exact mcnem;
run;


Running the above code yields a p-value of 0.125.