The description clarifies a lot now. And it confirms that your observations as you tabulated are not independent. Look at the extreme case for Pen=1. Assuming the Sum Dead Animals at Day=0 is an error, and should have been 0. The four observations are recording the responses from the same group of 22 animals.
Despite the problem can be handled differently, this type of studies are the subject of survival analysis. Following are some simplest questions of interest in your study.
- What is the survival rate in Pen = 1, through Day = 22? The answer is 100%. And the complement death rate is 0%.
- What is the survival rate in Pen = 5, through Day = 22? The answer is 21/22=95.5%, because one animal died between Day = 10 and Day = 22, assuming no animals are died precisely on Day = 0, 10, 22, or 35. The complement death rate is 4.5%.
- What is the survival rate in Pen = 5, through Day = 35? The answer is 20/22=90.9%,because another animal died between Day = 22 and Day = 35. The complement death rate is 9.1%.
This is the screenshot of Pen = 5 data.
In your study, what variable has a Binomial distribution? This is: the number of death (or survival) in a Pen within a given time interval.
The death rate over time in a Pen is also a distribution. But this is not a Binomial. This is the reason for the way that I commented earlier.
Now I explain how to conduct simple survival analysis like what I did above on this data. First you need to transform your data to a different format. Following is the transformed data for Pen = 5.
Step 1, I create two columns: "Time Interval Left" and "Time Interval Right", and enter values as in the following screenshot. This should be same for all pens. The first row of the two columns define a time interval from Day = 0 to Day = 10. The second and third rows define subsequent time intervals similarly. The last row define the time horizon after Day = 35.
Step 2, I create "Count" and put values as in the screenshot for Pen = 5. The values should be based on the death and survival counts in individual pens. For Pen = 5, the meanings are: there where no death in the 1st time interval; there is one death in the second time interval; there is one death in the third time interval; all remaining 20 survived at the time point Day = 35.
For more detailed explanation of this format, see the documentation for Life Distribution platform https://www.jmp.com/support/help/en/15.2/index.shtml#page/jmp/event-plot.shtml#
Notice, I only create a table for Pen = 5. And the following illustration is on that Pen only.
Next, go to Analyze menu, find "Reliability and Survival", the "Life Distribution", and specify the launch dialog like the following, then click "OK".
The default report shows results for "death rate". You may go to the red triangle menu in the report and find "Show Survival Curve" toggle between "death rate" and "survival rate" results.
Near the bottom of the report is the "Nonparametric Estimate" outline node, open it. It has the death rate estimates that I mentioned previously.
The above is just for one pen. You may be able to follow this path and go a long way after collecting the death (survival) rates for all pens at those time intervals. You can compare them by pen, treatment, etc.
If you convert all your data as I illustrated, you may also conduct more comprehensive analysis to estimate death rates with grouping variables simultaneously. If you can follow up with the converted data, I may have additional suggestions, depending what I can find in your data.
Another potentially useful analysis in this case is probit analysis. You might postulate these effects using Analyze > Fit Model:
You can use the GLM platform to explore signficant effects, lack of fit, over-dispersion, and profile the response, Prob( Dead ).
