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I have the following equation for relative change (RC):

RC = (P1 - P2)/P2 * 100

Here, P1 and P2 are both ratios. For example, P1 = A1/n1 and P2 = A2/n2, where n1 and n2 are the sample sizes of both P1 and P2, respectively.

How can I estimate the confidence interval for this using the delta method?

I have seen the following posts:

[1] Calculating standard deviation associated with percentage change

[2] Can we say delta% is significant if delta is significant?

But these two only applied the delta method for sample means.

Update:

Thanks @whuber for the comment/suggestion:

A1 and A2 are counts of extremes days. That is, the total number of days with rainfall amounts above the 90th percentile. They are from two independent samples. In our data set, A2 is always > 0. We did not find cases when this is 0.

I'll appreciate any help on this.

Lyndz
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    A little algebra simplifies the question to finding a confidence interval for the ratio of counts $A_1/A_2.$ The Delta method will run into problems if these counts have unusual distributions or if there's an appreciable chance $A_2=0,$ so if you would like good advice it would help to provide some more details about the $A_i.$ – whuber Dec 07 '20 at 18:49
  • @whuber thanks for the comment. I added details about A1 and A2. These are total counts of days with rainfall above the 90th percentile. In our data set, we did not encounter a value of 0 for A2. It is always > 0. – Lyndz Dec 09 '20 at 09:11
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    Thank you. It may be worthwhile to note that even when you don't *observe* zero values, if your model assigns an appreciable *chance* to a zero, then you had better be careful, especially when applying approximations like the Delta method. – whuber Dec 09 '20 at 14:53

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