Dear Kelvin,

Thanks very much for your question. I am not sure why you are putting confidence intervals around a mortality rate. If the mortality rate is derived from counting every death in a defined population of known size during a discrete time, and neither the number of deaths in the numerator nor the population size in the denominator are derived from random sampling, then there is no sampling error to account for using confidence intervals. You have measured the exact population value and have not estimated it based on a sample. However, others believe that given the random variation in the number of occurrences per time in biologic systems, confidence intervals are appropriate to express the extent of such variation. However, I would have no idea how to calculate a confidence interval for the difference between 2 mortality rates. How did you do this?

@Bradley A. Woodruff Thank you for your response. I completely agree with your submission. Though, I noticed that my question and text was confusing and I also noticed that the approach I used was wrong. I apologise for that. 

Going through the presentation where I saw this method, the author substracted the baseline mortality rate from the estimate and  confidence limits of the current mortality rate. 

What the presenter did was as follows:

given a baseline of 0.48/10000/day 

a new mortality rate of  0.30[0.10 , 0.40]  per 10000/day with a recall period of 90 days and 50000 population at risk. 

The excess mortality rate and confidence limit was calculated as follows:

0.30 - 0.48 = -0.18

new ll = 0.10 - 0.48 = -0.38

new cl = 0.40 - 0.48 = -0.08

excess mortality rate -0.18[ -0.38, -0.08] which translates to 

(-0.18*90*50000)/10000[ (-0.38*90*50000)/10000 , (-0.08*90*50000)/10000] 

- 81[-171,-36].