If I want to know the impact of two mutually exclusive risk factors on disease burden in my population using evidence-based PAFs and their 95% CIs, can I sum the total numbers of cases (estimates) and their uncertainty levels to calculate the total burden of disease?
Ex: assuming a population of 1000 subjects, I know that PAF for disease-1 is 20% (95%CI 15-25) and for disease-2 is 30% (95%CI 25-35), can I assume that the total burden is of 500 (400-600) cases or is this an inappropriate method?
Statistically, the sum of estimates is equal to estimate of a sum.
See https://stats.stackexchange.com/questions/223924/how-to-add-up-partial-confidence-intervals-to-create-a-total-confidence-interval
How did you add 20 + 30 to obtain 500?
The estimates are counts, so a Poisson distribution. Add the two estimates and take the square root of the sum for the standard deviation.
Thanks for you answer Joseph L Alvarez , but 20 and 30 are PAF (%) not observations. 50% of 1000obs=500.
Sorry. I misunderstood your second paragraph.
200 cases and 300 cases add to 500. 20% of 1000 is 200 cases. 200 cases has Poisson 1 sigma uncertainty of 14 cases or 2 sigma of 28 cases. Your 2 sigma is 50 cases. 30% of 1000 is 300 and has a Poisson 1 sigma uncertainty of 17 cases or 2 sigma of 34 cases. Your 2 sigma is again 50 cases. The total form both diseases is 500 and has a Poisson 1 sigma uncertainty of 22 or 2 sigma of 44. Adding the 2 sigmas uncertainties for 200 cases and 300 cases; 28 cases and 34 cases yields 62 cases not the 44 cases when the total is 500 cases.
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