1
$\begingroup$

Here is the scenario I am trying to model.

I have a population of people who are susceptible to developing a disease. I observe each person for a different amount of time, summing to a total of 3000 person-years of observation.

During the observation period, I record 50 cases of this disease. The point estimate would then be 16.6 events per 1000 person-years.

How could I best quantify the uncertainty surrounding this estimate? Would these techniques still work for very few cases, or no cases at all? Implementation in R or Python would be appreciated.

Improve this question
$\endgroup$
0

1 Answer 1

Reset to default
1
$\begingroup$

One option is to calculate the Wald confidence intervals for the incidence rate. The formula is $$I \pm 1.96 \times SE$$ where $SE$ is defined as $$SE = (\frac{a}{t^2})^{0.5}$$ where $a$ is the number of events and $t$ is person-time.

For your example, the 95% CL would be $(12.0, 21.3)$. Wald standard errors require 'enough' cases, where enough is usually defined to be at least 5. This approach would not work if there were no cases.

Improve this answer
$\endgroup$
2
  • $\begingroup$ Do you know of any methods that work for small counts? $\endgroup$
    – max
    Commented Feb 4, 2020 at 22:43
  • $\begingroup$ One option is to use exact confidence intervals. I'm not that familiar with the procedure for exact confidence intervals for incidence rates. Depending on your software of choice, there may be an option for exact confidence intervals $\endgroup$
    – pzivich
    Commented Feb 6, 2020 at 12:28

Not the answer you're looking for? Browse other questions tagged or ask your own question.