1
$\begingroup$

Suppose that I have two pre-computed Incidence Rates with 95% CI, calculated from the same sample. Let's say

IR1: 10.0% [8.0-12.0%] IR2: 21.0% [15.0-27.0%].

If I want to calculate an IR difference, without having the number underlying this IR, how can I compute the corresponding 95% Confidence Interval for the difference?

My guess is that I need to extract the Standard Error from each of the confidence interval, trying to estimate the SE for the difference. But I do not know how.

Thank you in advance.

Improve this question
$\endgroup$
4
  • $\begingroup$ What do you know about the sample sizes? How many observations. Are sample sizes the same for each CI? Are data normal? $\endgroup$
    – BruceET
    Commented Sep 2, 2021 at 23:46
  • $\begingroup$ @BruceET Yeah, I know the sample size, which are actually the same for each CI. I think that normality assumption on the data can be made. $\endgroup$
    – user89547235
    Commented Sep 3, 2021 at 17:43
  • 1
    $\begingroup$ Incidence rates and normal data? No way... $\endgroup$
    – Michael M
    Commented Sep 3, 2021 at 20:13
  • $\begingroup$ Normal approx to binomial CI: If $p$ is estimated by $\hat p =x/n,$ then for sufficiently large $n$ an approximate 95% CI is of the form $\hat p \pm 1.96\sqrt{\frac{\hat p(1-\hat p)}{n}}.$ For one of the CIs given it seems $\hat p = 0.1$ and the CI is $(.08, .12).$ From that you should be able to solve for aprox. value of $n.$ $\endgroup$
    – BruceET
    Commented Sep 3, 2021 at 20:34

1 Answer 1

Reset to default
1
$\begingroup$

So a variance estimator for the the incidence rate is $$ \widehat{Var}(\widehat{IR_1}) = \frac{A_1}{T_1^2}$$ where $A$ is the number of events and $T$ is time. A variance estimator for the incidence rate difference is $$ \widehat{Var}(\widehat{IR_1} - \widehat{IR_2}) = \frac{A_1}{T_1^2} + \frac{A_2}{T_2^2}$$ Under the assumption of $IR_1$ and $IR_2$ being independent, we can estimate the variance of the difference as the sum of the variances.

So to calculate the variance for the incidence rate difference, you need to first calculate the variance for each (which you can do via algebra remembering $LCL = IR - \alpha * SE$ where $\alpha=1.96$ for two-sided 95% confidence intervals). After you have both variances, add them together then take the square root.

Note: this process is more involved for the incidence rate ratio. Since we estimate the variance of the log incidence rate, you would need to use the delta method.

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

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