title: How to create a confidence interval for a weighted average of areas under the ROC curve in r?
body: <p>What I have is a vector with different areas under the ROC curve (of different studies), e.g,</p>
  
  <p><code>a &lt;- c(.91, .85, .76, .89)</code></p>
  
  <p>I also have the absolute number of participants in each study, e.g., </p>
  
  <p><code>n &lt;- c(50, 34, 26, 47)</code></p>
  
  <p>I calculated the weighted average for the areas with </p>
  
  <p><code>weighted.mean(a, n)</code> </p>
  
  <p>Is there a way in R to also calculate the 95% confidence intervals of the weighted mean, based on the information I have? I looked into <code>pROC</code>, but as far as I understood it, there you need the raw data for each ROC curve (which I don't have). I would be very thankful for any suggestions!</p>