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I'm looking at an old paper on the incidence of HPV infection by age cohorts. The authors present a plot of estimates from many different studies around Europe which looks like this - note the authors don't describe how they derived the fit line they added.

enter image description here

The collective data is somewhat messy, and after looking at the sources, I decided to only include the 16 sources that were sampled at random from the population of a given country, as opposed to those only collected opportunistically at sexual health clinics. Now, the resultant data is still messy and I don't have the raw rates, only the given tallies, but it's a little cleaner.

enter image description here

What I really would like is a useful phenomenological model for how HPV infection rate varies with age, so what I did very naively was to weigh each included study by the number of participants involved (so a study with 200 samples was twice the weight of one with only 100 etc) and then impose a linear fit with 95% confidence bounds to give a simple linear equation for estimates at any age.

My question is whether this approach is valid, and what might be a better way to do it - is there a better approach to this anyone could suggest? Thanks!

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    $\begingroup$ You might want to investigate meta-regression. If instead of age your x-axis was dose you would have meta-analysis of dose response data which might also be a worthwhile search term. We do have a tag meta-regression $\endgroup$
    – mdewey
    May 14 at 15:33

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