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I have some health survey data from multiple years. This includes the estimated prevalence of a flu vaccination in a population, then number of people surveyed, and the high/low confidence intervals.

Flu Season  Sample Size FluVaxView Estimate FluVaxView LL   FluVacView UL   CI ((+/-)
2014-2015   7909    46.10%  43.90%  48.30%  2.2
2015-2016   8754    45.30%  43.50%  47.10%  1.8
2016-2017   7697    46.10%  44.30%  47.90%  1.8
2017-2018   5937    40.40%  38.60%  42.20%  1.8

I would like to combine these estimates to get a multi-period or pooled estimate. Averaging the four flu seasons I get a mean of 44.5% flu vaccination coverage. My question is how can I combine the upper and lower confidence intervals? They are of different size (+/- points), and I lack the original data, the standard deviation, and the variance.

Thanks for any help you can provide.

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