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Vaccine efficacy against Omicron has to be estimated for three months since the second dose. Efficacy data are given for shorter periods comprising three months. For example, the table, based on Fig 10 of Technical Briefing 33, shows UK Omicron efficacy data for the Pfizer covid vaccine.

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Q: How to obtain a three-month efficacy estimate and a 95% confidence interval from these data?

(To simplify, we can assume a Normal distribution for the estimates.)

A naive solution is an average estimate weighted by the period lengths. However, it ignores the non-constant variance of the individual estimates. Another approach is inverse-variance weighted estimate, a la meta-analysis. This does not seem quite right, since there is (typically) a strong dependence of efficacy on the time post-dose. Another possibility is meta-regression, although I am not sure how this would work in this case.

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