The authors of this 2004 paper (Ben G Armstrong and colleagues) have alerted us to an error in their paper (BMJ 2004;329:660, doi:10.1136/bmj.38198.594109.AE). They say that the expression they used for estimating vaccine efficacy (VE) was only approximately consistent and that a consistent estimator is VE = (RR_u − RR_v)/(RR_u − 1) where RR_u and RR_v are the ratios of outcome rates in the flu period versus the non-flu period in vaccinated and unvaccinated people respectively. The authors state that re-estimating the vaccine efficacy for all cause mortality reported in the published paper changes the estimate little: from 83% (95% confidence interval 9% to 100%) to 85% (13% to 100%) for all cause mortality; from 80% to 83% for death from cardiovascular disease; and from 79% to 83% for deaths from respiratory disease. The latter two sets of 95% confidence intervals were unchanged, spanning the entire meaningful range (0 to 100).

The authors say that, although the revision made only a small difference in their data, it could be more important in other data. Specifically, the originally published estimator (VE₂₀₁₀ = RR_v × VE₂₀₀₄) is biased by a factor of RR_v^-1.

A derivation of the new estimator and its relation to the old one is available from ben.armstrong{at}lshtm.ac.uk.