Our manuscript was based on surveillance cases of COVID-19 identified before January 26, 2020. As of February 20, 2020, the total number of confirmed cases in mainland China has reached 18 times of the number in our manuscript. While the methods and the main conclusions in our original analyses remain solid, we decided to withdraw this preprint for the time being, and will replace it with a more up-to-date version shortly. Should you have any comments or suggestions, please feel free to contact the corresponding author.

In 1915, Greenwood and Yule noted that for valid vaccine efficacy studies, exposure to infection in the vaccinated and the unvaccinated must be equal (Proc R Soc Med 1915;8(part 2):113-94). The direct effect of a vaccine, however, needs to be defined by the protection it confers given a specific amount of exposure to infection, not just a comparable exposure. In this paper, two classes of parameters are distinguished along lines differing from the conventional distinction between efficacy and effectiveness. Efficacy parameters attempt to control for exposure to infection and represent direct effects on individuals. Direct effectiveness parameters represent a mixture of direct effects on individuals and indirect effects in the population.

Interpretation and estimation of vaccine efficacy is complicated when the vaccine effect is heterogeneous across vaccinated strata. If a person has a certain susceptibility, or probability of becoming infected conditional on a specified exposure to infection, then one effect of a vaccine would be to reduce that susceptibility, possibly to zero. Vaccine efficacy is a function of the relative susceptibilities in the vaccinated and unvaccinated persons. Under heterogeneity of vaccine effect, a general expression for a summary vaccine efficacy parameter is a function of the vaccine efficacy in the different vaccinated strata weighted by the fraction of the vaccinated subpopulations in each stratum. Interpretation and estimability of the summary vaccine efficacy parameter depends on whether the strata are identifiable, and whether the heterogeneity is host- or vaccine-related. Bounds are derived for the summary vaccine efficacy when the strata are not identifiable for the case of an outbreak of an acute infectious disease. The upper bound assumes that everyone is equally affected by the vaccine, and the lower bound assumes that some are completely protected while others have no protection. The biologic interpretation of the two bounds is different.