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.

There are many different effects to consider when evaluating vaccines in the field. In this review, we have covered some of the various measures and issues related to study design and interpretation of the different measures. We emphasize that in designing and understanding vaccine studies, it is necessary to be specific about what the effect of interest is and about the assumptions underlying the interpretation of the results. Halloran et al. (81) present design, analysis, and interpretation of vaccine studies in more detail.

The authors consider estimability and interpretation of vaccine efficacy based on time to event data, allowing that some of the population might have a very low probability of acquiring disease, and the rest have partial, possibly continuously distributed, susceptibility. The efficacy parameters of interest in the frailty mixing model include the fraction highly unlikely to acquire the infection or disease due to the vaccine, the degree of partial protection in those still susceptible, and the average protection or summary measure of efficacy under heterogeneity. The efficacy estimates can still be usefully interpreted when the heterogeneity results from heterogeneity in contact patterns, contact rates, or infectiousness of the contacts, as long as these are equal in the vaccinated and unvaccinated groups. A likelihood-based method allows estimation of the efficacy parameters of interest from grouped time to event data. Simulated vaccine studies assuming different levels and distributions of efficacy demonstrate that ignoring heterogeneity in susceptibility or exposure to infection generally results in underestimation of vaccine efficacy as well as incorrect interpretation of the estimates. The approach is also applicable to other covariates affecting susceptibility or exposure to infection in infectious diseases. Exploitation of the dependent happening structure of infectious diseases to obtain a shape for the baseline hazard may help identifiability. The authors recommend fitting several models to time to event data in vaccine studies.

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Current Phase III trials are designed to assess only a vaccine candidate's ability to reduce susceptibility to infection or disease, that is, vaccine efficacy for susceptibility (VES). Human immunodeficiency virus (HIV) vaccination, however, may reduce the level of infectiousness of vaccinees who become infected, producing an important indirect reduction in HIV transmission even if the vaccine confers only modest protection against infection. We propose two approaches for augmenting the information of a classic trial for estimating protective efficacy that enable the additional estimation of the vaccine's effect on infectiousness, that is, vaccine efficacy for infectiousness (VEI). In the first augmentation, steady sexual partners of trial participants are recruited but not randomized to vaccine or placebo. Their infection status is monitored throughout the trial. In the second augmentation, the sexual partners are randomized. Through computer simulations and analytic methods, we investigate the feasibility and statistical properties of the augmented designs. Phase III prophylactic HIV-1 vaccines trials are currently being planned. Employment of the augmented designs described in this paper would not only provide estimation of VEI but also increase the precision of the VES estimator and the power to reject the null hypothesis of no vaccine effect.

The authors present a nonparametric method for estimating vaccine efficacy as a smooth function of time from vaccine trials. Use of the method requires a minimum of assumptions. Estimation is based on the smoothed case hazard rate ratio comparing the vaccinated with the unvaccinated. The estimation procedure allows investigators to assess time-varying changes in vaccine-induced protection, such as those produced by waning and boosting. The authors use the method to reanalyze data from a vaccine trial of two cholera vaccines in rural Bangladesh. This analysis reveals the differential protection and waning effects for the vaccines as a function of biotype and age.