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.
PIP: Vaccine efficacy (VE) is typically estimated by the equation VE = 1 minus relative risk (RR), where RR is based on a comparison of vaccinated and unvaccinated groups. However, since vaccine effects do not follow a simplified model such as an exponential decline in protection, estimation of a rate ratio for time-to-event data is difficult. This paper presents a method for nonparametrically estimating VE(t) = 1 - RR(t) from time-to-event data when the protective effects of a vaccine can wane or boost over time. The method, based on smoothing scaled residuals from a proportional hazards model, is then applied to a reanalysis of data from a trial in rural Bangladesh of two cholera vaccines. The placebo and vaccine curves should be roughly parallel for all time if there are no time-varying effects. Application to the data from Bangladesh confirmed this method provides reliable estimation and analysis of field data. The reanalysis revealed the differential protection and waning effects for the vaccines as a function of biotype and age.