| This thesis compares the vaccine efficacy (VE) estimation performance of a discrete-time method and a continuous-time method, with special emphasis on the case where there are initially unvaccinated people who are vaccinated during the epidemic. The continuous-time method is proposed to account for this situation by keeping track of the vaccination status of every person in the study over time. The discrete-time method treats these people as censored after their vaccination during the study. For both methods, the likelihood functions for both methods are obtained, the maximum likelihood estimates of parameters are then derived, and the estimated vaccine efficacy is calculated based on the estimates. Both methods are applied to data from a measles study in Chad. Simulations are conducted to compare the performance of these two methods in different settings. The results suggest that the continuous-time method does not always perform better than the discrete-time method even when initially unvaccinated people become vaccinated during the epidemic. On the other hand, when the true value of VE and proportion of people initially vaccinated change, I found a cutoff point beyond which continuous method outperforms the discrete method. All these findings are based on two-parameter estimation results in the all/nothing model. |
