In the evaluation of vaccine seroresponse rates and adverse reaction rates, extreme test results often occur, with substantial adverse event rates of 0% and/or seroresponse rates of 100%, which has produced several data challenges. Few studies have used both the Bayesian and frequentist methods on the same sets of data that contain extreme test cases to evaluate vaccine safety and immunogenicity. In this study, Bayesian methods were introduced, and the comparison with frequentist methods was made based on practical cases from randomized controlled vaccine trials and a simulation experiment to examine the rationality of the Bayesian methods. The results demonstrated that the Bayesian non-informative method obtained lower limits (for extreme cases of 100%) and upper limits (for extreme cases of zero), which were similar to the limits that were identified with the frequentist method. The frequentist rate estimates and corresponding confidence intervals (CIs) for extreme cases of 0 or 100% always equaled and included 0 or 100%, respectively, whereas the Bayesian estimations varied depending on the sample size, with none equaling zero or 100%. The Bayesian method obtained more reasonable interval estimates of the rates with extreme data compared with the frequentist method, whereas the frequentist method objectively expressed the outcomes of clinical vaccine trials. The two types of statistical results are complementary, and it is proposed that the Bayesian and frequentist methods should be combined to more comprehensively evaluate clinical vaccine trials.
Keywords: BCIs, Bayesian credible intervals; Bayesian method; C, control group; CIs, confidence intervals; CLl, lower confidence limit; CLu, upper confidence limit; FDA/CBER, Food and Drug Administration/ Center for Biologics Evaluation and Research; HAV, hepatitis A virus; HPV 16/18 AS04-adjuvanted, human papillomavirus vaccine -16/18 AS04-adjuvanted vaccine; HPV 6/11/16/18, human papillomavirus 6/11/16/18 quadrivalent vaccine; Hib conjugate, haemophilus influenza type b conjugate vaccine; MMRV, measles, mumps, rubella and varicella vaccine; T, test group; adverse event rates; extreme data; frequentist method; seroresponse rates; vaccine.