A team of researchers wish to test a new vaccine that is hoped to provide protection against an additional strain of influenza beyond the strains included in the current vaccine.
They propose a two-arm study where participants are randomised to receive either the current vaccine or the new vaccine, with equal numbers in each treatment arm. The primary outcome of the study is the proportion of participants who exhibit at least a four-fold increase in serum antibody level from pre-vaccination to 28 days post-vaccination. a) 2 marks Write down the null and alternative hypotheses to test whether the proportion differs between treatments. Discuss briefly whether you think a one- or two-sided hypothesis would be more appropriate for this study. b) 2 marks Prior experience with the standard vaccine shows that the proportion who exhibit the required increase in antibody level is expected to be 0.67. Approximately 450 participants are available for the study. Assuming a = 0.05, i. What is the power of this study to detect a difference of 0.1 in proportions between the two vaccines? ii. What sample size is required to achieve 80% power? c) 1 marks The investigators decide that a difference in proportion of 0.07 between vaccines is more plausible. What sample size is required to detect that difference, assuming a = 0.05. d) 2 mark What options would you suggest to the investigators to design their study? e) 2 marks Not all participants will return for their 28-day post-vaccination measure. By what factor would you need to increase the sample size to account for an anticipated 5% loss to follow-up and still achieve the required statistical power?