A Markov model for sample size calculation and inference in vaccine cost-effectiveness studies

Sample size and power formulae are derived for designing trials of vaccine cost-effectiveness in healthy working adults. When existing trials of influenza vaccine have presented sample size calculations, these have been based on vaccine effectiveness. A Markov model is introduced to account for non-independence of working days lost. Two effect sizes need to be specified, one for a reduction in the number of episodes of absence and the second for a reduction in the mean duration of episodes. The relative cost of vaccine provision is also incorporated. Applying the resulting formulae to published studies indicates that most were underpowered to detect any financial benefit. Moreover, biased estimates of variance have led to led to incorrect inference.