Background When planning vaccine trials or interpreting results, it is not always clear which outcome measure best estimates the effect of the vaccine and at which time point it should be measured. We used a mathematical model to explore questions arising from the analysis of pneumococcal nasopharyngeal carriage data from conjugate vaccine trials, in which the acquisition-rate ratio (ARR) is the desired effect measure. We determine the time at which the prevalence ratio (PR) or prevalence POR, which are usually available, provide the best approximation.
Methods We created a hypothetical randomised controlled trial using a dynamic compartmental model which incorporated carriage of vaccine-type Streptococcus pneumoniae in vaccinated and unvaccinated groups. ARR was incorporated explicitly, linking the acquisition rate in the vaccinated to the acquisition rate in the unvaccinated and was assumed not to change for 2 years. Prevalence ratios and prevalence ORs for carriage were plotted over time.
Results The PR approximates the ARR well, after an initial period in which the PR decreases from one and stabilises. The length of this period is determined by the duration of carriage. During the period when the PR approximates the ARR, the POR overestimates the effect of vaccination. This is less marked when carriage is rare.
Conclusions This model illustrates the behaviour of outcome measures for pneumococcal carriage in a simple setting and can be elaborated to explore more complex situations. Mathematical models provide opportunities to explore study designs and analysis methods for both planned and completed vaccine trials.
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