Prevalence and sample sizes in pre-clinical studies

This work explores the relationship between event prevalence and event observation in the context of a study with a fixed number of subjects. For any given study size, one expects the number of occurrences of a given event to increase as the prevalence of that event increases. We use the Binomial distribution to characterize the likelihood of observing at least one specified event for a fixed sized study over a range of prevalence values. From this, we explore the marginal impact on that likelihood as the study size increases. We present findings regarding the value of prevalence that maximizes the marginal impact of adding one additional subject to a study. We then explicitly characterize the interaction of prevalence and sample size in yielding event observation and provide a vehicle by which study planners may design studies based on risk of non-detection as opposed to traditional power calculations.