Probabilistic precision calculations for the planning of studies assessing negative binomial rates.

Purpose: Outcome variables that are assumed to follow a negative binomial distribution are frequently used in both clinical and epidemiological studies. Epidemiological studies, particularly those performed by pharmaceutical companies often aim to describe a population rather than compare treatments. Such descriptive studies are often analysed using confidence intervals. While precision calculations and sample size calculations are not always performed in these settings, they have the important role of setting expectations of what results the study may generate. Current methods for precision calculations for the negative binomial rate are based on plugging in parameter values into the confidence interval formulae. This method has the downside of ignoring the randomness of the confidence interval limits. To enable better practice for precision calculations, methods are needed that address the randomness.

Methods: Using the well-known delta-method we develop a method for calculating the precision probability, that is, the probability of achieving a certain width. We assess the performance of the method in smaller samples through simulations.

Results: The method for the precision probability performs well in small to medium sample sizes, and the usefulness of the method is demonstrated through an example.

Conclusions: We have developed a simple method for calculating the precision probability for negative binomial rates. This method can be used when planning epidemiological studies in for example, asthma, while correctly taking the randomness of confidence intervals into account.