Sample size, replicability, and pre-test likelihoods - essential, overlooked, and critical components of statistical inference - A Journal of Neurotrauma Guide to Statistical Methods and Study Design.

Abstract

Perhaps one of the most overlooked components of statistical inference is the sample size. While in randomized controlled trials, power analysis is common and sample size justification is an integral component of the core statistical analysis plan, observational and laboratory research studies often rely on convenience samples or underpowered analyses. This increases uncertainty associated with the results and limits interpretability. Moreover, it increases the likelihood that the findings might be disproved in future replication studies. A scientific study can be compared to a diagnostic test for the "truth", i.e. whether a certain effect exists or whether a relationship is actually true. In this diagnostic analogy, the positive predictive value is dependent not only on the statistical power of the study in question, but also on the pre-test likelihood that any true relationship exists at all. The concept of the using an estimate of the pre-test likelihood to interpret observed results is another critical and often overlooked component of statistical inference. Even if a statistically significant relationship or an effect is found, however, the finding in itself may be insufficient. It often must be replicated, ideally in a more generalizable setting. Furthermore, if the effect size is small, replication may require sample sizes that are substantially larger than the original study. As an extreme example, previous research into brain-wide associations where large numbers of comparisons are being performed teaches us that the effects measured are usually small and often require thousands of patients in order to be reliably estimated. For most neurotrauma research, thousands of subjects are usually not required, but many studies do require substantially larger sample sizes than are typically presented in order to increase replicability. In this methodological tutorial, choice of sample size, pre-test probability, and the concept of positive predictive value for scientific findings will be discussed, together with suggestions to improve replicability of neurotrauma research in the future.