Optimal type I and type II error pairs when the available sample size is fixed.

OBJECTIVE: To model how to select the optimal pair of type I and type II errors that maximize study value when there are constrains on the available study sample size. STUDY DESIGN AND
SETTING: Correct inferences [true positives (TPs) and true negatives (TNs)] increase and wrong inferences (false positives and false negatives) decrease the value of a study. We model the composite value of a study based on these four inferences, their relative importance, and relative frequency using multiplicative and additive models. Numerical examples are presented for randomized trials, epidemiologic studies, and agnostic omics investigations with massive testing and variable sample size constraints.
RESULTS: The optimal choice of type I and type II errors varies a lot according to the available sample size and the plausible effect sizes in each field. We show how equations can be streamlined for special applications: when the value of all four inferences is considered equal, when the identification of TNs carries no value, and when a study carries no value unless at least one TP is discovered.
CONCLUSION: The proposed optimization equations can be used to guide the selection of the optimal type I and type II errors of future studies in which sample size is constrained.