Power calculator for instrumental variable analysis in pharmacoepidemiology

Venexia M Walker, Neil M Davies, Frank Windmeijer, Stephen Burgess, Richard M Martin

Instrumental variable analysis, for example with physicians' prescribing preferences as an instrument for medications issued in primary care, is an increasingly popular method in the field of pharmacoepidemiology. Existing power calculators for studies using instrumental variable analysis, such as Mendelian randomization power calculators, do not allow for the structure of research questions in this field. This is because the analysis in pharmacoepidemiology will typically have stronger instruments and detect larger causal effects than in other fields. Consequently, there is a need for dedicated power calculators for pharmacoepidemiological research. The formula for calculating the power of a study using instrumental variable analysis in the context of pharmacoepidemiology is derived before being validated by a simulation study. The formula is applicable for studies using a single binary instrument to analyse the causal effect of a binary exposure on a continuous outcome. An online calculator, as well as packages in both R and Stata, are provided for the implementation of the formula by others. The statistical power of instrumental variable analysis in pharmacoepidemiological studies to detect a clinically meaningful treatment effect is an important consideration. Research questions in this field have distinct structures that must be accounted for when calculating power. The formula presented differs from existing instrumental variable power formulae due to its parametrization, which is designed specifically for ease of use by pharmacoepidemiologists.