Repository logo

Power calculator for instrumental variable analysis in pharmacoepidemiology

Published version



Change log


Walker, VM 
Davies, NM 
Windmeijer, F 
Martin, RM 


Background: 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. Methods and Results: 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. Conclusions: 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.



pharmacoepidemiology, instrumental variable, power, binary exposure, continuous outcome, prescribing preference

Journal Title

International Journal of Epidemiology

Conference Name

Journal ISSN


Volume Title


Oxford University Press
Medical Research Council (G0700463)
Medical Research Council (MR/L003120/1)
Wellcome Trust (204623/Z/16/Z)
British Heart Foundation (None)
Medical Research Council (MC_UU_00002/7)
TCC (None)
Medical Research Council (G0700463/1)
This work was supported by the Perros Trust and the Integrative Epidemiology Unit. The Integrative Epidemiology Unit is supported by the Medical Research Council and the University of Bristol [grant number MC_UU_12013/9]. S.B. is supported by a Sir Henry Dale Fellowship jointly funded by the Wellcome Trust and the Royal Society (Grant Number 204623/Z/16/Z).
Is derived from: