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Pharmacoepidemiol Drug Saf. 2014 Feb;23(2):165-77. doi: 10.1002/pds.3555. Epub 2013 Dec 5.

Performance of instrumental variable methods in cohort and nested case-control studies: a simulation study.

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Division of Pharmacoepidemiology and Clinical Pharmacology, Utrecht Institute for Pharmaceutical Sciences, University of Utrecht, Utrecht, the Netherlands.



Instrumental variable (IV) analysis is becoming increasingly popular to adjust for confounding in observational pharmacoepidemiologic research. One of the prerequisites of an IV is that it is strongly associated with exposure; if it is weakly associated with exposure, IV estimates are reported to be biased. We aimed to assess the performance of IV estimates in various (pharmaco-)epidemiologic settings.


Data were simulated for continuous/binary exposure, outcome and IV in cohort and nested case-control (NCC) designs with different incidences of the outcome. Pearson's correlation, point bi-serial correlation, odds ratio (OR), and F-statistic were used to assess the IV-exposure association. Two-stage analysis was performed to estimate the exposure effect.


For all types of IV and exposure in the cohort and NCC designs, IV estimates were extremely unstable and biased when the IV was very weakly associated with exposure (e.g. Pearson's correlation < 0.15 for continuous or OR < 2.0 for binary IV and exposure; although specific cut-off values depend on simulation settings). For stronger IVs, estimates were unbiased and become less variable compared with weaker IVs in the case of continuous and binary (risk difference scale) outcomes. For a similar IV-exposure association (e.g. OR = 1.4 and 5% incidence of the outcome), the variability of the estimates was more pronounced in the NCC (standard deviation = 2.37, case : control = 1:5) compared with the cohort design (standard deviation = 1.14). The variability was even more pronounced for rare (≤1%) outcomes. However, IV estimates from the NCC design became less variable with an increasing number of controls per case. Moreover, estimates were biased when the IV was related to confounders even with strong IVs.


Instrumental variable analysis performs poorly when the IV-exposure association is extremely weak, especially in the NCC design. IV estimates in the NCC design become less variable when the number of control increases. As NCC does not use the entire cohort, in order to achieve stable estimates, this design requires a stronger IV-exposure association than the cohort design.


bias; cohort; confounding in epidemiology; instrumental variable; nested case-control; pharmacoepidemiology; rare outcome; simulation; variability; weak IV

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