Anna G C Boef1, Olaf M Dekkers2, Jan P Vandenbroucke3, Saskia le Cessie4. 1. Department of Clinical Epidemiology, C7-P, Leiden University Medical Centre, PO Box 9600, 2300 RC Leiden, The Netherlands. Electronic address: a.g.c.boef@lumc.nl. 2. Department of Clinical Epidemiology, C7-P, Leiden University Medical Centre, PO Box 9600, 2300 RC Leiden, The Netherlands; Department of Endocrinology and Metabolic Diseases, Leiden University Medical Centre, Leiden, The Netherlands. 3. Department of Clinical Epidemiology, C7-P, Leiden University Medical Centre, PO Box 9600, 2300 RC Leiden, The Netherlands. 4. Department of Clinical Epidemiology, C7-P, Leiden University Medical Centre, PO Box 9600, 2300 RC Leiden, The Netherlands; Department of Medical Statistics and Bioinformatics, Leiden University Medical Centre, Leiden, The Netherlands.
Abstract
OBJECTIVES: Instrumental variable (IV) analysis is promising for estimation of therapeutic effects from observational data as it can circumvent unmeasured confounding. However, even if IV assumptions hold, IV analyses will not necessarily provide an estimate closer to the true effect than conventional analyses as this depends on the estimates' bias and variance. We investigated how estimates from standard regression (ordinary least squares [OLS]) and IV (two-stage least squares) regression compare on mean squared error (MSE). STUDY DESIGN: We derived an equation for approximation of the threshold sample size, above which IV estimates have a smaller MSE than OLS estimates. Next, we performed simulations, varying sample size, instrument strength, and level of unmeasured confounding. IV assumptions were fulfilled by design. RESULTS: Although biased, OLS estimates were closer on average to the true effect than IV estimates at small sample sizes because of their smaller variance. The threshold sample size above which IV analysis outperforms OLS regression depends on instrument strength and strength of unmeasured confounding but will usually be large given the typical moderate instrument strength in medical research. CONCLUSION: IV methods are of most value in large studies if considerable unmeasured confounding is likely and a strong and plausible instrument is available.
OBJECTIVES: Instrumental variable (IV) analysis is promising for estimation of therapeutic effects from observational data as it can circumvent unmeasured confounding. However, even if IV assumptions hold, IV analyses will not necessarily provide an estimate closer to the true effect than conventional analyses as this depends on the estimates' bias and variance. We investigated how estimates from standard regression (ordinary least squares [OLS]) and IV (two-stage least squares) regression compare on mean squared error (MSE). STUDY DESIGN: We derived an equation for approximation of the threshold sample size, above which IV estimates have a smaller MSE than OLS estimates. Next, we performed simulations, varying sample size, instrument strength, and level of unmeasured confounding. IV assumptions were fulfilled by design. RESULTS: Although biased, OLS estimates were closer on average to the true effect than IV estimates at small sample sizes because of their smaller variance. The threshold sample size above which IV analysis outperforms OLS regression depends on instrument strength and strength of unmeasured confounding but will usually be large given the typical moderate instrument strength in medical research. CONCLUSION: IV methods are of most value in large studies if considerable unmeasured confounding is likely and a strong and plausible instrument is available.
Authors: Christel Häggström; Hans Garmo; Xavier de Luna; Mieke Van Hemelrijck; Karin Söderkvist; Firas Aljabery; Viveka Ströck; Abolfazl Hosseini; Truls Gårdmark; Per-Uno Malmström; Staffan Jahnson; Fredrik Liedberg; Lars Holmberg Journal: Cancer Med Date: 2019-04-01 Impact factor: 4.452
Authors: Kenneth S Kendler; Henrik Ohlsson; Sean Clouston; Abigail A Fagan; Jan Sundquist; Kristina Sundquist Journal: Psychol Med Date: 2020-01-07 Impact factor: 7.723