title: Sensitivity analysis for the effects of multiple unmeasured confounders.
abstract: Observational studies are prone to (unmeasured) confounding. Sensitivity analysis of unmeasured confounding typically focuses on a single unmeasured confounder. The purpose of this study was to assess the impact of multiple (possibly weak) unmeasured confounders.
  
  
  
  Simulation studies were performed based on parameters estimated from the British Women's Heart and Health Study, including 28 measured confounders and assuming no effect of ascorbic acid intake on mortality. In addition, 25, 50, or 100 unmeasured confounders were simulated, with various mutual correlations and correlations with measured confounders.
  
  
  
  The correlated unmeasured confounders did not need to be strongly associated with exposure and outcome to substantially bias the exposure-outcome association at interest, provided that there are sufficiently many unmeasured confounders. Correlations between unmeasured confounders, in addition to the strength of their relationship with exposure and outcome, are key drivers of the magnitude of unmeasured confounding and should be considered in sensitivity analyses. However, if the unmeasured confounders are correlated with measured confounders, the bias yielded by unmeasured confounders is partly removed through adjustment for the measured confounders.
  
  
  
  Discussions of the potential impact of unmeasured confounding in observational studies, and sensitivity analyses to examine this, should focus on the potential for the joint effect of multiple unmeasured confounders to bias results.
authors: Julius Center for Health Sciences and Primary Care, University Medical Center Utrecht, Utrecht, The Netherlands. Electronic address: r.h.h.groenwold@umcutrecht.nl.
authors: Rolf H H
authors: RH
authors: Groenwold
authors: School of Social and Community Medicine, University of Bristol, Bristol, UK; MRC Integrative Epidemiology Unit, University of Bristol, Bristol, UK.
authors: Jonathan A C
authors: JA
authors: Sterne
authors: School of Social and Community Medicine, University of Bristol, Bristol, UK; MRC Integrative Epidemiology Unit, University of Bristol, Bristol, UK.
authors: Debbie A
authors: DA
authors: Lawlor
authors: Julius Center for Health Sciences and Primary Care, University Medical Center Utrecht, Utrecht, The Netherlands.
authors: Karel G M
authors: KG
authors: Moons
authors: Julius Center for Health Sciences and Primary Care, University Medical Center Utrecht, Utrecht, The Netherlands.
authors: Arno W
authors: AW
authors: Hoes
authors: School of Social and Community Medicine, University of Bristol, Bristol, UK; MRC Integrative Epidemiology Unit, University of Bristol, Bristol, UK.
authors: Kate
authors: K
authors: Tilling
mesh_terms: D001205:Ascorbic Acid / Q000008:administration & dosage*; D002318:Cardiovascular Diseases / Q000453:epidemiology* / Q000517:prevention & control; D015986:Confounding Factors, Epidemiologic; D004812:Epidemiologic Methods; D005260:Female; D006801:Humans; D009026:Mortality / Q000639:trends*; D012107:Research Design; D012680:Sensitivity and Specificity; D016387:Women's Health
chemical_list: D001205:Ascorbic Acid
keywords: Bias; Confounding; Sensitivity analysis