title: Conditions for confounding of interactions.
abstract: OBJECTIVE
  Pharmaco-epidemiology increasingly investigates drug-drug or drug-covariate interactions. Yet, conditions for confounding of interactions have not been elucidated. We explored the conditions under which the estimates of interactions in logistic regression are affected by confounding bias.
  
  
  METHODS
  We rely on analytical derivations to investigate the conditions and then use simulations to confirm our analytical results and to quantify the impact of selected parameters on the bias of the interaction estimates.
  
  
  RESULTS
  Failure to adjust for a risk factor U results in a biased estimate of the interaction between exposures E1 and E2 on a binary outcome Y if the association between U and E1 varies depending on the value of E2. The resulting confounding bias increases with increase in the following: (i) prevalence of confounder U; (ii) strength of U-Y association; and (iii) heterogeneity in the association of E1 with U across the strata of E2. A variable that is not a confounder for the main effects of E1 and E2 may still act as an important confounder for their interaction.
  
  
  CONCLUSIONS
  Studies of interactions should attempt to identify-as potential confounders-those risk factors whose associations with one of the exposures in the interaction term may be modified by the other exposure.
authors.affiliation: Department of Epidemiology, Biostatistics and Occupational Health, McGill University, Montreal, Quebec, Canada.|Division of Clinical Epidemiology, Research Institute of the McGill University Health Centre, Montreal, Quebec, Canada.|Division of Population Health, CRCHUM Research Center, Montreal, Quebec, Canada.
authors.forename: Aihua
authors.initials: A
authors.lastname: Liu
authors.affiliation: Department of Epidemiology, Biostatistics and Occupational Health, McGill University, Montreal, Quebec, Canada.|Division of Clinical Epidemiology, Research Institute of the McGill University Health Centre, Montreal, Quebec, Canada.
authors.forename: Michal
authors.initials: M
authors.lastname: Abrahamowicz
authors.affiliation: Division of Population Health, CRCHUM Research Center, Montreal, Quebec, Canada.|Department of Social and Preventive Medicine, University of Montreal, Montreal, Quebec, Canada.
authors.forename: Jack
authors.initials: J
authors.lastname: Siemiatycki
mesh_terms: D015982:Bias; D003198:Computer Simulation; D015986:Confounding Factors, Epidemiologic; D004347:Drug Interactions; D006801:Humans; D016015:Logistic Models; D008175:Lung Neoplasms / Q000453:epidemiology / Q000209:etiology; D016017:Odds Ratio; D017891:Pharmacoepidemiology / Q000379:methods* / Q000706:statistics & numerical data*; D012107:Research Design / Q000706:statistics & numerical data*; D012307:Risk Factors; D012737:Sex Factors; D012907:Smoking / Q000009:adverse effects / Q000453:epidemiology; D012959:Socioeconomic Factors
keywords: confounding bias; effect modification; interaction; logistic regression; pharmacoepidemiology; simulations