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Table 4 Overview of all 7 different scenarios simulated, with DAGs illustrating the assumed causal pathway

From: Instrumental variable analysis to estimate treatment effects: a simulation study showing potential benefits of conditioning on hospital

  1. T: Treatment
  2. C: confounders; patient characteristics
  3. U: Unmeasured confounders
  4. H: Hospital
  5. Z: proportion of treated patients within each hospital
  6. βCT: Effect of C on T
  7. βUT: Effect of U on T; amount of unmeasured patient level confounding
  8. βCy: Effect of C on Y; amount of measured patient level confounding
  9. βUy: Effect of U on Y; amount of unmeasured patient level confounding
  10. βHt (a set of β’s for each level of H) Effect of H on T
  11. βHY (a set of β’s for each level of H) Effect of H on Y separate from Z;
  12. βT The ‘true’ treatment effect (unknown in empirical data)