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Table 1 5 different methods of analysis to estimate the association between treatment and outcome

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

  Analysis strategy Formula
a Univariable regression analysis logit(P[Y + 1]) = β0 + TβT
b Regression analysis with covariate adjustment logit(P[Y + 1]) = CβC + TβT
c Propensity score adjustment PS = CβC
logit(P[Y + 1]) = PSβPS + TβT
d IV analysis logit(P[Y + 1]) = ZβZ
e IV analysis with correction for hospital logit(P[Y + 1]) = ZβZ + HβH
f IV analysis with correction for hospital and all measured and unmeasured confounders logit(P[Y + 1]) = ZβZ + HβH + CβC + UβU
  1. Z: treatment preference as instrument: proportion of treated patients within each hospital
  2. H: hospital
  3. C: patient characteristics
  4. PS: propensity score
  5. T: treatment
  6. β0: intercept