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Table 2 Calculation and interpretation of propensity weights

From: Youth vaping and smoking and parental vaping: a panel survey

Estimand How predicted probabilities of exposure are used to calculate weightsa: Re-weighting of confounding characteristics in exposure groups: Estimated effect for youth vaping applies to … Estimated effect for Parental Vaping applies to …
Numerator Denominator Unexposed Exposed   
Average Treatment Effect
(ATE)
P P^ Resemble sample characteristics Resemble sample characteristics All youth All youth
Average Treatment Effect among the Treated
(ATT)
1 if exposed,
1-P^ if unexposed
1 if exposed,
P^ if unexposed
Resemble Exposed group Unchanged Youth who do vape Youth whose parents did vape
  1. P=Overall, unadjusted probability of individual’s observed exposure level
  2. P^=Predicted probability of individual’s observed exposure level conditional on confounders
  3. aWhen investigating effects of parental vaping within strata of parental smoking, both P and P^ were additionally conditional on parental smoking