Week 7 - PS for Continuous Treatments Flashcards
How does the concept of potential outcomes, which is the key part of Rubin’s causal model, generalize to continuous treatments?
For each dose of treatment, there is a vector of potential outcomes for all doses, and the individual treatment effect at a dose is the mean of the potential outcomes. (Both the generalized propensity score method and the inverse probability weighting method are anchored in Rubin’s causal model because they conceptualize the observed outcome of each treatment dose as part of a vector of potential outcomes.)
What is the assumption of weak unconfoundness in the context of continuous treatments?
The potential outcomes of the treatment at dose z is independent of treatment dosage assignment given covariates.
What is the generalized propensity score of a treatment dose?
The generalized propensity score for each individual (i) is the conditional density of the treatment evaluated at the individual’s specific values of Z (the dose) and X (covariates).
What are the steps of Hirano and Imbens (2000) generalized propensity score method?
1) Model the continuous treatment indicator as a function of covariates;
2) Obtain generalized propensity scores;
3) Model the outcomes as a function of treatment and generalized propensity scores.
4) Estimate the average potential outcome at each treatment dose of interest (the dose response function).
How did Hirano and Imben’s (2000) evaluate covariate balance?
Stratify the sample according to both treatment dosage and GPS, and perform t-tests across the strata.
What are the limitations of Hirano and Imben’s (2000) method to evaluate covariate balance?
Requires a large number of paired comparisons.
Covariate balance depends on sample size.
How are individual treatment responses estimated with the generalized propensity score method?
Individual treatment effects are the average potential outcome at treatment dose z given the coefficients of the outcome model.
How can the effect of two treatment doses be compared using the generalized propensity score method?
With a plot dose response function.
How is the dose response function plot constructed?
Individual treatment effects are the average potential outcome at treatment dose z given the coefficients of the outcome model. One plots the dose on the X and the outcome on the Y.
What is the inverse probability weight for continuous treatments?
The weight uses a denominator that is the conditional density of the treatment evaluated at the values of Z and X of individual i. Therefore, the denominator of the weight is the GPS. The numerator is the marginal density of the treatment variable.
How does the inverse probability weight reduce selection bias?
IPW balances distribution with respect to covariates by creating a pseudo-population, thereby standardizing the statistics.
How can covariate balance be evaluated with the inverse probability weight for continuous treatments?
- Estimate bivariate regressions of the treatment dosage on each covariate with and without the IPW.
- Compare the regression coefficients obtained with and without the use of the IPW.
- In the pseudo-population generated by the IPW, the treatment dose should be uncorrelated with the covariates.
- Coefficients of the regression of the treatment dose on the covariate should be close to zero.
How can the average treatment effect be estimated with inverse probability weights for continuous treatments?
Any parametric model can be used that incorporates the IPW into the estimation method.
What are the advantages of including covariates in the model for the outcome with inverse probability weights?
- Provide additional adjustment of selection bias.
- Increase power.
- Achieve double robustness.
