Week 3 - PS Weighting Flashcards
What is the difference between propensity score weights and sampling weights?
Sampling weights adjust for bias due to oversampling of individuals with certain characteristics so that the weighted sample is representative of the population of interest. Similarly, propensity score weights adjust for over-selection of participants with certain characteristics to treated or untreated groups.
What is the difference between the weights for estimating the ATE and the ATT?
The weight for the ATT is equal to one for treated individuals and the odds of treatment for untreated individuals (Harder, et al., 2010).
wi = Zi + (( 1 - Zi)(ei-hat/(1 - ei-hat)))
vs.
wi = (Zi/ei-hat) + ((1 - Zi)/(1 - ei-hat))
Zi = condition (1 or 0); ei-hat = propensity score
What are possible causes of extreme propensity score weights?
Lack of common support.
Model misspecification.
What are possible consequences of extreme propensity score weights?
Inadaquate covariate support.
Biased estimates.
Inflated standard errors.
(Last two make finding treatment effect difficult.)
What are possible methods to deal with extreme weights?
Re-specify the propensity score model.
Switch to another propensity score method.
Truncate weights.
Trim sample based on propensity scores.
Use stabilized weights.
What are the advantages and shortcomings of trimming the sample?
Advantage is it deals with lack of overlap in propensity score analysis, but it could also be used to remove extreme weights by creating a calculation of an optimal cutoff for gaining precision in the ATE estimates by trimming, and also show that a similar level of precision gain can be obtained trimming observations outside of the [0.1, 0.9] interval of the propensity scores.
Disadvantage is individuals with large weights are those that provide the most information about the outcome. (“Loss of a large piece of a sample/lots of cases.”)
What is the difference between propensity score weights and stabilized propensity score weights?
The ps weights sum ps’s (or differences; 1 - ps) divided by the group size for treatment and control respectively, while the stabilized weights sum the ps (or differences) times the weight and divide by the summed weights for each condition.
How should covariate balance be checked after propensity score weighting?
Both…
Comparison between standardized differences between weighted means of treated and control group for each covariate.
Comparison of ratios of weighted variances of treated and control groups for each covariate.
What are two options to estimate the treatment effect with propensity score weighting?
Horvitz and Thompson Estimator of the Treatment Effect (Rosenbaum, 1987)
OR
Weighted Least Squares Estimator of the Treatment Effect
OR
Doubly-Robust Estimation of Treatment Effects
How can sampling weights be incorporated into the treatment effect estimation with propensity score weights?
Horvitz and Thompson Estimator of the TE (Rosenbaum, 1987) is the difference between weighted means.
Describe two options to obtain standard errors of the estimated treatment effect.
Taylor series linearization (obtain the variance of statistics which are a non-linear combination of means and totals by finding linear functions analytically or numerically
that approximate the statistics)
Replication technique - Jackknife (divide into random groups, create subsamples, replicate the weights, estimate parameters, get new SE)
Replication technique - Bootstrap (take replacement samples with the same size of the original, estimate parameter, get new SE)
What is a doubly-robust estimator?
Doubly-robust estimation consists in removing bias due to covariates using both the propensity score model and the outcome model.
How can doubly-robust estimation be implemented with propensity score weighting?
- Estimate outcome means of the treated and untreated using separate regression models with weights.
- Calculate the difference between means.
