Week 4 - PS Stratification Flashcards
What are two strategies to perform propensity score stratification to estimate the ATE and ATT?
- pool strata-specific treatment effects
* obtain a marginal treatment effect across strata (marginal mean weighting through stratification)
What are the steps of propensity score stratification?
Step 1: Use the PS to stratify all observations into j = 1, 2, 3, … , k strata.
Step 2: Calculate observation weights.
Step 3: Obtain the effect within each stratum then average the effects weighted by strata proportions
How are strata obtained?
- Divisions (usually quintiles) based on the total sample.
* Divisions (usually quintiles) based the treated group only. (Better for ATT.)
What is an indication of common support problems in propensity score stratification?
If you don’t get at least one treated and control in each strata, there is a problem.
What is the relationship between the number of strata and bias reduction?
More strata remove more bias but there needs to be at least one treated and one control observation per stratum.
How can covariate balance be evaluated with propensity score stratification?
standardized mean differences and variance ratios for all covariates
What are three strategies that can be used if covariate balance within strata was not achieved?
1) Change the form of the propensity score model or the method to estimate propensity scores.
2) Remove within-stratum residual bias by combining stratification with weighting, matching, direct covariate adjustment with ANCOVA (Schafer & Kang, 2008), or regression estimation of group means within strata (Lunceford & Davidian, 2004).
3) Change the focus to marginal treatment effect across strata rather than pooled stratum-specific effects, in which case covariate balance can be evaluated across strata rather than within strata.
How can treatment effects estimated within each stratum be combined?
The treatment effect for the entire sample can be obtained with a weighted sum of within-stratum treatment effects.
How is marginal mean weighting similar to post-stratification in survey data analysis?
MMWS is similar to post-stratification in survey data analysis because post-stratification adjusts for differences between sample proportions within strata and population proportions.
What is the interpretation of the numerator of the marginal mean weight through stratification to estimate the ATE?
the expected number of units assigned to condition z in stratum s in a completely randomized experiment,
(ns X pr (Z = z) meaning number of units in stratum times the marginal proportion receiving condition z)
What is the advantage of marginal mean weighting through stratification over inverse probability of treatment weighting?
REVISED MMWS is more robust to misspecifications of the propensity score model than inverse probability of treatment weighting
(The fact that weights for MMWS are computed from strata rather than directly from propensity scores brings the advantage that MMWS is less likely to produce extreme weights, which can affect the performance of propensity score weighting.)
What is the limitation of propensity score stratification methods as compared to propensity score weighting methods?
Propensity score stratification is expected to provide less bias reduction than matching or weighting.
What are two options for doubly-robust estimation of treatment effects with propensity score stratification?
**For estimation with within-strata means, regression estimation can be used to obtain the within-stratum means of treated and untreated groups.
**For estimation with weighted least squares regression using the MMWS, the treatment effect estimate can be made doubly-robust by adding covariates to the model, and/or dummy stratum indicators.
