Making Apples-to-Apples Comparisons Between Internal and External Studies Using Propensity Scores (1)

 

Propensity score analysis attempts to replicate the properties of a randomized trial with respect to the observed variables X. The following three methods are commonly used in propensity score analysis:

  •  weighting, which creates weights that are appropriate for estimating the ATE and ATT
  •  stratification, which creates strata based on propensity scores
  •  matching, which matches treated units with control units.



A propensity score analysis usually involves the following steps (Guo and Fraser 2015, p. 131):

1. You specify a set of confounding variables that might be related to both the treatment assignment and the outcome.

2. You use this set of variables to fit a logistic regression model and compute propensity scores. The response is the probability of assignment to the treated group.

3. You choose a propensity method (weighting, stratification, or matching) to compute observation weights (weighting), to construct strata of observations (stratification), or to select matched observations (matching).

4. You assess the balance of variables by comparing the distributions (before and after the propensity score weighting, stratification, or matching) between the treated and control groups.

5. To improve the balance, you can repeat the process with a different set of variables for the logistic regression model, a different region of support, a different set of matching criteria, or a different matching method.

6. When you are satisfied with the variable balance of the propensity score analysis, you save the output data set for subsequent outcome analysis.

Note that the outcome variable is not used in this process, and the variable selection is not related to the observed outcomes (Rubin 2001; Stuart 2010, p. 5). Any variables that might have been affected by the treatment should not be included in the process (Rosenbaum and Rubin 1984; Stuart 2010, p. 5).

After adequate variable balance has been achieved and assuming that no other confounding variables are associated with both the treatment assignment and the outcome, you can add the response variable to the output data set and perform an appropriate outcome analysis that is the same as the analysis you would perform with data from a randomized study. For example, if you used propensity score matching, a simple univariate test or analysis might be sufficient to estimate treatment effect.







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