ASA Connect

You can use the propensity score, or the logit of the propensity score, as a covariate, but that approach seems to often be less optimal based on simulation studies. Our group is working on a decision tool (through a PCORI-funded methods project) to address such questions more systematically.

If your data set is large, there is an alternative technology that should be considered, Local Control. Very briefly, cluster the data on important covariates, then compute a statistic, e.g. the difference between two treatments, the correlation between two variables, within each cluster. Now use the centroids of the clusters as your Xs and the within cluster statistics as your Y. The objects within a cluster are statistical clones. Some of the ins and outs as well as a discussion of the advantages can be found in these publications.

Obenchain RL, Young SS. (2013) Advancing statistical thinking in health care research. Journal of Statistical Theory and Practice 7, 456-469.

Lopiano KK, Obenchain RL, Young SS. (2014) Fair Treatment Comparisons in Observational Research. Statistical Analysis and Data Mining 7, 376–384.

You can use the propensity score, or the logit of the propensity score, as a covariate, but that approach seems to often be less optimal based on simulation studies. Our group is working on a decision tool (through a PCORI-funded methods project) to address such questions more systematically.

You can use the propensity score, or the logit of the propensity score, as a covariate, but that approach seems to often be less optimal based on simulation studies. Our group is working on a decision tool (through a PCORI-funded methods project) to address such questions more systematically.

You are not restricted to a logistic model to compute a propensity score. You can use a non-linear model such as a classification tree (for instance), which can take care of interactions and non-linearities among covariates predicting group membership and doesn't require you to assume a specific model form (i.e., a linear equation). Not that classification trees are the modeling silver bullets, but the do require fewer assumptions compared to the more common logistic models. You can check if your propensity score model seems appropriate by using a residual analysis. The model residuals should not be associated to any of the covariates.

Once you have that, you can conduct the analysis of interest using a simpler linearized model predicting your outcome, but based on two variables: 1) the group indicator, and 2) the propensity score as the only covariate. This simplifies the modeling effort.    

You could also match based on the propensity score, or other metric such as a multivariate distance (Mahalanobis). There are some newer algorithms for that like GenMatch.

Here is a paper where we did both the propensity score adjustment (with propensity scores from a non-linear model), and matching (with Mahalanobis distance). Fortunately the conclusions from both analyses were similar.

http://www.ncbi.nlm.nih.gov/pubmed/27185053

You are not restricted to a logistic model to compute a propensity score. You can use a non-linear model such as a classification tree (for instance), which can take care of interactions and non-linearities among covariates predicting group membership and doesn't require you to assume a specific model form (i.e., a linear equation). Not that classification trees are the modeling silver bullets, but the do require fewer assumptions compared to the more common logistic models. You can check if your propensity score model seems appropriate by using a residual analysis. The model residuals should not be associated to any of the covariates.

Once you have that, you can conduct the analysis of interest using a simpler linearized model predicting your outcome, but based on two variables: 1) the group indicator, and 2) the propensity score as the only covariate. This simplifies the modeling effort.    

You could also match based on the propensity score, or other metric such as a multivariate distance (Mahalanobis). There are some newer algorithms for that like GenMatch.

Here is a paper where we did both the propensity score adjustment (with propensity scores from a non-linear model), and matching (with Mahalanobis distance). Fortunately the conclusions from both analyses were similar.

http://www.ncbi.nlm.nih.gov/pubmed/27185053