I have a data set that includes a primary dichotomous independent variable (e.g., smoking), a primary dichotomous dependent variable (e.g., chronic back pain), and several covariates (e.g., diagnosis of several mental disorders, age, sex). I have calculated propensity scores for smoking using the covariates of interest. As an output, I am given a data file that includes only individuals who have been matched. Lets say I have 1000 smokers and 1000 non-smokers, with both groups matched on the covariates. Note that by "matched" I mean the two samples share similar means on the covariates, not that smokers are matched with non-smokers with similar propensity scores.

I am interested in seeing if individuals who smoke are more likely to have chronic pain in this sample matched on the covariates of interest. To do this, I would typically cross tabulate smoking/non-smoking and pain/no pain and calculate odds ratios.

Is it still appropriate to calculate odds ratios after a sample is matched on propensity scores based on covariates?

Does changing the number of participants in the control group create any problems? For instance, I could perhaps have 1000 smokers and 4000 non-smokers and calculate odds ratios using these numbers.

My intuition tells me that doing this is fine, but I want to make sure since I have never seen it done.


Yes, it is appropriate to calculate odds ratios on samples stratified on covariates by means of propensity scores. Some researchers believe you need to take the matched nature of the data as a sign that the groups are not independent, but this is not necessarily the case (Schafer & Kang, 2008; http://www.ncbi.nlm.nih.gov/pubmed/19071996).

The number of individuals in your control group should not matter as the proportions of individuals who fit within your independent variable classes should be the same. Keep in mind current recommendations on the proportion of individuals to match in your control group compared to your treatment group (Austin, 2010; http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2962254/).

Note that matching on the propensity scores rather than stratifying on the propensity scores (as your are suggesting) would likely lead to less biased estimates (http://www.ncbi.nlm.nih.gov/pubmed/17187347).


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