Controlling for Damn Near Everything: Propensity Score Matching

Lately I have been on a roll looking at relatively less common statistical techniques, proportional hazards, survival analysis, etc.

In keeping with that, I have been taking a look at propensity score matching, fondly known as PSM by, – well, by no one actually.

The problem to be solved ….

Think about some of these comparisons:

  • Hospitals with special burn,cardiac or neonatal units versus general hospitals
  • Public schools versus parochial, private or charter schools
  • People who watch TV > 40 hours weekly versus those surfing the Internet > 40 hours

In all of these cases, and probably a lot more you can think of, there are very likely differences in certain “outcome” variables, whether it be survival in the case of hospital patients, academic achievement of students or annual income of TV versus Internet users. However, all of these comparisons also begin with groups who are already different.

For example …

You have two groups, say people who are treated at a hospital with a specialized unit for terminally ill patients and patients from another hospital without any such specialized unit.  Your outcome variable of interest is whether the patient lived or died.

The simplest way to test this is a chi-square. You compare the percentage of people who survived at St. George of Money Hospital versus Heart of Despair County Hospital.  There is a problem with that, though.  A simple comparison will almost always show WORSE outcomes for hospitals with special units for patients who are terminally ill, seriously burned, extremely premature births, etc. The reason is probably obvious  – if you get sicker patients, they are less likely to live.  If your interest is in knowing whether having a specialized unit increases your chances of survival, you would want to compare similar groups.

It isn’t as simple as just controlling for severity of condition, though. There are other variables, for example, people who are better educated, who have private insurance and who live in urban areas all may be more likely to be patients at more “elite” hospitals. Some of those factors may be related to survival as well. What we’d really like is to compare a  group of people from St. Money’s that is similar to patients from Despair.

In short, certain types of people have a greater propensity to be admitted to one type of place than the other.

Enter propensity score matching — to the sounds of trumpets and wearing a cape.

In fact, the first step is to do a logistic regression analysis and I will admit that it is not strictly necessary to wear a cape while doing so but it would probably be more comfortable than this business suit from Filene’s that I am wearing.

Using SPSS, go to the ANALYZE  menu, select REGRESSION, then select BINARY LOGISTIC. Your dependent variable will be the hospital to which the patient was admitted. Covariates are the variables such education, severity of illness and insurance that you want to control.  For variables that are categorical, e.g., insurance, which could be private, public (a.l.a. MediCal if it hasn’t disappeared in the latest round of state budget cuts) and none, click on the CATEGORICAL button and move those over to the “Categorical covariate” window.

Here’s the really important part  — click on SAVE and select PREDICTED PROBABILITIES – that is your propensity score.

This is what you are going to match on. Hence the name.

This is step one. I would say it gets easier after this point – but it doesn’t.

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  1. Once you have the scores, for every participant you match with a non-participant. That is the matching part. Say I am looking at 600 people who were admitted to St. Money’s and 7,200 admitted to Despair. For each of the 600, I find a person in Despair who has the identical propensity score. If there is more than one person, I randomly sample a person from those that match. If there is no one with the identical score, I sample the person as close as possible. So, I end up with 600 in each group and then do my analysis.

  2. AnnMaria,
    that is what I did as well, but it is very time consuming doing this manually. Do you have any tricks to doing the matching? I was only matching around 80, but 600 would have been huge to do manually.
    Appreciate the thread!

  3. Can I ask why you just don’t control for all covariates? Won’t controlling for severity of the condition, education, having private insurance and living in urban areas, and all the other covariates relating to hospital attended and survival chances, produce the same results as the work-intensive propensity score matching? In other words, what are the advantages of propensity score matching versus controlling for all covariates in your initial multivariate model? Thanx!

  4. That is a really interesting question and it is very timely because I wrote this post years ago and am writing part 2 at this very moment.

    Some people say there is no advantage of propensity score matching versus controlling for all covariates:

    Check out

    The Importance of Covariate Selection in Controlling for Selection Bias in Observational Studies

    by Steiner et al.

    They argue that having the right covariates is far more important than whether you use propensity scores or covariates. I agree.

  5. Dear AnnMaria,

    Thank you so much for the reference! It was enormously helpful. I agree too now 😉

    Take care!

  6. Thanks so much. I was almost lost while reading this topic in many of the books/documents etc. but was unable to get the crux.
    It was really helpful.


  7. One more thing to ask, is there any criteria that where to apply a logit or a probit model for propensity scores or it simply works using the basics of modelling (Regression)

  8. Stata would be more easier to perform this propensity matching..without any macros

  9. Dear AnnMaria,
    I have a dilema – I have two experimental groups – roughly the same size- and these could be combined and a comparison group that is roughly equivalent in size to one of the experimental groups or half the combined experimental groups. I know I can weigh propensity scores as well as use them for matching but my sample sizes are small to start with. I also thought I could compare each experimental group separately to the control. Any suggestions?

  10. If your two groups are very small, propensity scores are not going to be a good choice. Comparing the experimental groups separately would give you a higher Type I error because each test would have a .05 probability of error. If you can reasonably combine your experimental groups, e.g., they were just people sampled on two different days to see the targeted ad, that is a possibility. Or, you could an an ANOVA with the three groups if you don’t think it is justifiable to combine the two control groups.

  11. Hi! Have you ever used SPSS Complex Samples with Propensity Score Matching (v22)? I’m encountering an issue with my large dataset… It seems to just keep running without any results. Is it possible that missing data is causing the analysis to crash? Any insight?

    Thank you!!!

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