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.

Comments

20 Responses to “Controlling for Damn Near Everything: Propensity Score Matching”

  1. Cristina Barattoni on July 22nd, 2010 6:35 am

    Please….. What’s step no. two????

    thank-you..

  2. Jack on September 14th, 2010 9:15 pm

    Yes, what is step two?!

  3. AC on October 17th, 2010 8:20 am

    and step 2???

  4. dave on January 17th, 2011 10:22 pm

    this is quite helpful. what’s the next step

  5. lisa kiesel on January 27th, 2011 3:19 pm

    Yes, Please, what is the next step????

  6. Gbogbo Emmanuel on March 10th, 2011 9:53 am

    Thank you, but desperately need the follow up step to enable me finish up with my thesis.

  7. susan on March 25th, 2011 3:08 pm

    Do you describe Step 2?

  8. annie on September 17th, 2011 8:09 pm

    what’s the step 2?

  9. AnnMaria on January 12th, 2012 3:55 am

    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.

  10. sandra on January 25th, 2012 11:38 am

    I think I love you. Just got a job where they expect me to do this!

  11. Cate on January 27th, 2012 9:04 pm

    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!
    Cheers,
    Cate

  12. AnnMaria on January 27th, 2012 10:03 pm

    In step 2 you run a macro to match the scores. You can do this in SPSS or SAS and there are a number of macros available you can customize to your own needs. Here is one example in SPSS

    http://www.spsstools.net/Syntax/RandomSampling/MatchCasesOnBasisOfPropensityScores.txt

  13. Jannick on February 13th, 2012 5:22 am

    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!

  14. AnnMaria on February 13th, 2012 5:32 am

    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.

  15. AnnMaria on February 13th, 2012 5:43 am
  16. SPSS Propensity Scores – Part 2 : AnnMaria’s Blog on February 13th, 2012 5:44 am

    [...] I wrote Part 1 a couple of years ago, so I guess I’m due for a part 2. In this case, I started with a data set in SAS but because it was going to be used by a group who had some SAS users and some SPSS users, they wanted to have the code for both SPSS and SAS. [...]

  17. Jannick on February 13th, 2012 10:39 am

    Dear AnnMaria,

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

    Take care!
    jannick

  18. Pankaj on February 18th, 2012 12:09 am

    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.

    Pankaj

  19. Pankaj on February 18th, 2012 12:49 am

    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)

  20. Kari on March 9th, 2012 1:36 am

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

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