# Multiple regression vs propensity score matching for covariates in observational study [duplicate]

I want to determine if smoking is related to this cancer in an observational study. I have data from 1000 subjects with following variables:

age (continuous numeric)
gender (male/female)
income (continuous numeric)
smoking (yes/no)
cancer (yes/no)


However, since this is an observational study, groups may not be balanced. To determine relation between smoking and cancer while correcting for covariates (age, gender and income), I think both of following methods can be used:

1. Propensity score matching
2. Logistic regression analysis: cancer ~ smoking + age + gender + income


Are both these methods valid for such an analysis? If so, which is better and why? Or some other method is most appropriate for this? Thanks for your insight.

Edit: Cancer (outcome variable) is present in about 100 subjects while 900 subjects have no cancer. Also, I would like to have suggestions on this particular set of data rather than a general answer.

• Does this answer your question? Propensity score matching - What is the problem?. Also, see this thread. You might look into inverse propensity score weighting, which has the advantage of not discarding cases in the way that matching does
– EdM
Oct 17 '20 at 13:43
• Thanks for the links which are useful, but I would like to have suggestions on this particular set of data rather than a general answer.
– rnso
Oct 17 '20 at 17:14
• Does this answer your question? Survival Analysis, Cox Regression in randomized trial vs. observational study and propensity score matching. This addressed survival analysis but the responses are identical with a binary outcome. It specifically focuses on the differences between propensity score methods and regression. I don't think the "Propensity score matching - What is the problem?" question will help you decide how to proceed.
– Noah
Oct 17 '20 at 20:57
• If you need help with a specific dataset, hire a statistical consultant. We can only provide general answers. There is nothing about that dataset that makes the general answers any less applicable, but it's up to you to apply what you learn in the given answers to your dataset.
– Noah
Oct 17 '20 at 21:01
• I was concerned whether size of study and also number and type of different variables (both outcome and predictor) involved could influence the decision. The links are very helpful and my question is well answered.
– rnso
Oct 18 '20 at 1:36

Both of these methods require satisfaction of Conditional Independence Assumption, so as long there are unobserved confounders (i.e. selection variables), or other endogeneity problems, both methods are invalid and biased.

These two methods base on different model: regression models outcome, propensity score models selection. If it is more easy/difficult to model one of those phenomena, one of those methods may have actual advantage. In this case it is important to notice, that both of these methods are parametric, and dependent on functional form assumptions. However there are many matching methods, and some of them are less parametric.

Matching methods need high enough number of observationally similar observations (common support). If there is not enough matches, regression may have the advantage here.

There is of course noticeable discussion between scientist how those methods compete, and when is better to use regression over matching or vice versa. Some of influential works were already mentioned in comments and great stack answers linked there.

Let me also suggest looking at chapter 3.3 from "Mostly Harmless Econometrics" by J.D. Angrist and J.S. Pischke. While they mention, that of course there are situations where one of the methods may have actual advantage, they claim, that generally "...the differences between regression and matching are unlikely to be of major empirical importance.".

It is likely, that the results of using both methods would be more or less the same. Maybe it is more important to concentrate on research design, understand its limitations and alternatives, than on merits of methods, that are not so different in the end.

• If someone wants to use regression all the time for such situations, is there any problem?
– rnso
Oct 17 '20 at 13:19
• Straightforward answer to this question has to be be very opinion-based. I upgraded the answer to show the important point of view, that those methods are not that different in results. Of course showing results of both methods, when they are similar, is trustworthy. Also I mentioned some cases, where actual advantage may happen. Personally (and very opinion-based) I do not see a situation, when I would discredit a research for not using a matching method.
– cure
Oct 18 '20 at 0:20