Multiple regression vs propensity score matching for covariates in observational study 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.
 A: 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.
