Introduction
I am reading the book “Causal Inference” by Paul R. Rosenbaum [1]. The fourth chapter of the book is named “Adjustments for Measured Covariates”. In this chapter, pair matching by means of propensity scores is explained. I would like to express my opinion on pair matching by means of propensity scores from the perspective of causality within the framework of Judea Pearl.
The Context
In this section, the context in which this article is written is tried to be detailed. There is a population of people. The data about this population has the following features: Age, sex, income, education, race, smoking and dental health. The treatment group contains smokers and the control group contains non-smokers. The treatment and the control group will be created using propensity score matching. Propensity score of smoking based on age, sex, income, education and race is the probability of smoking given age, sex, income, education and race. Since the treatment and the control groups are created by means of smoking propensity score matching, if a person from the treatment group and another from the control group are selected at random, then their smoking behaviour cannot be differentiated by examining their age, sex, income, education and race features. It is said that when the treatment and the control group are matched in terms of propensity scores of smoking, then the effect of smoking on dental health can be determined. It is said that due to the propensity score matching, the features other than smoking are balanced in the two groups and any difference in dental health is due to smoking behaviour.
The Pearlian Causality Perspective
From the perspective of Pearlian causality or causality within the framework of Judea Pearl, the following thought immediately comes to the mind: Without knowing the cause-effect relationships behind the data, how can it be claimed that dental health difference between propensity-score-matched groups is due to smoking? An example from the book [1] is to be commented on. The related sentences from the book [1] are as follows:
One person is a woman aged forty-nine with a high school degree and a family income of 1.97 times the poverty level. The other is a man aged fifty-two with two years of college and a family income 4.07 times the poverty level. Both are not Black people. Men are more likely than women to smoke, but wealthier, better-educated people are less likely to smoke, and for these two people, these two conflicting tendencies balance one another perfectly to yield the same one- fifth chance of being a smoker. Given the information that one of these two people is a smoker, the detailed information about age, sex, income, education, and race is of no help in guessing which individual is the actual smoker.
Hence, if there is a difference in dental healths, then this is due to smoking. But, this dental disease may be due to some hormone which is in greater amounts in men than in women. This dental disease may be very common in white people. This dental disease may be due to a life style which is prevalent among rich people. So, without knowing the cause-effect relationships behind the available data and the strengths of these relationships, it is not possible to determine smoking as the reason for the dental disease only by means of smoking-propensity-score matching.
Conclusion
Determining causes depending on propensity score matching has been criticised from the perspective of causality within the framework of Judea Pearl.
References
[1] Paul R. Rosenbaum, “Causal Inference”, The MIT Press.