We are considering age, sex, and nationality as confounding factors for matching. If nationality is matched, would it be correct to understand that it will be matched with similar countries? Thank you very much.
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Hello.
My name is Ono, and I am a senior tester at the JMP Japan division of SAS Institute Japan.
I may not understand your question, but assuming that your question is: "In propensity score matching, if nationality, sex, and age are included in the explanatory variables of the logistic model to calculate the propensity score, are the pairs matched by propensity score matching people of "similar nationalities?"," I will state my personal opinion below.
As the saying goes, "The collective noun for statisticians is "a quarrel," I believe there are many different ways of thinking about statistics, so the following is just one way of thinking.
Propensity score matching primarily matches pairs with similar propensity scores. Therefore, pairs with similar confounding factors (covariates) are not necessarily matched. This feature of propensity score matching has often been strongly criticized. The following is a well-known critical paper on propensity score matching.
Gary King and Richard Nielsen. 2019. “Why Propensity Scores Should Not Be Used for Matching.” Political Analysis, 27, 4, Pp. 435-454. Publisher's Version Copy at https://tinyurl.com/y5b5yjxo
To understand the gist of this criticism, it is best to imagine what would happen if propensity score matching was performed in a fully randomized controlled trial. In a fully randomized controlled trial, all propensity scores are 0.5, so it is OK to match with any patient. Therefore, a 60-year-old Japanese man could be matched with a 30-year-old Mexican woman (because both have a propensity score of 0.5). Even if it is not as extreme as this, if a 60-year-old Japanese man and a 30-year-old Mexican woman have similar propensity score values, they could be matched in propensity score matching.
I think the hypothetical example in the Japanese translation of What is Causal Inference? by Rosenbaum, PR (translated by Takada Yuya and Takahashi Koji), pp. 49-53, will also help you intuitively understand what propensity score matching does.
If the confounding factors (covariates) are the same, the propensity score will be the same. However, the reverse is not true; even if the propensity score is the same, the confounding factors (covariates) will not be the same. (In more complex technical terms, the propensity score (and its monotonically transformed form) is characterized by being the crudest balancing score.)
Even if propensity score matching is performed by obtaining propensity scores using a logistic regression model with nationality, sex, and age as explanatory variables, it does not necessarily result in matching with "similar countries" (for example, countries with similar dietary habits, countries with similar medical practices, countries with similar insurance systems, countries with similar concomitant medications, countries with similar age structures, etc.). In fact, there is a possibility that a 60-year-old Japanese man may be matched with a 30-year-old Mexican woman.
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