Propensity Score Matching
In the statistical analysis of observational data, propensity score matching (PSM) is a methodology attempting to provide unbiased estimation of treatment-effects. The possibility of "bias" arises here because the effectiveness of a treatment may depend on characteristics that are associated with whether or not a participant in an observational study chooses, or is chosen, to receive a given treatment. A treatment-effect is just jargon for the effect of something that is being studied -- like the consequences of smoking or the consequences of going to university. The people 'treated' are simply those -- the smokers, or the university graduates -- who undergo whatever it is that is being studied by the researcher. The language of 'treatment effects' comes originally from the medical literature where medical researchers have always hoped to isolate the true causal effects of different ways of dealing with disease. One way to do that is to run experiments. In randomized experiments, the randomization enables unbiased estimation of treatment effects; for each covariate, randomization implies that treatment-groups will be balanced on average, by the law of large numbers. Unfortunately, for observational studies, the assignment of treatments to research subjects has been haphazard and not randomized; lacking randomization, observational studies frequently provide biased estimation of treatment effects and have imbalance on covariates. In observational studies, the "treatment"-groups (or "exposure" groups) often exhibit imbalance on covariates. This covariate imbalance is confounded with treatments: It is difficult to attribute differences in responses to the "treatment" or "exposure" because the covariates are also believed to influence the response. The propensity score matching attempts to reduce the confounding effects of covariates, and so allow differences of responses to be attributed to differences of treatments (exposures). Researchers try to decide how the world works, and, in particular, what causes what. To do this properly, it is not enough to observe correlations. It is necessary to try to understand causality. In other words, even when it is seen that smoking and cancer tend to occur together in a sample of human beings, the basic questions remain: 1,is the smoking itself having a causal effect, or could it just be that cancer is caused by, say, poor diet and those who smoke tend not to eat healthy foods, or 2,is some gene that leads to cancer and also by coincidence that that gene increases a person's enjoyment of cigarettes? Similarly, people with university degrees tend later in their lives to earn more money than others without degrees, but is that because the education is actually causing the higher earnings?
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