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Extra info for A Clockwork Orange by Anthony Burgess (A Lively Learning Guide by Shmoop)

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One disadvantage of the propensity matching approach is that subjects may not be able to find a matched subject in the control group. For example, if the treatment and control groups have comparable sample size, it will be very likely that there will be more subjects with high propensity scores in the treatment group than in the control group. Similarly, there will be more subjects with low propensity scores in the control group than in the treatment group. , more subjects without matched subjects.

The propensity score is defined as the probability of treatment assignment conditioning on some observed baseline characteristics and it provides a balanced score for the treatment conditions as conditioning on the propensity score, the treatment groups are comparable in terms of the baseline covariates. In this chapter, we will first provide an overview of the propensity score and the underlying assumptions for using propensity score, we will then discuss four methods based on propensity score: matching on the propensity score, stratification on the propensity score, inverse probability of treatment weighting using the propensity score, and covariate adjustment using the propensity score, as well as the differences among the four methods.

Variables that cause selection bias are called confounding variables, confounders, or covariates, etc. When there are confounders, treatment effects cannot be simply assessed as the observed group differences. The issue can be better illustrated under the counterfactual outcome framework for causal inference. H. He ( ) • J. edu J. cn © Springer International Publishing Switzerland 2016 H. He et al. 1007/978-3-319-41259-7_2 29 30 H. He et al. Suppose we are interested in the effect of a new treatment on an outcome, say blood pressure, measured in a continuous scale.

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