– Bias Reduction Using Propensity Score Matching in Observational Data –
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ABSTRACT
In observational studies, ―case-control groups‖ often exhibit imbalance on covariates. This covariate imbalance is confounded with treatments.
It is difficult to attribute differences in responses to the ―treatment‖ because the covariates are also believed to influence the response.
Propensity score matching attempts to reduce the confounding effects of covariates, and so allows differences of responses to be attributed to differences of treatments.
In addition, the values of the propensity scores can serve as a diagnostic tool to evaluate the comparability of the groups in a quantitative way.
When two groups are being compared, the propensity score can be calculated as the predicted probability of group membership from a logistic regression. It represents the ‗tendency‘ for an observation to be in one group or the other.
By adjusting for the value of the propensity score in a linear model, one effectively adjusts for any group differences attributed to the variables used to create the propensity score.
Here we present an experiment where propensity scores were used to adjust for differences between a case and a control group (treatment group and a non-randomized control group).
INTRODUCTION
In order to make group comparisons, the generally accepted pattern in research consists of the following method:
- Formation of treatment and experimental groups, sometimes with a single group serving as its own control.
- Mapping treatments to the groups.
- Analysing group differences.
- Generalising findings based on groups to tendencies among future individuals.
Defining groups is a crucial first step and once they are defined, one would want their composition to be identical. Statistical adjustments, often in the form of blocking variables, variables or covariate analysis could be used to adjust for the pre-treatment group differences.
The random assignment of treatment to groups before comparison is often resorted to because, in theory, this assures that the groups are identical.
This, however, is not always practical and does not necessarily result in groups that are equivalent in terms of all the important covariates. It is the expected values of the covariates over numerous replications that are equal.
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