Propensity score
Encyclopedia
In the design of experiments
, a propensity score is the probability
of a unit (e.g., person, classroom, school) being assigned to a particular condition in a study given a set of known covariates. Propensity scores are used to reduce selection bias by equating groups based on these covariates.
In the analysis of treatment effects, suppose that we have a binary treatment T, an outcome Y, and background variables X. The propensity score is defined as the conditional probability
of treatment given background variables:
The propensity score was introduced by Rosenbaum and Rubin (1983) to provide an alternative method for estimating treatment effects when treatment assignment is not random, but can be assumed to be unconfounded. Let Y(0) and Y(1) denote the potential outcomes under control and treatment, respectively. Then treatment assignment is (conditionally) unconfounded if treatment is independent
of potential outcomes conditional on X. This can be written compactly as
where
denotes statistical independence
.
Rosenbaum and Rubin showed that if unconfoundedness holds, then
Pearl (2000) has shown that
a simple graphical criterion called backdoor provides
an equivalent definition of unconfoundedness.
Design of experiments
In general usage, design of experiments or experimental design is the design of any information-gathering exercises where variation is present, whether under the full control of the experimenter or not. However, in statistics, these terms are usually used for controlled experiments...
, a propensity score is the probability
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
of a unit (e.g., person, classroom, school) being assigned to a particular condition in a study given a set of known covariates. Propensity scores are used to reduce selection bias by equating groups based on these covariates.
In the analysis of treatment effects, suppose that we have a binary treatment T, an outcome Y, and background variables X. The propensity score is defined as the conditional probability
Conditional probability
In probability theory, the "conditional probability of A given B" is the probability of A if B is known to occur. It is commonly notated P, and sometimes P_B. P can be visualised as the probability of event A when the sample space is restricted to event B...
of treatment given background variables:
The propensity score was introduced by Rosenbaum and Rubin (1983) to provide an alternative method for estimating treatment effects when treatment assignment is not random, but can be assumed to be unconfounded. Let Y(0) and Y(1) denote the potential outcomes under control and treatment, respectively. Then treatment assignment is (conditionally) unconfounded if treatment is independent
Statistical independence
In probability theory, to say that two events are independent intuitively means that the occurrence of one event makes it neither more nor less probable that the other occurs...
of potential outcomes conditional on X. This can be written compactly as
where
denotes statistical independenceStatistical independence
In probability theory, to say that two events are independent intuitively means that the occurrence of one event makes it neither more nor less probable that the other occurs...
.
Rosenbaum and Rubin showed that if unconfoundedness holds, then
Pearl (2000) has shown that
a simple graphical criterion called backdoor provides
an equivalent definition of unconfoundedness.