Propensity Score Analysis

Reviewed and revised 9 August 2013

OVERVIEW

• Propensity analysis refers to statistical methods used to control for treatment selection bias in observational studies
• Treatment selection bias occurs when the effects of receiving a treatment are partly or wholly determined by confounders (such as differences in the patients who receive treatments or co-interventions) rather than than the treatment itself
• Propensity analysis was described by Rosenbaum and Rubin in 1983

THE PROPENSITY SCORE

• The propensity score is the probability of treatment assignment conditional on observed baseline characteristics
• Statistical definition: Propensity score e(x) is the conditional probability of receiving the exposure given the observed covariates x
  e(x) = Pr(Exposure | Xsubject= x)
• The propensity score allows one to design and analyze an observational (nonrandomized) study so that it mimics some of the characteristics of an RCT

RATIONALE FOR PROPENSITY SCORE ANALYSIS

• unlike RCTs, observational studies cannot rely on randomised allocation to negate the effects of confounders
• in a randomised study the propensity score is known, it is defined by the study design
• in non-randomised studies the propensity is not known, but can be estimated (often by a logistic regression model; there are other methods)
• in a set of subjects all of whom have the same propensity score, the distribution of observed baseline covariates will be the same between the treated and untreated subjects
• Propensity score analysis compares subjects with similar propensity scores to attempt to control for confounders

“Just as randomization will, on average, result in both measured and unmeasured covariates being balanced between treatment groups, so conditioning on the propensity score will, on average, result in measured baseline covariates being balanced between treatment group”
— Austin, 2011

METHODS OF PROPENSITY SCORE ANALYSIS

Methods include:

• propensity score matching
• stratification (or subclassification) on the propensity score
• inverse probability of treatment weighting (IPTW) using the propensity score
• covariate adjustment using the propensity score

PROS AND CONS OF PROPENSITY SCORE ANALYSIS

Advantages

• cheaper and quicker than performing RCTs
• can use patients that would be excluded from RCTs
• can study treatments that it would be infeasible or unethical to randomise
• can be used to adjust for differences via study design (matching) or during estimation of treatment effect (stratification/regression)
• useful when adjusting for a large number of risk factors and small number of events per variable

Disadvantages

• no causal claim can be established by a purely statistical method (this is sometimes forgotten!)
• propensity analysis assumes there are no unmeasured confounders that influenced treatment assignment — propensity scores are invalid if an important variable in the propensity regression is missed out
• there is a lack of consensus in the applied literature as to which variables to include in the propensity score model
• inclusion of irrelevant covariates in the propensity model may reduce efficiency

References and Links

• Rosenbaum PR and Rubin DB (1983). The central role of the propensity score in observational studies for causal effects. Biometrika 70(1):41–55. doi:10.1093/biomet/70.1.41
• Austin PC. An Introduction to Propensity Score Methods for Reducing the Effects of Confounding in Observational Studies. Multivariate Behav Res. 2011 May;46(3):399-424. PMC3144483.