# 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

• 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

• 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

• 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.

## Critical Care

Compendium

##### Chris Nickson

Chris is an Intensivist and ECMO specialist at the Alfred ICU in Melbourne. He is also a Clinical Adjunct Associate Professor at Monash University. He is a co-founder of the Australia and New Zealand Clinician Educator Network (ANZCEN) and is the Lead for the ANZCEN Clinician Educator Incubator programme. He is on the Board of Directors for the Intensive Care Foundation and is a First Part Examiner for the College of Intensive Care Medicine. He is an internationally recognised Clinician Educator with a passion for helping clinicians learn and for improving the clinical performance of individuals and collectives.

After finishing his medical degree at the University of Auckland, he continued post-graduate training in New Zealand as well as Australia’s Northern Territory, Perth and Melbourne. He has completed fellowship training in both intensive care medicine and emergency medicine, as well as post-graduate training in biochemistry, clinical toxicology, clinical epidemiology, and health professional education.

He is actively involved in in using translational simulation to improve patient care and the design of processes and systems at Alfred Health. He coordinates the Alfred ICU’s education and simulation programmes and runs the unit’s education website, INTENSIVE.  He created the ‘Critically Ill Airway’ course and teaches on numerous courses around the world. He is one of the founders of the FOAM movement (Free Open-Access Medical education) and is co-creator of litfl.com, the RAGE podcast, the Resuscitology course, and the SMACC conference.

His one great achievement is being the father of three amazing children.