Conducting a randomized controlled trial is not always possible. Because of ethical constraints, cost, or time requirements, researchers often have to work with retrospective patient data. In that case the two groups, treated and untreated, may have different characteristics from the start. Propensity score matching is used to correct this imbalance.
What Is a Propensity Score?
A propensity score is the probability that a patient is assigned to the treatment group, given the patient's observed characteristics. It is calculated with logistic regression: the dependent variable is treatment status (treated/untreated), and the independent variables are confounding factors such as age, sex, comorbidity, and disease severity.
For each patient, a propensity score between 0 and 1 is obtained. When patients with similar scores are compared, the observable differences between the groups are balanced as if they had been randomized.
When Is It Used?
Propensity score matching is preferred in the following situations:
- When the two groups differ in baseline characteristics in retrospective cohort studies
- When an RCT is not feasible but strong causal inference is desired
- When the number of patients is sufficient for matching (at least 30 to 50 patients per group is recommended)
Caution: The propensity score only balances the measured confounding factors. It does not solve the problem of unmeasured confounding.
Step-by-Step Application
Step 1: Calculating the propensity score
Decide which variables to include in the model based on clinical rationale. The factors that influence the choice of treatment, not the outcome of the treatment, should be included in the model.
Step 2: Choosing the matching method
The most common approach is 1:1 nearest-neighbor matching. For each treated patient, the control patient with the closest propensity score is matched.
Caliper: The maximum acceptable distance in matching. A caliper of 0.2 times the standard deviation of the propensity score is commonly used.
Step 3: Balance check
After matching, whether the groups are balanced is checked. A Standardized Mean Difference (SMD) < 0.10 indicates good balance. This check is reported with a table and a "love plot."
Step 4: Analysis on the matched data
Standard statistical tests are performed on the matched data. However, the dependent structure of the matched data (paired data) must be taken into account: for continuous variables the paired t-test or Wilcoxon signed-rank test is used, and for categorical variables the McNemar test is used.
Propensity Score Matching with R
The cobalt package for the love plot:
Alternative Approaches
In addition to matching, you can use the propensity score in different forms:
Weighting (IPTW): Assigning each patient the inverse of their propensity score as a weight. It preserves all the data, so you do not lose patients as you do in matching.
Stratification: Dividing patients into groups by propensity score quintiles and analyzing within each group.
Including it as a covariate in the model: Using the propensity score as a covariate in multivariate analysis. It is the simplest method but the least powerful.
Request a free consultation for propensity score matching analysis.
Where Do People Get Stuck Most in This Analysis?
- You lost too many patients after matching, and the remaining sample became too small.
- There are still variables with SMD > 0.10, and balance cannot be achieved.
- It is unclear whether to use a paired test or an independent test on the matched data.