science

Propensity score matching

Propensity score matching is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Propensity score matching rather than just read about it. In short: In the statistical analysis of observational data, propensity score matching (PSM) is a statistical matching technique that attempts to estimate the effect of a treatment, policy, or other intervention by accounting for the covariates that predict receiving the treatment. PSM attempts to reduce the bias due to confounding variables that could be found in an estimate of the treatment effect obtained from simply compa…

Key takeaways

Propensity score matching belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Propensity score matching to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Propensity score matching from memory before moving on to harder problems.

Reference excerpt

In the statistical analysis of observational data, propensity score matching (PSM) is a statistical matching technique that attempts to estimate the effect of a treatment, policy, or other intervention by accounting for the covariates that predict receiving the treatment. PSM attempts to reduce the bias due to confounding variables that could be found in an estimate of the treatment effect obtained from simply comparing outcomes among units that received the treatment versus those that did not. Paul R. Rosenbaum and Donald Rubin introduced the technique in 1983, defining the propensity score as the conditional probability of a unit (e.g., person, classroom, school) being assigned to the treatment, given a set of observed covariates. The possibility of bias arises because a difference in the treatment outcome (such as the average treatment effect) between treated and untreated groups may be caused by a factor that predicts treatment rather than the treatment itself. In randomized experiments, the randomization enables unbiased estimation of treatment effects; for each covariate, randomization implies that treatment-groups will be balanced on average, by the law of large numbers. Unfortunately, for observational studies, the assignment of treatments to research subjects is typically not random. Matching attempts to reduce the treatment assignment bias, and mimic randomization, by creating a sample of units that received the treatment that is comparable on all observed covariates to a sample of units that did not receive the treatment. The "propensity" describes how likely a unit is to have been treated, given its covariate values. The stronger the confounding of treatment and covariates, and hence the stronger the bias in the analysis of the naive treatment effect, the better the covariates predict whether a unit is treated or not. By having units with similar propensity scores in both treatment and control, such confounding is reduced. For example, one may be interested to know the consequences of smoking. An observational study is required since it is unethical to randomly assign people to the treatment 'smoking'. The treatment effect estimated by simply comparing those who smoked to those who did not smoke would be biased by any factors that predict smoking (e.g.: gender and age). PSM attempts to control for these biases by making the groups receiving treatment and not-treatment comparable with respect to the control variables. PSM employs a predicted probability of group membership—e.g., treatment versus control group—based on observed predictors, usually obtained from logistic regression to create a counterfactual group. Propensity scores may be used for matching or as covariates, alone or with other matching variables or covariates.

General procedure

1. Estimate propensity scores, e.g. with logistic regression:

Dependent variable: Z = 1, if unit participated (i.e. is member of the treatment group); Z = 0, if unit did not participate (i.e. is member of the control group). Choose appropriate confounders (variables hypothesized to be associated with both treatment and outcome) Obtain an estimation for the propensity score: predicted probability p or the log odds, log[p/(1 − p)]. 2. Match each participant to one or more nonparticipants on propensity score, using one of these methods:

Nearest neighbor matching Optimal full matching: match each participants to unique non-participant(s) so as to minimize the total distance in propensity scores between participants and their matched non-participants. This method can be combined with other matching techniques. Caliper matching: comparison units within a certain width of the propensity score of the treated units get matched, where the width is generally a fraction of the standard deviation of the propensity score Radius matching: all matches within a particular radius are used – and reused between treatment units. Kernel matching: same as radius matching, except control observations are weighted as a function of the distance between the treatment observation's propensity score and control match propensity score. One example is the Epanechnikov kernel. Radius matching is a special case where a uniform kernel is used. Mahalanobis metric matching in conjunction with PSM. Stratification matching. Difference-in-differences matching (kernel and local linear weights). Exact matching. 3. Check that covariates are balanced across treatment and comparison groups within strata of the propensity score.

Use standardized differences or graphs to examine distributions If covariates are not balanced, return to steps 1 or 2 and modify the procedure 4. Estimate effects based on new sample

Typically: a weighted mean of within-match average differences in outcomes between participants and non-participants. Use analyses appropriate for non-independent matched samples if more than one nonparticipant is matched to each participant

Formal definitions

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Propensity score matching

Start with the simplest possible case. Write down what Propensity score matching claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Propensity score matching before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Propensity score matching ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Propensity score matching

In research: Propensity score matching appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Propensity score matching in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Propensity score matching is common in secondary-school and first-year university syllabi. It links to neighbouring topics Causal inference, Epidemiology, Observational study, so understanding it makes those chapters shorter.
In everyday life: Look for Propensity score matching outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Propensity score matching in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Propensity score matching means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Propensity score matching out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Propensity score matching in simple terms?

Why does Propensity score matching matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Propensity score matching?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Propensity score matching.