Dynamic Propensity Score Matching
Dynamic Propensity Score Matching for Sequential Treatments · Also known as: dynamic PSM, sequential propensity score matching, longitudinal propensity matching, DPSM
Dynamic Propensity Score Matching (DPSM) extends classic propensity score matching to settings where treatment is assigned repeatedly over time and earlier treatment choices influence later ones. It estimates the causal effect of entire treatment sequences or regime changes by constructing matched comparisons at each decision point using the full history of covariates and prior treatments.
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When to use it
Use Dynamic PSM when treatment is assigned at multiple time points and earlier treatment affects both future treatment selection and outcomes — as in longitudinal clinical trials, labour market programmes, or policy roll-outs with repeated eligibility decisions. The data must include rich time-varying covariate measurements taken before each treatment decision. The key identifying assumption is sequential conditional independence (no unmeasured time-varying confounding given observed history). Do not use when: (a) treatment occurs only once, in which case standard PSM is sufficient; (b) time-varying confounders are heavily unmeasured, because no observable matching strategy can adjust for them; or (c) the panel is very short, leaving too few decision points to build informative histories.
Strengths & limitations
- Handles the full complexity of dynamic treatment regimes rather than collapsing multi-period exposures into a single binary variable.
- Removes confounding at every sequential decision point, not just at baseline, which is essential when past treatment shapes both future selection and future outcomes.
- More transparent and intuitive than marginal structural models for audiences unfamiliar with inverse-probability weighting.
- Produces direct comparisons between well-defined treatment trajectories, making results straightforward to communicate to policymakers.
- Compatible with any outcome type — continuous, binary, or time-to-event — and with regression adjustment after matching for additional precision.
- Requires rich, high-frequency longitudinal covariate data measured before each treatment decision; sparse panels make sequential balancing infeasible.
- Sequential sample pruning can severely reduce the effective sample size, particularly when there are many treatment periods or when treatment histories are heterogeneous.
- Relies on sequential conditional independence, which is untestable and may fail if important time-varying confounders are unobserved.
- Computationally demanding: a separate propensity model is required for each period, and bootstrap inference for standard errors multiplies the burden.
- Does not directly target a population-level average treatment effect (ATE); the ATT is estimated only among those who actually followed the reference trajectory.
Frequently asked
How does Dynamic PSM differ from standard propensity score matching?
Standard PSM matches on a single propensity score computed at one point and treats treatment as a fixed event. Dynamic PSM computes a propensity score at each period, conditioning on the full history of covariates and past treatments, and matches sequentially so that only units with comparable treatment paths are compared at each step.
What is sequential conditional independence and why does it matter?
Sequential conditional independence states that, conditional on observed covariate and treatment history up to period t, assignment to treatment at t is independent of potential outcomes. This is the identifying assumption of DPSM. If important time-varying confounders are unmeasured, the assumption fails and estimates will be biased.
What happens to sample size with many treatment periods?
Every matching step removes unmatched units. With many periods or diverse treatment histories, the matched sample can become very small. It is advisable to use caliper matching to retain more units and to report the matched sample size at each period.
Is Dynamic PSM preferable to a marginal structural model?
Both target the same causal estimand under the same identifying assumptions. DPSM is more transparent and avoids extreme inverse-probability weights that can destabilise MSM estimates. MSMs are generally more efficient under correct model specification. Running both and comparing results is a useful robustness check.
Can I use Dynamic PSM with a binary outcome?
Yes. After sequential matching, the treatment effect can be expressed as a difference in proportions, a risk ratio, or an odds ratio. Logistic regression adjustment on the matched sample is also valid and often improves precision.
Sources
- Lechner, M., & Miquel, R. (2010). Identification of the effects of dynamic treatments by sequential conditional independence assumptions. Empirical Economics, 39(1), 111-137. DOI: 10.1007/s00181-009-0297-3 ↗
- Robins, J. M. (1986). A new approach to causal inference in mortality studies with a sustained exposure period — application to control of the healthy worker survivor effect. Mathematical Modelling, 7(9-12), 1393-1512. DOI: 10.1016/0270-0255(86)90088-6 ↗
How to cite this page
ScholarGate. (2026, June 3). Dynamic Propensity Score Matching for Sequential Treatments. ScholarGate. https://scholargate.app/en/causal-inference/dynamic-propensity-score-matching
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Doubly Robust EstimationCausal inference↔ compare
- Dynamic Difference-in-DifferencesCausal inference↔ compare
- Inverse Probability WeightingCausal inference↔ compare
- Marginal Structural ModelCausal inference↔ compare
- Propensity Score MatchingResearch Statistics↔ compare
- Propensity Score WeightingCausal inference↔ compare