STATISTICAL METHOD
Propensity Score Matching Analysis
Statistical Consulting for Observational Studies
We apply propensity score matching analysis within your study design, fixing the estimand and covariates in advance, showing overlap and balance with standardized differences, and reporting the effect with its 95% confidence interval and a sensitivity analysis.
No Commitment Required
Strictly Confidential
In-House PhD-Level Statisticians
Fixed Project Fee
Same-Day Response
METHOD OVERVIEW
What Is Propensity Score Matching?
Propensity score matching estimates the effect of a treatment or exposure from observational data by comparing treated and untreated participants who had a similar probability of treatment given their measured characteristics. That probability is the propensity score, usually estimated with logistic regression. Matching on it can balance the measured covariates, but only those, so the method assumes no unmeasured confounding, which the data cannot test. It also needs overlap between the groups and a stated estimand, most often the average effect in the treated. OnlineSPSS, a specialist statistical consultancy for academic, clinical and professional research, provides propensity score matching analysis within your study design, with the relevant checks, effect estimates, uncertainty measures, interpretation and publication-ready reporting.
WHEN TO ENGAGE
When Is Propensity Score Matching Appropriate?
Matching fits an observational comparison of a treatment or exposure when measured confounders are many, and these are the situations in which researchers most often ask us to apply or confirm it.
Observational Treatment Comparison A cohort or claims database compares treated and untreated patients whose age, severity or history differ enough to bias a raw comparison.
Many Confounders, Few Events Outcome events are rare and confounders numerous, too many for a stable outcome model, so the treatment model carries the adjustment instead.
Estimand Fixed Before Analysis The question concerns treated patients or the whole population, and the covariates, caliper and balance targets are set before outcomes are seen.
Reviewing a Completed Matching A matched analysis exists and a reviewer has questioned its balance or overlap. Independent Statistical Review re-examines the matching and its reporting.
ANALYTICAL APPROACH
How We Apply Propensity Score Matching
Within the family of Clinical, Survival & Epidemiological, the matched design is built from the confounders measured before treatment, and its balance is shown before any outcome is compared.
Covariates and Score Model We include pre-treatment covariates related to the outcome, never post-treatment variables, which can block part of the effect. Balance, not score model fit, is the target.
Overlap and Common Support We inspect the score distributions of both groups. Poor overlap shrinks the matched sample and can change the population the estimate describes, so we state who remains.
Matching, Caliper and Balance We justify the ratio, the caliper and matching with or without replacement, and judge success by standardized differences, not p-values. Tighter matching is not always better.
Estimand and Uncertainty We state whether the estimate is for the treated or the population, use variance estimators suited to matched data and assess sensitivity to unmeasured confounding, often with E-values.
DELIVERABLES
What You Receive
As part of our Quantitative Data Analysis service, the matched comparison is delivered with the diagnostics, estimates and files needed to report and defend it.
Data & Variable Review Treatment definition, the timing of covariates relative to treatment, missing data and the intended estimand are reviewed before any score is estimated.
Method-Specific Checks Score distributions, standardized differences before and after matching, matched sample size and, where balance is poor, weighting or stratification as an alternative.
Statistical Results The treatment effect with its 95% confidence interval for the stated estimand, the numbers matched and dropped, and a sensitivity analysis for unmeasured confounding.
Publication-Ready Tables & Figures A balance table, a love plot and an overlap figure, prepared in line with STROBE reporting or the journal's requirements, ready to insert.
Interpretation The effect is read for the matched population, as an association adjusted for measured confounders, with the limits of unmeasured confounding stated plainly.
Reproducible Analysis Files R scripts, Stata do-files or SAS programs for the score model, matching and diagnostics are provided where applicable, so the analysis can be rerun if the data change.
ALTERNATIVE METHODS
When Another Method May Be More Appropriate
Matching adjusts only for measured confounders. These methods fit better when a source of exogenous variation exists, when outcomes are tracked over time or when ordinary adjustment suffices.
01
Instrumental Variable Analysis
When a credible instrument exists, it can address unmeasured confounding that matching cannot, though the estimate then applies to a narrower group of compliers.
02
Difference-in-Differences (DiD)
With outcomes observed before and after an intervention in treated and comparison groups, this method removes stable group differences that matching on baseline traits leaves.
03
Logistic Regression
With few confounders and enough events, a direct outcome model adjusting for them is simpler, and it gives conditional estimates, not the average effect in a matched sample.
04
Cox Regression
For time-to-event outcomes, a hazard model can be fit within a matched or weighted sample, or with covariate adjustment alone, and the target estimand is stated either way.
CASE EXAMPLE
How We Work in Practice
An illustration of how a matched comparison moves from a prespecified plan to balanced groups and a defensible estimate.
ILLUSTRATIVE EXAMPLE · PHARMACY BENEFIT ANALYTICS · UNITED STATES
An analytics team at a pharmacy benefit manager wanted to compare hospitalization rates between members who joined a new medication adherence program and those who did not.
Enrollment was voluntary, so program members were healthier and more engaged than the rest. Before any outcomes were extracted, we fixed the estimand as the effect in enrolled members and chose baseline covariates from the pre-enrollment year only. The plan set the caliper and the balance criterion as standardized differences below a stated threshold. Few non-members resembled the most engaged enrollees, so we documented which enrolled members went unmatched and how that narrowed the population. We also planned an E-value analysis for unmeasured confounding such as motivation, and variance estimation that accounts for the matching.
Outcome: The team received the estimate for enrolled members with its 95% confidence interval, the balance table and love plot, the overlap figure, the E-value sensitivity analysis and the analysis code.
This example does not describe a real client or project. We never share details of actual client work, in line with the confidentiality we promise every researcher. This illustrative example is included to show the type, scope, and standard of work involved in this kind of analysis.
SOFTWARE
Statistical Software for Matched Comparisons
Propensity scores and matching are run in the statistical software researchers already use, with syntax or scripts provided where applicable.
RESEARCH DISCIPLINES
Matched Comparisons Across Research Fields
Propensity score methods are used across research fields, each with its own treatments, confounders and reporting conventions.
A Defined Process for Your Analysis
We review your dataset, research question and design before any work begins, so the scope, deliverables, timeline and fixed project fee are clear from the outset.
01
Share Your Research Materials
Send your dataset, research question, study design and any existing analysis plan or output. We will let you know if anything else is needed to assess the project.
02
Receive Your Assessment
Your statistically trained Research Coordinator reviews the project and confirms the required analysis, deliverables, timeline and fixed project price before work begins.
03
Analysis & Delivery
Once you confirm the scope, an in-house statistician completes the agreed analysis and delivers the outputs, interpretation and reporting files.
RESEARCHER VOICE
What Researchers Say
Feedback from a policy researcher whose matched analysis needed its model checked and its reporting made defensible.
“I had results from Propensity Score Matching (PSM), but the interpretation still felt shaky because of model fit and whether any changes were theoretically defensible. They checked the model, corrected the parts that needed attention, and made the final reporting much more defensible. The final output was concise, clearly interpreted, and ready to use in our research reporting.”
RESEARCH RESPONSIBILITY
Statistical Support Without Taking Over Your Research
We provide the statistical work for your matched comparison, and the study, its meaning and its authorship stay entirely with you.
Agreed Statistical Support We provide the agreed methodological, analytical and statistical reporting support for your propensity score analysis, within the scope confirmed before work begins.
No Intellectual Contribution OnlineSPSS claims no intellectual contribution to your research. Our work is statistical support, and authorship remains yours.
Your Research Decisions The choice of confounders, the research question and your conclusions remain with you, and our interpretation stays within what the matched estimates and the design support.
Confidential Handling Research data and project details are handled confidentially and are not published. An NDA is available where required, and can be arranged before sensitive materials are shared.
FREQUENTLY ASKED QUESTIONS
Questions About Propensity Score Matching
Short answers to what researchers ask before matching treated and untreated groups, from balance and calipers to confidentiality and the assessment process.
Does propensity score matching remove unmeasured confounding?
No. A propensity score balances only the covariates that were measured and included, and the assumption of no unmeasured confounding cannot be tested from the data. We justify the covariate set from subject knowledge and add a sensitivity analysis, such as an E-value, to show how strong an unmeasured confounder would need to be to change the conclusion.
How do I show that the matching has worked well?
Check covariate balance, not the fit of the score model. We compare standardized mean differences before and after matching, often against a threshold such as 0.1, and look at variance ratios and the score distributions. Significance tests of baseline differences are not used, because they depend on the sample size, which matching itself changes.
Should I use a caliper, or weighting instead of matching?
A caliper limits how far apart matched pairs can be, and its width trades closeness against the number retained, so we justify it and show balance under reasonable alternatives. Weighting keeps every participant and can target either the treated or the whole population, but weights for the whole population become extreme where overlap is poor. The choice follows the estimand and the overlap.
Can you review an analysis that has already been completed?
Yes, we can review a completed matched analysis before submission or a response to reviewers. We check which covariates entered and when they were measured, the overlap, the balance diagnostics, how the variance was estimated after matching and the stated estimand, and confirm what stands or needs to change.
How do you protect my dataset and research confidentiality?
Your dataset, output files and any protocol or analysis plan are handled confidentially, and project information is not published. An NDA is available where required and can be arranged before sensitive materials are shared. Read more about confidentiality and data security.
What happens when I request an assessment, and how long does it take?
You share your research question, design and relevant materials, and a statistically trained Research Coordinator reviews the request and responds the same day. The analysis, deliverables, timeline and one fixed project fee are then confirmed before any work begins, so the timeline follows from the agreed scope.
Still have a question? Find more answers in our full FAQ.
NEXT STEP
Need Support With
Propensity Score Matching?
Share your research question, treatment definition and data. We assess whether matching fits your comparison and confirm the approach before any work begins.
No Commitment Required
Strictly Confidential
Fixed Project Fee
In-House PhD-Level Statisticians
Same-Day Response
Serving Researchers Since 2014