What this tool does
Propensity Score Analysis is Module 18 of Analysis Studio. It estimates the effect of a binary exposure on a continuous, binary, or count outcome from observational data, adjusting for confounders that you choose. The tool never selects confounders on its own, because that choice is a subject-matter judgment and automating it would hide the most important decision in the analysis.
The workflow holds a discipline that quick tools skip:
- Before any result displays, you acknowledge the working assumptions in plain language: no unmeasured confounding, overlap between the exposed and unexposed, and a correctly specified propensity model. The acknowledgment is recorded and printed with the results.
- Balance comes before results. After weighting or matching, the module reports standardized mean differences and variance ratios for every confounder, with a Love plot. Unresolved imbalance blocks the results until it is acknowledged, so a failed adjustment cannot slip past as a clean estimate.
- The outcome analysis is a weighted regression, optionally doubly robust, which stays consistent if either the propensity model or the outcome model is right.
- An E-value accompanies the estimate: the minimum strength an unmeasured confounder would need, with both the exposure and the outcome, to explain the estimate away.
The default analysis is inverse probability weighting for the average treatment effect, or for the effect on the treated, with stabilized weights and optional percentile truncation. One-to-one nearest-neighbor matching on the logit propensity score, inside a caliper of 0.2 standard deviations, is available for the effect on the treated. Intervals come from a bootstrap over the full procedure, one thousand replications with a recorded seed, so the uncertainty in the propensity step itself is inside the interval rather than ignored.
Promotion, stated with its date: through March 31, 2027, this module runs free on screen, like every module. Downloads and Copy Results stay with the subscription throughout. After the promotion, the module returns to the subscription set at $299 per year.
The method, in plain terms
The propensity score is each case's probability of being exposed, given its confounders, estimated here by the logistic regression engine. Weighting by the inverse of that probability builds a pseudo-population in which the confounders are balanced between exposed and unexposed, as randomization would have balanced them, in expectation, had randomization been possible:
Weight for an exposed case = 1 ÷ propensity score. Weight for an unexposed case = 1 ÷ (1 − propensity score).
The estimate is then the weighted difference in outcomes. It answers a causal question only to the extent that the confounders chosen are the ones that matter and the exposed and unexposed overlap across their range, which is why the balance report and the E-value travel with the number.
Worked example
Eight cases, one confounder x that takes values zero and one, with treatment probability 0.75 when x is one and 0.25 when x is zero. Outcomes for the treated: 10, 12, and 11 at x of one, and 6 at x of zero. Outcomes for the untreated: 7 at x of one, and 4, 5, and 3 at x of zero.
- Naive difference, no adjustment: treated mean 9.75 minus untreated mean 4.75 = 5.0
- Inverse probability weighted estimate: 3.0
The naive comparison credits the exposure with five points. Two of those points belong to the confounder: high-x cases both receive the exposure more often and score higher without it. Weighting removes the confounder share and leaves an estimate of three. The example is small enough to check by hand, and that is the point of it: the adjustment is arithmetic with a stated logic, not a black box.
When the tool fits, and when it does not
It fits when:
- The exposure was not randomized, randomization is impossible or unethical, and the confounders are measured and named by someone who knows the subject.
- Overlap is real: across the confounder range, both exposed and unexposed cases exist.
- The report will carry the assumptions, the balance table, and the E-value beside the estimate.
It does not fit when:
- A randomized design is available. Randomization answers the question directly, and no adjustment machinery improves on it.
- A decisive confounder is unmeasured and plausibly strong. The E-value quantifies how strong it would have to be, and sometimes the honest reading of that number ends the causal claim.
- The exposure groups barely overlap. Weighting then rests on a handful of enormous weights, and the module shows that in the weight distribution rather than smoothing it over.
Run it
Module 18: Propensity Score AnalysisOpen in Analysis Studio →Load your data, name the exposure and the outcome, choose the confounders yourself, and read the balance report before the estimate.
Questions
What is the difference between weighting and matching? Weighting keeps every case and rebalances by inverse probability weights. Matching pairs each treated case with a similar untreated case and sets the rest aside, which changes the population the estimate describes to the treated group. Weighting answers for the whole sample or for the treated, chosen in advance; matching answers for the treated who found matches.
What balance is good enough? The working standard is a standardized mean difference under 0.1 on every confounder, with variance ratios near one. The module prints every value, and results stay blocked until imbalance past the standard is acknowledged in writing on the results.
What does the E-value tell me? How strong an unmeasured confounder would need to be, associated with both exposure and outcome, to reduce the estimate to zero. A large E-value means only a strong hidden factor could explain the result away. A small one means the causal reading is fragile, and the report should say so.
Can the tool pick my confounders for me? No, by design. Confounder choice is the analysis. The tool fits the propensity model from the variables you name and shows you the balance those choices achieve.
Does it combine with survey weights? Yes. Where survey weights exist, the design weights multiply the propensity weights and design-based variances are used. Matching is not offered in that combination, because matched designs and survey designs do not compose honestly.