Research map / Probabilistic and scientific modeling / Treatment effects
Mediation Analysis for Probabilities of Causation
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Introduces controlled direct, natural direct, and natural indirect probabilities of necessity and sufficiency (CD-PNS, ND-PNS, NI-PNS), with evidence-conditioned variants, and gives identification theorems from observational data under sequential ignorability and monotonicity, illustrated on the JOBS II dataset.
Problem
Probabilities of causation (PNS) do not decompose by causal pathway through a mediator, so it is unclear how much a treatment's necessity and sufficiency for an outcome operates directly versus through a mediator; existing mediated PoC answer different questions.
Approach
Defines mediator-based direct and indirect variants of PNS (CD-PNS, ND-PNS, NI-PNS) with the decomposition T-PNS = ND-PNS + NI-PNS, extends them to subpopulations via post-treatment evidence, and derives identification formulas in terms of conditional CDFs under sequential ignorability and monotonicity assumptions.
Key results
- On JOBS II, estimated T-PNS is 23.840% (CI 19.021%-29.254%), with NI-PNS equal to 23.840% and ND-PNS 0%, so the necessity and sufficiency is entirely indirect via the mediator.
- In simulations with N=10000, estimates closely match ground truth (T-PNS 0.074 vs truth 0.074; NI-PNS 0.008 vs 0.008) and CIs narrow as N grows.
- With evidence on the subpopulation, T-PNS is 57.899% and NI-PNS 57.899% while CD-PNS and ND-PNS are 0%.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| increase the simulation sample size from N=100 to N=10000 | Proposed T-PNS estimator · Simulated SCM | estimation precision: 0.083 (CI: [0.000,0.228]) -> 0.074 (CI: [0.060,0.088]) | Helped |
| increase the simulation sample size from N=100 to N=10000 | Proposed ND-PNS estimator · Simulated SCM | estimation precision: 0.074 (CI: [0.000,0.220]) -> 0.067 (CI: [0.052,0.082]) | Helped |
| increase the simulation sample size from N=100 to N=10000 | Proposed NI-PNS estimator · Simulated SCM | estimation precision: 0.009 (CI: [0.000,0.046]) -> 0.008 (CI: [0.005,0.011]) | Helped |
| evaluate the evidence-defined subpopulation instead of the whole population | T-PNS and NI-PNS · JOBS II | T-PNS: 23.840% -> 57.899% | Mixed |
| attribute the treatment's necessity and sufficiency to the indirect pathway via the mediator | JOBS II mediation analysis · JOBS II | PNS: ND-PNS: 0.000%; NI-PNS: 23.840%; T-PNS: 23.840% | Mixed |
Surprising findings
- Direct PNS (ND-PNS and CD-PNS) is zero on JOBS II even though prior work reported a significant direct effect of treatment on depression.
Limitations
- Identification requires sequential ignorability and monotonicity assumptions, which may not hold in general.
- Bounding and sensitivity analysis are left to future work when assumptions fail.
- CD-PNS confidence interval is very wide (0% to 41.676%) on the real data.
Experimental setup
Datasets: JOBS II job search intervention study (n=899) simulated binary SCM data
Benchmarks: JOBS II (depression outcome, job-search self-efficacy mediator)
Metrics: point estimates bootstrap 95% confidence intervals bias versus ground truth in simulations
Baselines: T-PNS Mediated PoC (Mueller et al.)
Builds on: Probability of necessity and sufficiency (Pearl) Natural direct and indirect effects (Pearl 2001) Sequential ignorability (Imai et al.) Multivariate PoC (Dawid et al.)
Closest papers by meaning
- Intervention and Conditioning in Causal Bayesian Networks (NeurIPS 2024 · similarity 0.84)
- Probabilities of Causation with Nonbinary Treatment and Effect (AAAI 2024 · similarity 0.84)
- Challenges and Considerations in the Evaluation of Bayesian Causal Discovery (ICML 2024 · similarity 0.82)
- Resolution of Simpson's paradox via the common cause principle (NeurIPS 2025 · similarity 0.81)
- On Positivity Condition for Causal Inference (ICML 2024 · similarity 0.80)
- Detecting and Measuring Confounding Using Causal Mechanism Shifts (NeurIPS 2024 · similarity 0.80)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.