Counterfactual Risk Assessments, Evaluation, and Fairness

1 INTRODUCTION

• Risk assessments trained and evaluated on observed outcomes reflect historical decisions, while decision-makers need risk under proposed interventions.When interventions affect outcomes, models that appear successful under standard evaluation can underperform for cases historically receptive to intervention.Source: §1 · p. 1
• Parity in a standard fairness metric often does not yield parity in its counterfactual analogue; fairness-corrective methods can increase counterfactual disparity.The paper also reports that standard and counterfactual fairness align only under strong conditions that are unlikely to hold generally.Source: §1 · p. 2
• The authors define counterfactual predictive-performance and fairness metrics and propose doubly robust estimation for evaluating them.Their contributions include empirical comparisons on synthetic and real-world child welfare hotline screening data.Source: §1 · pp. 1–2
• The paper reports empirical support that its evaluation outperforms existing methods on synthetic and real-world child welfare hotline screening data.It also proposes three counterfactual fairness metrics and shows that existing corrective methods can increase disparity on the counterfactual metric they target.Source: §1 · p. 2

2.1 Counterfactual learning and evaluation

• Risk assessment informs human decisions by estimating outcomes under an intervention, rather than learning a decision policy as in contextual-bandit work.Prior bandit methods use propensity weighting or doubly robust policy evaluation [14]; this paper instead makes counterfactual classification metrics explicit.Source: §2.1 · p. 2
• Propensity-score weighting can be biased when the historical policy model is poor, whereas doubly robust methods tolerate propensity-model misspecification if the outcome regression is correctly specified.Prior work also uses doubly robust estimation for offline bandit policy learning and evaluation [14].Source: §2.1 · p. 2
• Earlier temporal counterfactual risk-assessment work evaluated with observed and simulated outcomes, while this paper adapts doubly robust policy-evaluation techniques to counterfactual risk metrics [44].The authors note that evaluation against observed outcomes can mislead when treatment was not randomly assigned.Source: §2.1 · p. 2
• The paper assumes no hidden confounders for its evaluation method, while its theoretical analysis holds even with hidden confounding.It identifies incorporating hidden-confounder techniques as future work; prior approaches include minimax-regret policy learning [18] and latent-variable modeling.Source: §2.1 · p. 2

2.2 Fairness and causality

• Counterfactual fairness literature intervenes on the protected attribute and asks whether the decision would change [26] [53], whereas this paper considers interventions on treatment decisions and future outcomes.Related path-specific-effect work characterizes discrimination through interventions on the protected attribute [35].Source: §2.2 · p. 2
• Protected-attribute counterfactual fairness can require excluding important predictors or fully specifying a structural causal model, constraints the authors consider too restrictive for their settings.They also argue that such definitions may be ill-suited to child welfare screening because decisions based on counterfactual protected attributes may cause further harm to protected groups.Source: §2.2 · p. 2
• Unlike selection-bias work on screened-out cases, this paper observes outcomes for all cases under different treatments and defines fairness measures that account for treatment effects.The related work finds fairness corrections insufficient for parity in settings such as loan approvals where outcomes for denied applicants are unobserved [19].Source: §2.2 · pp. 2–3

3.2 Learning models of risk

• The observational risk model estimates E[Y | X] under historical decisions, while the counterfactual model targets baseline risk E[Y 0 | X].Under the identifying assumptions, E[Y 0 | X] = E[Y | X, T = 0], which can be estimated by training a probabilistic classifier on control cases, with reweighing to correct covariate shift.Source: §3.2.1 · p. 3, §3.2.2 · pp. 3–4

3.2.2 Counterfactual.

• Counterfactual identification relies on assumptions including no interference, exchangeability given measured covariates, and a nonzero chance of baseline treatment for each example.In child welfare, the authors consider these assumptions reasonable because one investigation is unlikely to affect another case and measured variables may capture most information used by screeners.Source: §3.2.2 · pp. 3–4

3.3 Evaluation

• Observational evaluation tests predictions against outcomes under historical decisions, while control-only evaluation can mislead when control cases are not representative of the full population.In child welfare, cases with an abuse history are more likely to be screened in, so performance on control cases may not reflect performance on treated cases.Source: §3.3.2 · p. 4, §3.3.1 · p. 4

3.3.2 Evaluation on the Control Population.

• Doubly robust evaluation estimates counterfactual outcomes across treated and control cases, yielding representative population assessment and robustness to misspecification of either nuisance function.With sample splitting and n^1/4 convergence of nuisance-function errors, the estimates are √n-consistent and asymptotically normal, enabling confidence intervals.Source: §3.3.3 · p. 4

3.4.1 Synthetic example.

• DR evaluation most closely matches true counterfactual performance in synthetic data, where observational evaluation incorrectly favors the observational model.The figure caption also notes that control evaluation produces inaccurate curves because it does not assess performance on treated cases.Source: §3.4.1 · p. 5, Figure 1 · p. 6

3.4.2 Child Welfare.

• DR evaluation finds the counterfactual model well-calibrated by race and shows that the observational model underestimates risk for both Black and White cases.Observational evaluation instead suggests that the counterfactual model is poorly calibrated by race.Source: §3.4.2 · pp. 6–7
• In child welfare, doubly robust evaluation favors the counterfactual model, while observational evaluation favors the observational model; the true counterfactual is unavailable for validation.The DR evaluation also shows better discrimination and calibration for re-referral risk under screen-out.Source: §3.4.2 · pp. 5, 7

3.4.3 Expert Evaluation.

• Expert risk rankings align with the counterfactual model, whereas the observational model assigns the screened-out group the most high-risk cases and underestimates risk in treated groups.The expected ordering is highest risk among children placed out-of-home, followed by those offered services, those screened in, and those screened out.Source: §3.4.3 · p. 7
• At every proportion classified as high-risk, the counterfactual model has significantly higher recall for both serviced and placed cases.The comparison varies the proportion classified as high-risk.Source: §3.4.3 · p. 7

3.4.4 Task adaptation: Predicting Placement.

• The observational model performs worse than random on placement prediction, while the counterfactual model shows discrimination and transfers to this related risk task.The task assesses how well models of E[Y 0|X] estimate E[Y 1|X], using out-of-home placement as the outcome.Source: Table 1 · p. 7, §3.4.4 · p. 7
• Ignoring treatment effects can lead to wrong conclusions and potentially deploy a model that underestimates risk for those who stand to gain most from treatment.The expert assessment and downstream placement-task results support the doubly robust evaluation's conclusion that the counterfactual model outperforms the observational model.Source: §3.4.4 · p. 7

4 COUNTERFACTUAL FAIRNESS

• The fairness definitions concern interventions on treatment, not hypothetical changes to protected attributes; treatment-mitigated outcomes can otherwise be mistaken for model errors.The tutoring examples show how intervention effects can create observational false-positive disparities even for a model that predicts untreated risk perfectly.Source: §4 · pp. 7–8

4.1 Theoretical results

• For three fairness notions, observational parity implies counterfactual parity if and only if a balance condition holds; independence conditions are sufficient but generally unlikely.The theoretical analysis concludes that equalizing an observational fairness metric often will not equalize its counterfactual counterpart.Source: §4.1 · pp. 8–9, §4.1.3 · p. 10

4.1.1 Base Rate Parity.

• Base-rate parity distinguishes observational Y ⊥ A from counterfactual Y^0 ⊥ A; the sufficient independence condition is unlikely where treatment assignment or treated-risk distributions differ by group.The theorem assumes a positivity-like condition, and the text notes that indBP requires no group differences in treatment assignment given untreated risk or in risk under treatment.Source: §4.1.1 · pp. 9–10

4.1.2 Predictive parity.

• Predictive parity compares group outcomes conditional on predicted class; observational parity implies its counterfactual analogue only under a balance condition.The sufficient independence condition is unlikely when treatment assignment is group-biased or risk under treatment differs by group.Source: §4.1.2 · p. 10

4.1.3 Equalized odds.

• Equalized odds requires prediction to be independent of group conditional on the outcome, using Y observationally or Y^0 counterfactually; the implication also requires balance.Its sufficient independence conditions include base-rate parity and are unlikely with treatment-assignment discrimination or group differences in treated risk.Source: §4.1.3 · p. 10

4.2 Experiments on synthetic data

• On synthetic data, equalizing an observational fairness metric can increase disparity in its counterfactual counterpart.The experiments were not run on child welfare data because its race-specific base rates and FPR/TPR were balanced.Source: §4.2 · p. 10

4.2.1 Reweighing.

• Reweighting achieves observational base-rate parity but induces counterfactual base-rate disparity when treatment assignment is biased toward group A = 1.Before reweighting, counterfactual base rates are equal while observational rates diverge for k > 0.Source: §4.2.1 · p. 11, Figure 6 · p. 11

4.2.2 Post-processing for equalized odds.

• Post-processing that equalizes observational generalized error rates induces imbalance in counterfactual rates; the disparity disadvantages the group less likely to receive beneficial treatment.The original model achieved counterfactual equalized odds, but post-processing induced disparity.Source: §4.2.2 · p. 11

5 CONCLUSION

• Post-processing that equalizes observational rates induces counterfactual disparities and can compound inequities in treatment assignment.The reported disparity harms group A = 0, which was less likely to be treated; treatment is beneficial.Source: Table 2 · p. 11, Figure 7 · p. 11, §5 · p. 11
• Evaluating with observed outcomes can misestimate risk for those most receptive to treatment, potentially misallocating resources.The conclusion states that this misestimation can lead to resource misallocation.Source: §5 · p. 11
• Counterfactual approaches to learning, evaluation, and fairness assessment provide more accurate and relevant indications of model performance.Source: §5 · p. 11

A IDENTIFICATIONS

• Identification expresses a counterfactual quantity in terms of observable quantities based on causal assumptions.Source: A IDENTIFICATIONS · p. 14
• The identifications rely on the causal assumptions specified in § 3.2.Source: A IDENTIFICATIONS · p. 14
• Separate training and test partitions ensure that predictions are functions of features X during evaluation.Source: A IDENTIFICATIONS · p. 14

A.1 Identification of the Counterfactual Outcome

• The counterfactual outcome target E[Y^0 | X] is identified as E[Y | X, T = 0].Source: §A.1 · p. 14
• The derivation uses exchangeability to relate the counterfactual target to observed quantities.Source: §A.1 · p. 14
• The derivation then uses consistency to complete the identification.Source: §A.1 · p. 14

A.2 Identification of Counterfactual TPR

• Counterfactual TPR identification separately handles numerator and denominator, using test-set predictions as functions of X and exchangeability and consistency.Source: §A.2 · p. 14

A.3 Identification of Counterfactual Precision

• Counterfactual precision is identified as E[E[Y | X, T = 0] | Ŷ = 1] under exchangeability and consistency.Source: §A.3 · p. 14

A.4 Identification of Counterfactual Calibration

• Counterfactual calibration uses the same derivation as precision because the score ŝ(X) is a function of X.Source: §A.4 · p. 14

A.5 Identification of Counterfactual FPR

• Counterfactual FPR identification follows the TPR derivation, identifying the numerator and denominator with exchangeability and consistency.The numerator uses the counterfactual event Y^0 = 0.Source: §A.5 · p. 14

B PROOFS

• The proofs in this section assume consistency.Consistency is defined in § 3.2.2.Source: B PROOFS · p. 15
• For base-rate parity, observational parity plus balBP is sufficient for counterfactual parity; with a positivity-like assumption, the proof concludes Y0 is independent of A.The stated positivity-like assumption is P(T = 0 | y0,a) ≠ 0.Source: B PROOFS · p. 15
• indBP is sufficient for oBP to imply cBP when T ⊥ A | Y0 and (Y1,T) ⊥ A.These conditions imply balBP, which is sufficient for the implication.Source: B PROOFS · p. 15
• The predictive-parity proofs use the same techniques as the base-rate-parity proofs.Source: B PROOFS · p. 15
• For equalized odds, the stated independencies make balEO hold, which is sufficient for oEO to imply cEO.The proof lists the independencies as Ŷ ⊥ A | Y1; Y ⊥ A; Y1 ⊥ A; Y0 ⊥ A; T ⊥ A | Ŷ,Y0; and T ⊥ A | Ŷ,Y1.Source: B PROOFS · p. 16

C CHILD WELFARE EVALUATION VIA TASK ADAPTATION ON SERVICES

• The observational model performs worse than a random classifier, while the counterfactual model performs better on the services task.Table 3 reports AuROC and AuPR for accepting a case for services and describes the counterfactual model as transferring to this related risk task.Source: Table 3 · p. 17, C CHILD WELFARE EVALUATION VIA TASK… · p. 17

D FURTHER SYNTHETIC EVALUATION

• With c = 0.1 and k = 1, DR most accurately represents the true counterfactual evaluation, while observational evaluation incorrectly ranks the observational model above the counterfactual model.The control evaluation also gives inaccurate curves; lower k reduces treatment imbalance and rates, improving the observational model relative to k = 1.6, but it still underperforms the counterfactual model.Source: Figure 8 · p. 19
• With c = 0.5 and k = 1.6, the counterfactual and observational models’ PR and ROC curves are closer than at c = 0.1, but the counterfactual model still has better calibration.Control and observational evaluations give incorrect calibration and PR curves; DR most closely resembles true counterfactual evaluation.Source: Figure 9 · p. 20
• With c = 0.1 and k = 2, higher propensity to treat group A = 1 increases treatment imbalance and treatment rates; DR most accurately represents true counterfactual evaluation.Source: Figure 10 · p. 21

D.1 Controlling for Treatment in the Regression

• Including T as a feature does not appropriately control for treatment effects: the observational model underperforms relative to the counterfactual model on the treated population.Source: §D.1 · p. 22, Figure 11 · p. 23, Figure 12 · p. 24
• Control-only evaluation misses the observational model’s severe treated-population underperformance; DR and true counterfactual evaluation reveal it, though true counterfactual evaluation is not feasible in practice.Source: §D.1 · p. 22
• The observational model underestimates treated-population risk at c = 0.1 and c = 0.5, although the underestimation is less severe at c = 0.5.The higher c reduces the treatment effect, but the observational model still underperforms on the treated population.Source: Figure 11 · p. 23, Figure 12 · p. 24

• The analysis varies c, the treatment-effect parameter, and k, the treatment-assignment-bias parameter.Source: E FAIRNESS-CORRECTIVE METHODS ON… · p. 25
• The analysis displays counterfactual ROC curves and generalized observational and counterfactual FPR and FNR at threshold t = 0.5.Source: E FAIRNESS-CORRECTIVE METHODS ON… · p. 25
• Figures 13–16 show post-processing results across four synthetic-data parameter settings: (c, k) = (.1, .8), (.1, 1.6), (.3, .8), and (.3, 1.6).Source: Figure 13 · p. 26, Figure 14 · p. 26, Figure 15 · p. 26