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Evaluating Index-based Treatment Allocation in Underresourced Communities
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Introduces a subgroup estimator with valid asymptotic confidence intervals for evaluating index-based allocation policies in RCTs, and re-evaluates the mMitra mHealth field trial.
Problem
Evaluating index-based resource allocation policies with RCTs is hard because agents' treatment depends on other agents, which breaks independence assumptions of standard statistical tests, and the existing base estimator has low power and no validated confidence intervals.
Approach
A subgroup estimator that compares agents selected by the policy in the policy arm against agents the policy would have selected in the control arm, with asymptotic normality (adapted from Imai and Li 2024) giving valid confidence intervals and higher statistical power than the base estimator.
Key results
- Subgroup and base estimators both give approximately valid 95% confidence intervals (error under 1.5% across three domains).
- The subgroup estimator's confidence intervals are typically about a third the width of the base estimator's, with power gains up to a factor of 8 in scarce-resource settings.
- Reevaluating the mMitra RCT, ML Method 2 shows statistically significant positive effects for agents called in the first week, a conclusion the base estimator could not establish.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the subgroup estimator instead of the base estimator | Index-based policy evaluation · Synthetic | CI half-width: 0.426 -> 0.178 | Helped |
| Use the subgroup estimator instead of the base estimator | Index-based policy evaluation · TB | CI half-width: 0.778 -> 0.293 | Helped |
| Use the subgroup estimator instead of the base estimator | Index-based policy evaluation · mMitra | CI half-width: 0.668 -> 0.221 | Helped |
| Use the subgroup estimator instead of the base estimator | Index-based policy evaluation · Synthetic | 95% CI coverage: 0.952 -> 0.935 | No clear effect |
| Use the subgroup estimator instead of the base estimator | Index-based policy evaluation · TB | 95% CI coverage: 0.946 -> 0.947 | No clear effect |
| Use the subgroup estimator instead of the base estimator | Index-based policy evaluation · mMitra | 95% CI coverage: 0.956 -> 0.938 | No clear effect |
| Use the subgroup estimator rather than the base estimator to evaluate ML Method 2 calls to beneficiaries in the first x weeks | mMitra field-trial evaluation · mMitra, first x weeks for x in [1, 5] | average intervention effect on engagement | Helped |
Surprising findings
- With the base estimator, the Whittle policy cannot be shown to significantly differ from random allocation, whereas the subgroup estimator can.
Limitations
- Asymptotic validity guarantees do not cover the extended settings (covariate correction, multi-step effects, sequential allocation), which rely on empirical validation with Welch's z-test.
- Experiments rely on simulators built from real or synthetic MDP models rather than live deployments.
Experimental setup
Datasets: mMitra field trial data (ARMMAN) Tuberculosis medication adherence data (Killian et al. 2019) synthetic MDP simulators
Benchmarks: synthetic MDP simulator Tuberculosis adherence simulator mMitra simulator mMitra RCT re-evaluation
Metrics: coverage of 95% confidence intervals confidence interval half-width statistical power
Baselines: base estimator random allocation policy ML Method 1
Builds on: Imai and Li (2024) Whittle index restless multi-armed bandits
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