Measuring Model Performance in the Presence of an Intervention

TL;DR

This work investigates how to measure and compare predictive performance when an intervention affects outcomes. It proves that naive augmentation of AUROC with treated data introduces bias and can invert model rankings, and it derives conditions under which this occurs. The authors propose NPW, a weighting-based method that reweights treatment-group samples to mimic non-intervened distributions, yielding unbiased AUROC estimates while using all available data. Empirically, NPW improves AUROC estimation accuracy, model ranking (C-index), and statistical power in both synthetic and real-world RCT datasets, enabling more data-efficient evaluation in social-impact settings.

Abstract

AI models are often evaluated based on their ability to predict the outcome of interest. However, in many AI for social impact applications, the presence of an intervention that affects the outcome can bias the evaluation. Randomized controlled trials (RCTs) randomly assign interventions, allowing data from the control group to be used for unbiased model evaluation. However, this approach is inefficient because it ignores data from the treatment group. Given the complexity and cost often associated with RCTs, making the most use of the data is essential. Thus, we investigate model evaluation strategies that leverage all data from an RCT. First, we theoretically quantify the estimation bias that arises from naïvely aggregating performance estimates from treatment and control groups and derive the condition under which this bias leads to incorrect model selection. Leveraging these theoretical insights, we propose nuisance parameter weighting (NPW), an unbiased model evaluation approach that reweights data from the treatment group to mimic the distributions of samples that would or would not experience the outcome under no intervention. Using synthetic and real-world datasets, we demonstrate that our proposed evaluation approach consistently yields better model selection than the standard approach, which ignores data from the treatment group, across various intervention effect and sample size settings. Our contribution represents a meaningful step towards more efficient model evaluation in real-world contexts.

Figures (6)

• Figure 1: Overview of an RCT and different model evaluation approaches using RCT data. The standard evaluation is unbiased but only uses data from the control group. Naïve Augmented Evaluation uses data from both the control and treatment groups but is biased. Our proposed nuisance parameter weighting (NPW) augmented Evaluation is unbiased and uses all RCT data.
• Figure 2: Empirical results with the synthetic dataset. (A) MAEs of different AUROC estimates for models with various ground true AUROCs. (B) C-index of model rankings induced by different AUROC estimates evaluated under interventions of various ATEs. In both figures, NPW consistently outperforms the standard approach, and its advantage over the standard approach increases as the variance ($v$) of nuisance parameter estimates decreases. Error bars are bootstrapped 95% confidence intervals.
• Figure 3: LACE and Epic's readmission prediction performance in terms of the AUROC, estimated using all control data. Error bars are bootstrapped 95% confidence intervals.
• Figure 4: Empirical results with the real-world datasets. (A): C-index of model performance rankings induced by different AUROC estimates on the AMR-UTI dataset. (B): Statistical power for testing whether Epic outperforms LACE using different AUROC estimates on the Readmission dataset. On both figures, NPW achieves the highest C-index and statistical power across all sample size settings ($n$). Error bars are bootstrapped 95% confidence intervals.
• Figure 5: Mean absolute errors (MAEs) of different AUROC estimations under various ATE and true model AUROCs with the synthetic dataset. Our proposed NPW approach has consistent performance across different ATE settings.

Theorems & Definitions (2)

• Theorem 1: Bias of Naïve Augmented AUROC (Eq. \ref{['eq:naive-auroc']})
• Theorem 2: Condition for Incorrect Model Selection with Naïve Augmented AUROC