Interpretable Causal Inference for Analyzing Wearable, Sensor, and Distributional Data

TL;DR

The paper tackles causal questions where outcomes are distributions from wearable data, arguing that distributional representations preserve information lost by scalar summaries. It develops ADD MALTS, an end-to-end framework that learns a distributional distance metric, estimates CATEs via distributional matching, and provides theoretical consistency results. Through simulations, ADD MALTS outperforms baselines in CATE estimation and offers explicit overlap checks to validate positivity. Applied to CGM data from a type 1 diabetes trial, ADD MALTS finds minimal average effects but meaningful heterogeneity in subgroups, illustrating its practical utility for wearables and distributional outcomes.

Abstract

Many modern causal questions ask how treatments affect complex outcomes that are measured using wearable devices and sensors. Current analysis approaches require summarizing these data into scalar statistics (e.g., the mean), but these summaries can be misleading. For example, disparate distributions can have the same means, variances, and other statistics. Researchers can overcome the loss of information by instead representing the data as distributions. We develop an interpretable method for distributional data analysis that ensures trustworthy and robust decision-making: Analyzing Distributional Data via Matching After Learning to Stretch (ADD MALTS). We (i) provide analytical guarantees of the correctness of our estimation strategy, (ii) demonstrate via simulation that ADD MALTS outperforms other distributional data analysis methods at estimating treatment effects, and (iii) illustrate ADD MALTS' ability to verify whether there is enough cohesion between treatment and control units within subpopulations to trustworthily estimate treatment effects. We demonstrate ADD MALTS' utility by studying the effectiveness of continuous glucose monitors in mitigating diabetes risks.

Figures (10)

• Figure 1: For patients older than 55 years, we measure the effectiveness of CGMs as the percent change of time in healthy range. The plot shows how changing the healthy range's upper bound (x-axis) affects the treatment effect (y-axis). 70 is the lower bound.
• Figure 2: The figure displays the Integrated Relative Error (%) (y-axis) of the different methods we consider for different simulation setups (x-axis). We consider the following baseline methods: Lin PSM and RF PSM represent propensity score matching fit with linear and random forest models, respectively; FT and FRF represent decision tree and random forest methods for functional outcomes qiu2022random; LR represents outcome regression fit at each quantile with a linear regression lin2023causal; LR + Lin PS and LR + RF PS represent augmented inverse propensity weighting methods combining the linear outcome regression with linear and random forest propensity score models, respectively.
• Figure 3: The plot displays which units should be pruned in red according to each method: (from left to right) propensity score estimated with logistic regression using L1 regularization, propensity score estimated with a random forest, and the diameter of matched groups estimated with ADD MALTS. The background displays the true propensity score; the bottom, left corner marks the region of the covariate space with no overlap.
• Figure 4: Quantile functions of glucose levels measured at baseline. The thick black line represents the average quantile function while the other colors represent the quantile functions for 50 patients.
• Figure 5: (a) Average treatment effect of glucose-monitoring with CGM on the distribution of glucose concentrations before pruning positivity violations (pink) and after (gold). (b) Conditional average treatment effect of glucose monitoring with CGM on the distribution of glucose concentrations for patients older than 55 years of age (green) and for those with low HbA1c levels at baseline (blue). The x-axes display the probability level and the y-axes display the difference in the related quantiles of the outcomes.

Theorems & Definitions (11)

• Remark 1
• Remark 2
• Remark 3
• Lemma 1
• Theorem 1
• Proposition 1: lin2023causal
• proof
• Lemma : \ref{['lemma:barycenter_consistency']}
• proof
• Theorem : \ref{['thm:cate_consistency']}