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Measurement-Error-Aware Causal Distributed-Lag Quantile Modeling of Indoor Air Pollution and Short-Term Lung-Function Deterioration

Shayma Alkobaisi, Anas Ali

arXiv:2609.31646v1stat.APcs.AIcs.CYcs.LG

TL;DR

Short-horizon asthma analysis must contend with noisy indoor exposure measurements, delayed effects, time-varying confounding, and heterogeneous outcome tails. CAUSALQUANT-ASTHMA combines sensor calibration, sequential weighting, and quantile distributed-lag modeling, then evaluates recovery against known counterfactual truth in a semi-synthetic benchmark. It achieves lower dose-response error than the strongest measurement-error and propensity-weighted baseline, but the evidence is not clinical validation.

  • Problem

    No authorized cohort available to the study combined dense indoor PM2.5 sensing, sparse reference co-location, time-varying behavior and medication measures, and repeated outcome-compatible adult PEF.

    Source: §I · p. 2

  • Method

    CAUSALQUANT-ASTHMA combines sparse-reference sensor calibration, stabilized sequential generalized-propensity weighting, and susceptibility-modulated smooth noncrossing quantile distributed-lag estimation.

    Source: §I · p. 2

  • Results

    24.2 percent lower dose–response IAE than ME-GPS-QDLM: CAUSALQUANT achieved 0.304±0.094 versus 0.401, and its factual pinball loss was 1.065.

    Source: C. Main Counterfactual and Predictive… · p. 7

  • Takeaways & Limitations

    The five generated causal-truth benchmarks establish methodological feasibility and reproducibility, not clinical effectiveness.

    Source: §I · p. 2, §VI · p. 10

    The outcome is simulated PEF, and there is no evidence that acting on the estimated curve improves health, adherence, or equity.

    Source: G. Threats to Validity and Transition… · p. 10

Abstract

from arXiv · show

Low-cost indoor air-quality sensors could support personalized asthma prevention, but their nonlinear measurement error, delayed exposure effects, time-varying confounding, and heterogeneous lower-tail responses limit risk estimation. We present CAUSALQUANT-ASTHMA, a measurement-error-aware causal quantile distributed-lag framework for short-horizon peak expiratory flow analysis. Sparse reference measurements train a nonlinear calibration model; stabilized sequential generalized-propensity weights address measured exposure assignment; and a susceptibility-modulated, smooth, noncrossing quantile model estimates lag-specific and sustained-exposure contrasts. Because no authorized cohort simultaneously provided dense indoor sensing, reference co-location, and outcome-compatible longitudinal data, evaluation used five semi-synthetic panels with known counterfactual truth, 150 patients and 12,600 patient-days per realization. Across eight methods, CAUSALQUANT achieved a dose-response integrated absolute error of 0.304 plus or minus 0.094, improving 24.2 percent over the strongest measurement-error and propensity-weighted baseline. It also obtained the lowest overall pinball loss, 1.065, while maintaining zero quantile crossings and 78.1 percent coverage for the nominal 80 percent interval. Sensor calibration reduced held-out exposure RMSE by 33.7 percent. Stress tests quantified degradation under sensor noise, missing personal measurements, and hidden confounding. These findings establish methodological feasibility and reproducibility, not clinical effectiveness; prospective, governance-approved external validation is required before patient-level interpretation or deployment.

I. INTRODUCTION

Personalized short-horizon asthma analysis is challenged by variable indoor exposure, sensor error, delayed effects, time-varying confounding, and heterogeneous lower-tail responses. CAUSALQUANT-ASTHMA combines calibration, weighting, and quantile distributed-lag modeling; evaluation uses semi-synthetic data with known counterfactual truth, not clinical validation.

I. INTRODUCTION

  • The study targets individualized, short-horizon analysis because indoor PM2.5 varies across microenvironments and asthma responses may differ in the vulnerable lower tail.Prior findings can be weak or unstable for several reasons, including exposure error, limited samples, confounding, averaging-window choice, or focusing on conditional means.Source: §I · p. 1
  • Low-cost sensor error can distort lag profiles, while ordinary adjustment may be biased when time-varying covariates are affected by prior exposure.Repeated measurements alone do not remove exposure-error distortion; observational weighting also cannot remove unmeasured confounding.Source: §I · pp. 1–2
  • CAUSALQUANT-ASTHMA links sparse-reference sensor calibration, longitudinal generalized-propensity weighting, smooth noncrossing QDLM estimation, and susceptibility modulation.The framework targets a sustained seven-day PM2.5 intervention contrast across PEF quantiles and a lag-effect profile.Source: §I · p. 2
  • The evaluation uses a semi-synthetic causal-truth benchmark because no authorized dataset combined dense indoor sensing, reference co-location, time-varying covariates, and repeated compatible adult PEF.Patient-disjoint partitions keep calibration and exposure-density fitting on training patients, use validation patients for model selection, and reserve test outcomes for final evaluation.Source: §I · p. 2
  • The benchmark tests recovery of the estimator's target quantity, but does not substitute for clinical validation.The contributions also include reproducible calibration, weighting, optimization, and sustained-intervention algorithms, plus an eight-method, five-seed benchmark.Source: §I · p. 2

II. RELATED WORK

Prior work supplies pieces of indoor monitoring, sensor calibration, distributed-lag modeling, and continuous-exposure causal inference, but not their full integration for asthma quantiles. The paper positions its contribution at that intersection and describes the longitudinal monitoring variables it uses.

A. Asthma, Indoor Exposure, and Personal Monitoring

  • Indoor and personal monitoring studies provide repeated exposure and health signals, but small samples, incomplete adherence, sensor differences, and weakly aligned outcomes limit causal interpretation.Prior studies report substantial divergence between personal and fixed-site exposure, without a consistent lagged relationship in thirteen adults.Source: A. Asthma, Indoor Exposure, and… · p. 2

B. Exposure Error and Distributed Lags

  • Existing QDLM work models tails and critical windows, while sensor-calibration methods address exposure error; the literature does not combine sparse-reference calibration with continuous-treatment weighting for longitudinal indoor asthma data.The related methods are complementary, but existing QDLMs assume adequately observed exposure.Source: B. Exposure Error and Distributed Lags · pp. 2–3

C. Continuous-Exposure Causal Inference

  • Continuous-exposure causal methods and predictive models do not directly solve lower-tail lag recovery, quantile crossing, and nonlinear sensor error together.The paper addresses this intersection without claiming that any single component is unprecedented, combining sparse-reference calibration, sequential weighting, and a structured QDLM.Source: C. Continuous-Exposure Causal Inference · p. 3

A. Longitudinal Monitoring System

  • The monitoring system defines morning PEF as a percentage of personal best and treats latent daily indoor PM2.5 as exposure; sensor readings and sparse co-located references are distinguished from that latent exposure.Measured time-varying covariates include outdoor PM2.5, temperature, humidity, occupancy, activity, medication adherence, infection, and prior PEF.Source: A. Longitudinal Monitoring System · p. 3

B. Identification Assumptions and Target Estimand

The target is a quantile-specific contrast between sustained exposure histories, interpreted causally only under consistency, sequential exchangeability, and positivity. The paper uses sequential stabilized generalized-propensity weights and treats the assumptions as unprovable from observational data.

B. Identification Assumptions and Target Estimand

  • The causal interpretation requires consistency, sequential conditional exchangeability across the lag window, and positivity on the intervention support.These assumptions cannot be proven from observational data, motivating positivity diagnostics and hidden-confounding stress tests.Source: B. Identification Assumptions and… · p. 3
  • For continuous exposure, the generalized-propensity density is the conditional exposure density given history, and sequential stabilized weights are used over the lag window.The implementation uses log densities, a short rolling history, percentile clipping, and partition-specific mean-one normalization to limit numerical instability.Source: B. Identification Assumptions and… · p. 3
  • The primary estimand contrasts quantile outcomes under sustained high and lower exposure histories; the evaluation uses 35 versus 10 µg/m3 and also recovers a grid from 5 to 45 µg/m3.This is a methodological contrast under the stated intervention and assumptions, not a recommendation to expose or de-expose a patient.Source: B. Identification Assumptions and… · p. 3

A. Pipeline Overview

CAUSALQUANT-ASTHMA reconstructs exposure from sparse reference measurements, then uses corrected histories and measured covariates in a weighted, structured quantile distributed-lag model. Reference measurements are confined to the measurement stage, and outcome-informed selection is confined to validation.

A. Pipeline Overview

  • Corrected exposure histories and measured covariates enter a generalized-propensity model whose stabilized weights, smooth lag coefficients, susceptibility interactions, and joint noncrossing objective form the final estimator.Validation patients determine early stopping, while test patients remain untouched until final evaluation.Source: A. Pipeline Overview · p. 4

B. Sparse-Reference Measurement Reconstruction

  • The calibration function uses sparse training references and sensor, environmental, temporal, and source inputs to reconstruct exposure.The reference monitor and latent exposure are used only to train or evaluate the measurement stage in the benchmark.Source: B. Sparse-Reference Measurement… · p. 4, Figure 1 · p. 5
  • Histogram gradient boosting handles missing personal-sensor values and nonlinear sensor behavior, but estimates a calibrated exposure proxy rather than exact exposure.The reference target itself includes small residual error.Source: B. Sparse-Reference Measurement… · p. 4
  • Centering susceptibility makes the main lag coefficients approximate the average patient effect while interactions allow stronger lower-tail responses in more susceptible profiles.Source: B. Sparse-Reference Measurement… · p. 5

C. Structured Quantile Distributed-Lag Model

The structured model estimates quantile-specific lag effects and sustained-exposure contrasts while retaining interpretable lag coefficients and personalized marginal effects. Smoothness and noncrossing constraints regularize the fitted quantiles.

C. Structured Quantile Distributed-Lag Model

  • The structured model produces lag coefficients, personalized marginal effects, and counterfactual predictions by substituting a sustained exposure history.It uses an interpretable local approximation over the intervention range; spline bases may add nonlinear high-concentration behavior.Source: C. Structured Quantile Distributed-Lag… · p. 5
  • Second-difference penalties smooth average and susceptibility-specific lag coefficients, while a separate penalty discourages quantile crossings.In primary runs, the learned solution already produced zero test crossings.Source: C. Structured Quantile Distributed-Lag… · p. 5
  • For B design features, Q quantiles, n patient-days, and E epochs, joint training costs O(EnBQ), while evaluating G exposure values costs O(GnBQ).The model stores O(nB + BQ) and is described as far smaller than tree ensembles while retaining an interpretable lag surface.Source: C. Structured Quantile Distributed-Lag… · p. 5
  • Training evaluates the quantile model and objective, selects parameters using validation loss and crossings, then substitutes each exposure-grid value across all lags to estimate contrasts and lag-specific effects.Source: C. Structured Quantile Distributed-Lag… · p. 6

A. Research Questions and Benchmark Design

The benchmark uses five causal-truth panels to evaluate dose-response recovery, calibration, lag reconstruction, robustness, and computational cost. Eight methods are compared on patient-disjoint splits using outcome, calibration, coverage, lag, and runtime metrics.

A. Research Questions and Benchmark Design

  • Five independent causal-truth panels each contain 150 patients and 12,600 patient-days, with temporal dependence, measured time-varying confounding, sensor error, and analytically available counterfactual outcome quantiles.The panels were used because no authorized dataset available to the project jointly contained the required sensing, reference, medication, activity, and outcome-compatible longitudinal data.Source: A. Research Questions and Benchmark… · p. 6
  • Patient-disjoint 60/20/20 splits assign 90, 30, and 30 patients per realization to training, validation, and test, respectively.Calibration and propensity models use training patients; validation patients guide tuning, and test outcomes and latent exposures are used only after the pipeline is frozen.Source: A. Research Questions and Benchmark… · p. 6

B. Comparators, Metrics, and Statistical Analysis

  • Eight methods share identical patient splits, including sensor-based, smooth QDLM, predictive-quantile, propensity-weighted, and measurement-error-plus-weighting comparators.CAUSALQUANT adds the complete interaction and constraint structure; ME-GPS-QDLM omits susceptibility interactions.Source: B. Comparators, Metrics, and… · p. 6
  • The primary metric is dose–response integrated absolute error averaged over nine sustained PM2.5 levels and five outcome quantiles, alongside treatment-effect bias, prediction, calibration, coverage, lag, and computational measures.Main values average five seeds; paired tests use seed-level IAE, with Holm adjustment across four primary comparator tests.Source: B. Comparators, Metrics, and… · p. 7
  • Runtime measurements characterize a CPU-only Linux container with nine logical CPUs and approximately 5.8 GiB RAM, rather than a clinical device.Source: B. Comparators, Metrics, and… · p. 7

C. Main Counterfactual and Predictive Results

CAUSALQUANT had the lowest dose–response IAE in the five-seed benchmark, though its advantage over ME-GPS-QDLM was not statistically significant after correction. Calibration and lag diagnostics, component ablations, and stress tests characterize where performance held and where inference remains constrained.

C. Main Counterfactual and Predictive Results

  • CAUSALQUANT’s QCE was 0.012 and its central interval coverage was 78.1% for the nominal 80% interval; ME-GPS-QDLM had QCE 0.0106 and SC-QDLM 0.0117.The interval width was 9.47 PEF points; QRF coverage was 63.5%.Source: C. Main Counterfactual and Predictive… · p. 7

D. Measurement Correction, Lag Recovery, and Calibration

  • Training-only calibration reduced test exposure RMSE from 3.986 to 2.643 µg/m3 (33.7%); median-lag RMSE was 0.0161 versus 0.0168 for ME-GPS-QDLM and 0.0179 for SC-QDLM.CAUSALQUANT recovered the delayed peak near lag two more closely than the raw-sensor models; calibration did not eliminate genuine temporal variation.Source: D. Measurement Correction, Lag… · p. 7, Figure 4 · p. 9

C. Main Counterfactual and Predictive Results

  • 0.304±0.094 dose–response IAE beat ME-GPS-QDLM by 24.2%; CAUSALQUANT also had the lowest mean AQTE bias (0.533) and factual pinball loss (1.065).The paired comparison against ME-GPS-QDLM was not significant after Holm correction (pH = 0.2188), so the benchmark does not establish definitive superiority.Source: C. Main Counterfactual and Predictive… · p. 7, Table V · p. 8, Figure 2 · p. 8
  • Under sustained seven-day interventions, CAUSALQUANT tracked analytical truth across quantiles; its estimated AQTEs were −12.17, −11.89, and −11.31 PEF points at the 0.10, 0.50, and 0.90 quantiles.The corresponding analytical AQTEs were approximately −12.33, −11.69, and −11.05 PEF points; these are benchmark recovery values, not estimates in actual patients.Source: C. Main Counterfactual and Predictive… · p. 7, Figure 3 · p. 8

E. Ablations, Stress Tests, and Subgroups

  • Removing measurement correction increased IAE from 0.157 to 1.762, the largest ablation deterioration; removing weighting raised it to 0.350 and removing susceptibility interaction to 0.223.Without smoothness and noncrossing constraints, IAE changed only from 0.1573 to 0.1571, but quantile crossings reached 0.8%. The ablations used one diagnostic realization.Source: E. Ablations, Stress Tests, and… · p. 7, Table VII · p. 8
  • The weight product used a three-day rolling history rather than the full seven-day outcome lag, leaving possible residual confounding from earlier exposure assignment.The mean training effective sample size was 1,834 from 7,560 rows; the full product had produced unstable finite-sample weights in pilot runs.Source: E. Ablations, Stress Tests, and… · pp. 8–9
  • Stress diagnostics worsened with sensor noise and strongest hidden confounding; missingness raised calibration RMSE, while downstream IAE was non-monotonic across fresh realizations.Sensor-noise tests showed corrected sensor RMSE increasing from about 2.03 to 4.13 and causal IAE varying from 0.27 to 0.86; diagnostic trajectories are not confidence intervals.Source: E. Ablations, Stress Tests, and… · pp. 7–8, Figure 6 · p. 9
  • CAUSALQUANT severity-stratified pinball loss rose from approximately 0.89 in mild profiles to 1.33 in severe profiles; the benchmark supports no fairness claim.Race, socioeconomic status, housing quality, and access to mitigation resources were not encoded in the benchmark.Source: E. Ablations, Stress Tests, and… · p. 9

F. Efficiency and Reproducibility

The structured model had short recorded fit and prediction times and a smaller reported model footprint than QRF. The computational measurements exclude one-time calibration and exposure-density stages and are specific to the recorded container.

F. Efficiency and Reproducibility

  • The structured model fitted in 0.23 s on average and evaluated 1,000 patient-days in about 0.68 ms in the recorded container.These measurements exclude one-time sensor-calibration and exposure-density stages and should not be extrapolated to another processor or distributed system.Source: F. Efficiency and Reproducibility · pp. 9–10
  • Figure 7 summarizes stabilized generalized-propensity weights, held-out sensor reconstruction, and average quantile treatment-effect recovery.Source: Figure 7 · p. 10
  • CAUSALQUANT used 145 fitted coefficients, compared with more than 92,000 tree nodes for QRF; QRF took 5.04 s to fit and 22.49 ms per 1,000 rows.The nonlinear PLSI-QDLM adaptation was also slower than the structured models.Source: F. Efficiency and Reproducibility · p. 10

G. Threats to Validity and Transition to Real Data

CAUSALQUANT-ASTHMA achieved lower error than the strongest baseline in generated causal-truth benchmarks, but its validity depends on simulator alignment, causal assumptions, and calibration support. The study does not establish clinical effectiveness or patient-level treatment effects.

G. Threats to Validity and Transition to Real Data

  • Alternative data-generating mechanisms may change method rankings because the simulator favors smooth distributed effects, measured confounding, and calibratable sensors.Although hyperparameters used validation patients, the same benchmark family informed model development.Source: G. Threats to Validity and Transition… · p. 10
  • Consistency requires a meaningful sustained-exposure intervention, while positivity may fail for histories that do not support 10 or 35 µg/m3.Misspecified propensity models and three-day weight truncation may leave residual bias; sequential exchangeability is demanding when symptoms, medication, ventilation, or activity are incompletely observed.Source: G. Threats to Validity and Transition… · p. 10
  • Calibration beyond the humidity, concentration, device, season, and home ranges covered by sparse reference co-location can appear precise but be wrong.Field studies would need traceable instruments, collocation schedules, drift monitoring, and uncertainty propagation.Source: G. Threats to Validity and Transition… · p. 10
  • Simulated PEF percentage leaves effects on exacerbations, symptoms, or healthcare utilization—and benefits to health, adherence, or equity—untested.The authors call for a preregistered, powered, multi-site adult-asthma panel with patient- and site-disjoint external testing.Source: G. Threats to Validity and Transition… · p. 10

VI. CONCLUSION

  • 0.304 mean dose-response integrated absolute error, 24.2% below the strongest baseline, with more accurate sustained contrasts across lower, median, and upper quantiles.The method also achieved the lowest factual pinball loss of 1.065, maintained zero quantile crossings, and reduced exposure RMSE by 33.7%.Source: §VI · p. 10
  • No authorized prospective cohort combined dense indoor exposure, reference sensing, behavioral and medication data, and repeated lung function; the results therefore do not estimate an actual patient treatment effect.The current outcome is simulated PEF percentage, not exacerbation, symptom burden, or healthcare utilization.Source: §VI · p. 10, G. Threats to Validity and Transition… · p. 10
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