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

Shayma Alkobaisi; Anas Ali

stat.APSep 12, 2026

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

Authors: Shayma Alkobaisi, Anas Ali

Organizations: Department of Computer Science and Software Engineering, United Arab Emirates University, Al Ain, United Arab Emirates · Department of Computer Science, National University of Modern languages, Lahore, Pakistan

Abstract

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.

Figures & tables

Study	Setting	Principal method	L	M	C	Q	Main limitation relative to the present objective
Bae et al. [ 9 ]	Adult asthma, indoor IAQ	Logistic and quantile regression with fixed summaries	$\circ$	–	–	$\bullet$	Small panel; fixed exposure windows; no causal weighting or reference-sensor correction.
Marín et al. [ 5 ]	Moderate/severe asthma	Personalized sensor ecosystem with lagged association analysis	$\circ$	$\circ$	–	–	Feasibility-focused study; thirteen adults and no stable exposure–health association.
González-Colom et al. [ 6 ]	Chronic respiratory homes	Two-month low-cost household screening	–	$\circ$	–	–	Retrospective clinical outcomes and category-level IAQ summaries cannot identify short-horizon effects.
Evoy et al. [ 12 ]	Adults with asthma	Panel regression for temperature and pollution	$\circ$	–	–	–	Ambient exposure and mean effects; limited treatment of indoor sensor error and tails.
Tsang et al. [ 15 ]	Connected asthma monitoring	Multimodal longitudinal benchmark and predictive modeling	$\circ$	–	–	–	Rich monitoring but not a causal indoor-exposure dose–response estimator.
Wilson et al. [ 35 ]	Environmental epidemiology	Partially linear single-index QDLM	$\bullet$	–	–	$\bullet$	Flexible quantile lags without sensor observation model or longitudinal causal weighting.

TABLE I: Closest literature and capability comparison. L: explicit distributed lags; M: measurement-error correction; C: causal adjustment for continuous exposure; Q: quantile/tail-specific outcome modeling. A filled circle denotes a central capability, an open circle denotes partial or indirect treatment, and a dash denotes absence.

Symbol	Meaning
$i,t,s$	Patient, day, and sensor-channel indices
$Y_{it}$	PEF outcome, percentage of personal best
$X^{*}_{it}$	Latent indoor PM 2.5 concentration ( $\mu$ g/m 3 )
$W_{its},R_{it}$	Low-cost and reference PM 2.5 readings
$\bm{H}_{it}$	Measured exposure and outcome history before day $t$
$\bm{Z}_{i}$	Baseline susceptibility variables

TABLE II: Principal notation.

Panel of Figure 3 — Fig. 1: CAUSALQUANT-ASTHMA pipeline. The reference monitor and latent exposure are used only to train or evaluate the measurement stage in the benchmark. Outcome-informed model selection is restricted to the validation partition.

Characteristic	Value
Patients per realization	150
Patient-days per realization	12,600
Train/validation/test patients	90 / 30 / 30
Reference-monitor training days	1670 $\pm$ 42
Indoor PM 2.5 , mean $\pm$ SD	16.2 $\pm$ 8.0 $\mu$ g/m 3
PEF, mean $\pm$ SD	93.2 $\pm$ 5.6%

TABLE III: Executed benchmark characteristics.

Item	Setting
Lag horizon	0–6 days
Quantiles	$0.10,0.25,0.50,0.75,0.90$
Seeds	$11,23,37,51,79$
GPS history	3 days
GPS clipping	2nd–98th percentile
Intervention grid	$5$ – $45~\mu$ g/m 3

TABLE IV: Core experimental configuration.

Method	Dose-response IAE	AQTE bias	Pinball	QCE	10–90 coverage
CAUSALQUANT	0.304 $\pm$ 0.094	0.533	1.065	0.0120	78.1%
ME-GPS-QDLM	0.401 $\pm$ 0.208	0.717	1.068	0.0106	77.9%
SC-QDLM	1.771 $\pm$ 0.305	3.247	1.074	0.0117	78.9%
GPS-QDLM	1.938 $\pm$ 0.272	3.544	1.083	0.0154	77.9%
QRF	2.184 $\pm$ 0.140	3.083	1.140	0.0607	63.5%
PLSI-QDLM	2.486 $\pm$ 0.243	4.000	1.094	0.0211	76.0%

TABLE V: Primary patient-disjoint benchmark results across five independent data-generating seeds. Lower is better for IAE, AQTE bias, pinball loss, and quantile calibration error (QCE); coverage is for the nominal 80% interval.

Panel of Figure 7 — Fig. 2: Primary results across five independently generated causal-truth panels. Error bars in (a) and (b) show one standard deviation. CQ denotes CAUSALQUANT and ME-GPS denotes ME-GPS-QDLM.

Comparator	Improvement	$p$	$p_{H}$	$d_{z}$
SC-QDLM	1.467	0.0312	0.125	5.49
PLSI-QDLM	2.182	0.0312	0.125	14.13
QRF	1.880	0.0312	0.125	15.00
ME-GPS-QDLM	0.097	0.2188	0.219	0.47

TABLE VI: Paired one-sided Wilcoxon comparisons for dose–response IAE over five seeds.

p_{H}

is Holm-adjusted over four planned comparisons. Positive improvement favors CAUSALQUANT.

Panel of Figure 9 — Fig. 3: Average counterfactual PEF quantiles under sustained seven-day PM 2.5 interventions. Curves are generated from machine-readable result files; the black line is the simulator’s analytical truth.

Panel of Figure 10 — Fig. 4: Measurement and temporal diagnostics: (a) representative held-out exposure trace, (b) average median lag profile across seeds, and (c) empirical quantile reliability.

Variant	IAE	Pinball	Crossing
CAUSALQUANT	0.157	1.085	0.0%
without GPS weighting	0.350	1.077	0.0%
without measurement correction	1.762	1.102	0.0%
without susceptibility interaction	0.223	1.095	0.0%
without smooth/noncrossing constraints	0.157	1.088	0.8%

TABLE VII: Component ablation on a designated held-out diagnostic realization.

Panel of Figure 12 — Fig. 5: Component and optimization diagnostics. The ablation and severity analyses use a designated diagnostic realization and are descriptive rather than independent confirmatory tests.

Panel of Figure 13 — Fig. 6: Robustness diagnostics under (a) low-cost sensor noise, (b) missing personal-sensor observations, and (c) a deliberately omitted common cause of exposure and outcome.

Method	Fit (s)	ms/1000	MB	Params/nodes
CAUSALQUANT	0.23	0.68	412	145
ME-GPS-QDLM	0.19	0.54	412	110
SC-QDLM	0.18	0.57	402	110
GPS-QDLM	0.15	0.58	411	110
QRF	5.04	22.49	410	92,734
PLSI-QDLM	1.44	18.78	403	450

TABLE VIII: Computational profile (mean across seeds). Node counts are reported for tree ensembles.

Causal Effect Estimation

Causal effect estimation measures how outcomes would change under interventions, using experiments or observational data and explicit assumptions.

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1ETSI Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Plaza Cardenal Cisneros, 3, Madrid, 28040, Spain · 2Air Quality Consultants Ltd., 3rd Floor, St. Augustine’s Court, St. Augustine’s Place,2026 Bristol, BS1 4UD, United Kingdom

Model Calibration

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Low-cost air quality sensors (LCS) provide a practical alternative to expensive regulatory-grade instruments, making dense urban monitoring networks possible. Yet their adoption is limited by calibration challenges, including sensor drift, environmental cross-sensitivity, and variability in performance from device to device. This work presents a deep learning framework for calibrating LCS measurements of PM

_{2.5}

, PM

_{10}

, and NO

_2

using a Long Short-Term Memory (LSTM) network, trained on co-located reference data from the OxAria network in Oxford, UK. Unlike the Random Forest (RF) baseline, which treats each observation independently, the proposed approach captures temporal dependencies and delayed environmental effects through sequence-based learning, achieving higher

R^2

values across training, validation, and test sets for all three pollutants. A feature set is constructed combining time-lagged parameters, harmonic encodings, and interaction terms to improve generalization on unseen temporal windows. Validation of unseen calibrated values against the Equivalence Spreadsheet Tool 3.1 demonstrates regulatory compliance with expanded uncertainties of 22.11% for NO

_2

, 12.42% for PM

_{10}

, and 9.1% for PM

_{2.5}

Abstract

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