We developed a two-stage modeling approach to estimate indoor NO2 exposure among pregnant individuals, leveraging the use of home characteristics, residential behavior, meteorological conditions, and predictions from a previously developed hybrid outdoor NO2 model. This framework was applied to one of the largest indoor air sampling campaigns conducted in an urban setting, based on 1528 paired collocated indoor and outdoor NO2 measurements. Seasonal differences in the correlation between indoor and outdoor NO₂ further support the relevance of the model. Spearman correlations were stronger during warmer months (r = 0.53), consistent with increased air exchange and greater outdoor infiltration, and weaker during colder months (r = 0.28), likely reflecting reduced ventilation and a greater influence of indoor sources. Together, these dynamics suggest a seasonal balancing effect that stabilizes indoor NO₂ concentrations throughout the year: in colder months, higher outdoor pollution concentrations are partially offset by reduced infiltration due to closed windows and lower air exchange, whereas in warmer months, lower outdoor concentrations are accompanied by increased ventilation and infiltration.

In the first stage, we modeled the I/O NO2 ratio as a proxy for infiltration using a linear mixed-effects model. This allowed us to capture both fixed effects (e.g., structural and behavioral determinants) and random effects associated with repeated measurements within participants. The I/O model achieved a CV R2 of 0.27 under a leave-one-subject-out CV, indicating modest predictive ability when accounting only for fixed effects. However, when including subject-specific random effects, model performance improved substantially, with an R2 of 0.70. This highlights the importance of accounting for individual variability in I/O ratios, suggesting that questionnaire-based housing characteristics are insufficient to predict infiltration and subsequently indoor NO2 concentrations. Direct measurements, therefore, appear indispensable for more accurate exposure assessment, as they capture unobserved structural leaks and ventilation behaviors that are not adequately reflected by questionnaire variables. The predicted I/O ratios also exhibited clear seasonal trends, with higher values observed during the warmer months, likely reflecting increased natural ventilation, such as open windows. These seasonal dynamics were consistent with patterns in the measured data and were effectively captured by the model, supporting the validity of the I/O ratio estimates as a dynamic exposure proxy for infiltration. In the second stage, the predicted I/O ratio was used as an input to estimate weekly indoor NO2 concentrations. The indoor model included modeled outdoor NO2, meteorological variables, and selected behavioral predictors and home characteristic predictors, explaining 25% of the variability without the I/O ratio. When the predicted I/O ratio was included, performance improved substantially, with the R2 increasing from 0.25 to 0.53 and the RMSE decreasing from 1.37 to 1.28 µg/m3. The predicted indoor NO2 concentrations showed substantial variability across individuals and time, ranging from 5.1 to 55.2 µg/m3, with a median (IQR) of 23.6 (11.6) µg/m3 in the test dataset. The QRF approach used in the second stage also provided uncertainty intervals, with over 80% of observed indoor NO2 concentrations within the predicted 10th–90th. These uncertainty estimates will allow the propagation of uncertainty in future epidemiological studies. When model performance was evaluated by season using the test dataset, predictive performance yielded similar results between cold and warm seasons. The model achieved an r = 0.69, R2 = 0.47, RMSE = 6.1 µg/m3 for the cold season, and r = 0.65, R2 = 0.42, RMSE = 6.4 µg/m3 for the warm season. The results suggest that the indoor NO2 model performed consistently across seasonal conditions.

Our two-stage modeling approach yielded comparable results to previous studies, although the existing literature remains limited in terms of modeling indoor NO2 exposure in cohort settings [15]. Previous works have primarily focused on identifying determinants of indoor concentrations rather than implementing a comprehensive exposure modeling framework [12, 44,45,46]. By modeling the I/O ratio as a proxy for infiltration in the first stage and estimating indoor concentrations in the second stage, our approach provides a more transparent and interpretable structure. This design enables the disentanglement of observed building-level characteristics, individual behavior patterns, and the contribution of outdoor NO2, allowing for a more refined characterization of indoor exposure variability. In this modeling framework, the fixed-effect components capture the effects of observed covariates, whereas the random effects account for the unobserved individual or building-level characteristics. This approach is particularly relevant in urban environments heavily impacted by TRAP, such as Barcelona [25].

To the best of our knowledge, only one study has applied a similar two-stage modeling approach, developed in the United States using 287 paired I/O measurements under the framework of the ancillary study of Subpopulations and Intermediate Outcome Measures in COPD Study (SPIROMICS) [18]. Their models reported CV R2 values ranging from 0.21 to 0.51 for indoor NO2, depending on the different combinations of predictors and modeling assumptions. Our indoor NO2 model, with a CV R2 of 0.53 and RMSE of 1.28 µg/m3, falls slightly above the reported range. Several differences between the two studies are worth mentioning. First, our analysis was based on a substantially larger number of collocated measurements (n = 1528), allowing for more robust model development and validation. Second, we modeled weekly indoor NO2 concentrations, capturing short-term variability, whereas Zusman et al. [18] focused on long-term average exposure.

Another study conducted in 43 homes in the metropolitan Boston area, as part of the Asthma Coalition for Community Environment and Social Stress (ACCESS) project [47], found that indoor NO2 concentrations were influenced by both traffic-related outdoor and indoor sources. Notably, window opening, used as a proxy for ventilation, was identified as an important factor, highlighting the role of air exchange in modulating indoor concentration levels. In addition, Baxter et al. [48] emphasized the need for questionnaire-based data to capture behavioral and building variables essential for modeling indoor exposures. Their model reported an R2 of 0.25, which aligns with the performance of our indoor NO2 model when the predicted I/O ratio was not included. A more recent study conducted in 344 Canadian homes (Windsor, Regina, Halifax, and Edmonton) by Sun et al. [17] reported similar findings to ours, highlighting that the presence of gas stoves and lack of adequate ventilation were associated with higher indoor NO2 concentrations. However, one important difference was the strong seasonal variations of indoor NO2 levels during winter in that study. In contrast, our results showed only modest seasonal variation in indoor concentrations. This difference may be explained by the relatively mild winters in Barcelona, where seasonal changes in heating and ventilation practices are less pronounced than in colder climates such as Canada.

Importantly, our model incorporates a dynamic, weekly predicted I/O ratio throughout pregnancy, an improvement over previous studies that often assume a constant infiltration rate. The inclusion of behavioral variables, such as cooking duration, window opening habits, smoking, and candle or incense use, allows us to refine the assessment of indoor exposure, which have been shown to be relevant predictor variables in previous studies [47, 49,50,51,52]. Our findings showing that indoor-outdoor correlations were higher in warmer months are consistent with previous studies showing that increased natural ventilation enhances infiltration during these periods [52, 53]. This seasonal pattern has also been reported in other studies for schools in Barcelona [53, 54]. Our first-stage model was able to capture this seasonal effect in predicted I/O ratios, highlighting its potential to improve temporal variations in exposure assessment in the indoor NO2 model due to climate-related factors.

Additionally, in the second-stage model, we use the QRF model to generate uncertainty intervals with the aim of propagating uncertainty in future health studies. To our knowledge, few studies in this area have incorporated uncertainty estimates in indoor exposure models, despite their value in epidemiological studies. While such approaches have been recently adopted in outdoor air pollution modeling frameworks [21,22,23], incorporating uncertainty in indoor exposure estimates is equally important, especially given the influence of individual behaviors and building-specific characteristics that introduce additional variability. Several of the determinants identified as important in our models are consistent with findings from previous studies examining indoor air pollution exposures, particularly for PM2.5, which is more commonly studied than NO2 in indoor environments [55]. Factors such as ventilation habits, window type, cooking frequency, and indoor sources (e.g., smoking, incense, and candle use) have been widely recognized as key contributors to indoor air quality across pollutants [51, 53]. However, no studies have applied predictive modeling frameworks for indoor NO2, particularly in the context of pregnant participants. In our analysis, several of these known determinants were also among the most important predictors of the I/O ratio and indoor NO2 concentrations, highlighting the consistency of exposure patterns across pollutants. Nonetheless, the integration of both behavioral and building characteristics within a two-stage modeling approach for predicting indoor NO2 exposure across pregnancy remains relevant.

The strengths and novelty of our study lie in several key aspects. First, we applied a two-stage modeling framework to estimate indoor NO2 exposure. Second, we leveraged one of the largest indoor sampling campaigns to date in an urban setting, using 1528 collocated indoor and outdoor NO2 measurements, which allowed for robust model development and validation. Third, we incorporated building characteristics and detailed behavioral data collected at two time points during pregnancy, enabling a more accurate assessment of infiltration dynamics and indoor NO2 exposure. Fourth, we implemented a QRF model to provide uncertainty estimates, a novel feature in indoor exposure modeling. The QRF model also enables complex interactions between predictors, offering a more flexible representation of exposure variability in indoor concentrations. Lastly, by capturing weekly temporal resolution, we offer a dynamic approach that can support studies investigating exposure windows of susceptibility, advancing current studies that often rely on long-term averages.

The findings of this study need to be carefully considered in light of their limitations. First, while our model estimates indoor NO2 concentrations based on a microenvironment approach for predicting concentrations in homes, individual exposures may differ due to personal behavior (e.g., due to exposure in other microenvironments such as the workplace and commuting). Second, our model estimates indoor concentrations using a microenvironmental approach without separating indoor- and outdoor-generated NO2. Studies aiming to disentangle the health effects of indoor and outdoor-generated NO2 require a different approach, such as the one developed using continuous personal measurements by Zhang et al. [53]. Third, our model explained a modest proportion of the overall variability in indoor NO2 concentrations, indicating that some exposure variability remained largely unexplained. However, the substantial increase in model performance from an R2 of 0.27 under leave-one-subject-out to 0.70 under leave-one-observation-out validation underscores the importance of household-specific factors. This contrast suggests that unobserved dwelling characteristics, captured through the participant random effect, are stronger determinants of infiltration than the use of only observed building characteristics. Fourth, while our model estimates weekly indoor NO2 exposure, it inherently smooths short-term peak concentrations (e.g., during cooking events) due to the aggregated nature of the weekly NO2 measurements. Given that NO2 is an acute respiratory irritant, this smoothing may mask biologically relevant spikes in exposure, particularly in homes with gas appliances, potentially leading to an underestimation of health risk associated with acute peak events. Despite this, we obtained comparable performance to the limited studies reported in the literature, with CV R2 similar to that commonly achieved in outdoor air pollution models. Moreover, the uncertainty estimates produced by our QRF model can be propagated in subsequent analyses, remaining useful for future epidemiological studies, since moderate R2 values may attenuate estimated effects and introduce limited bias, generally toward the null. Fourth, passive samplers provide weekly average concentrations, meaning that our model cannot capture short-term exposure peaks associated with indoor activities such as cooking. Nevertheless, our LASSO regression showed the expected direction when analyzing key determinants of the I/O ratio, indicating that the model can capture relevant behavior and building-related variability at weekly resolution. Finally, this modeling framework may be most applicable to cohort-based study design in which detailed home characterization, behavioral, and ventilation information could be collected. Its generalizability to broader population-based exposure assessment settings remains limited when detailed information is unavailable. Nevertheless, the increasing availability of sensor data and online questionnaires may make the application of this framework more feasible in future studies.

In this study, we developed a two-stage modeling framework to estimate weekly indoor NO2 exposure during pregnancy in an urban setting, leveraging detailed information on home characteristics, behavioral and meteorological data, and previously derived outdoor NO2 estimates. Our findings highlight the importance of accounting for dynamic infiltration processes and individual-level behaviors to accurately estimate indoor exposures. By modeling the I/O NO2 ratio as a proxy for infiltration and combining it with key indoor determinants, our model was able to capture the temporal variability in indoor concentration. The results demonstrate that a significant portion of indoor exposure can be explained by outdoor levels, building characteristics, and behavioral factors. Given the challenges in directly measuring indoor pollution, especially in vulnerable populations such as pregnant individuals, this modeling approach provides a scalable method to be used in future epidemiological studies.

Future studies should consider measuring indoor and outdoor NO2 concentrations continuously to enable the separation of indoor and outdoor generated sources. This distinction is particularly relevant in settings like Barcelona, where outdoor air pollution, especially from traffic, is a dominant source of personal NO2 exposure. While recent studies have made methodological advances in source attribution using continuous personal exposure, none to date have focused specifically on pregnant individuals. Addressing the gap is relevant, as it could provide insights into how much of the indoor exposure is driven by outdoor pollution infiltrating into indoor environments.