Although the models performed similarly in separating sensitized from non-sensitized participants, the Bayesian network supplied an auditable structure and the ability to update probability estimates in either direction. Its output was also well calibrated: the out-of-fold Brier score was 0.171, the calibration slope was 0.9998, with a 95% confidence interval of 0.9563 to 1.0434, and the intercept was −0.0001, with a 95% interval of −0.0522 to 0.0520. The study defines serological sensitization as an allergen-specific IgE concentration of at least 0.35 kUA/L for one or more allergens in a 19-allergen panel. This is a laboratory outcome and is not equivalent to clinically manifest allergy, which also depends on relevant exposure and compatible symptoms. The network therefore estimates the probability of seropositivity rather than the probability that a person will experience an allergic reaction.

The analytic cohort had a median age of 23 years, an interquartile range of 12 to 48 years, and included 51.2% women. Overall, 47.1% of participants met the laboratory definition of sensitization. Sensitized participants were younger on average than non-sensitized participants, with mean ages of 28.8 and 33.1 years, respectively, and men were more common among those classified as sensitized: 50.8% compared with 43.7% among non-sensitized participants. Physician-diagnosed asthma was reported by 19.5% of sensitized participants, compared with 9.3% of non-sensitized participants. The association was much weaker for self-reported allergic symptoms: among the 2,251 participants with a valid symptom response, symptoms were present in 66.7% of sensitized and 63.7% of non-sensitized participants. These cross-sectional differences describe associations in the cohort and do not establish a causal relationship between sensitization and either clinical outcome.

For probabilistic stratification, the researchers divided posterior sensitization probabilities into three prespecified groups: low risk below 0.40, intermediate risk from 0.40 to 0.70 and high risk above 0.70. In the cohort, the observed sensitization rates were 13.8%, 46.1% and 81.6% in those respective groups. The model’s three strata corresponded exactly to its three total-IgE tertiles: every conditional probability in the low-IgE group fell below 0.40, every value in the middle group fell between 0.40 and 0.70, and every value in the high group exceeded 0.70. Eosinophil category changed probabilities within these groups but did not move any participant across a stratum boundary. The nearly equal group sizes—2,767, 2,759 and 2,759—reflect the construction of equal-width IgE tertiles rather than an independent property of the observed outcomes.

The contribution of eosinophils was therefore modest but measurable in continuous prediction. A Bayesian network using total IgE alone had an AUC of 0.7985, compared with 0.8081 when eosinophil category was added, a difference of 0.0096. However, the categorical net reclassification improvement was zero because no participant changed among the three probability strata. This distinction matters because a marker can shift a posterior probability and improve ranking without changing a person’s assigned stratum. The underlying sensitization table nevertheless showed numerical variation within IgE groups. For example, the probability was 0.129 in the low-IgE, reference-eosinophil cell, rising to 0.211 with mild eosinophilia. Middle-IgE probabilities ranged from 0.443 to 0.569, while high-IgE probabilities ranged from 0.788 to 0.868. These values describe variation in estimated serological sensitization probability within the model, without establishing clinical relevance for any particular group.

The network’s graph made these dependencies inspectable. Age and sex were root nodes; total IgE was conditioned on age and sex; eosinophil percentage was conditioned on age and total IgE; and sensitization was conditioned on both immunological markers. Asthma and allergic symptoms were placed downstream of sensitization, allowing the model to represent serological sensitization as distinct from clinical outcomes. The model used discretized variables: age was divided into five bands, total IgE into log-tertiles of no more than 26.0 kU/L, 26.0 to 97.7 kU/L and more than 97.7 kU/L, and eosinophil percentage into reference values below 4%, mild values of 4% to 8% and marked values above 8%. Bayesian-information-criterion evaluation did not support any direct edge from race or ethnicity to downstream variables, so that variable was removed from the predictive architecture and retained only as a descriptive cohort variable.

The retained network contained 70 free conditional-probability parameters and could be queried through exact variable-elimination inference. Its maximum in-degree was two, which kept the treewidth low and made inference computationally tractable. The conditional probability table for sensitization encoded nine combinations formed from three IgE tertiles and three eosinophil categories. The network was refitted from scratch within each of five stratified cross-validation folds, including re-estimation of the sensitization table, so the out-of-fold scores reflected generalization rather than in-sample fitting. Confidence intervals were derived from 2,000 stratified bootstrap resamples. Because the Bayesian network’s continuous posterior probability takes only nine values—one for each sensitization-table cell—the plotted calibration curve was a staircase, making the Brier score and calibration intercept and slope more informative summaries than the curve alone.

One distinguishing feature was bidirectional inference. The model could use a confirmed asthma diagnosis as evidence to update its estimate of sensitization, rather than using sensitization only to predict asthma. In the asthma subsample of 8,275 participants, the prior probability of sensitization was 0.472. Entering asthma as present raised the posterior to 0.651, a shift of 0.179, while asthma classified as absent lowered it to 0.442. Incorporating the reverse-direction evidence increased AUC from 0.808 to 0.814, a gain of 0.006. The study characterizes this as a structural capability that would require a separately trained reverse model in a conventional unidirectional classifier, rather than as evidence of superior predictive performance. The allergic-symptoms node could not undergo an equivalent empirical evaluation because the relevant questionnaire was unavailable for 72.8% of the analytic cohort.

Uncertainty also varied across parts of the network. Sparse evidence combinations produced wider bootstrap intervals than combinations represented by large numbers of participants. The low-IgE, marked-eosinophilia cell had a probability of 0.132 but was estimated from only 36 people, making its parameter less precise than, for example, the high-IgE, mild-eosinophilia cell at 0.868, which was based on 724 participants. The investigators distinguished irreducible biological heterogeneity, represented by genuinely mixed outcomes within some marker groups, from estimation uncertainty that could potentially be reduced with more data. The largest calibration deviation occurred in the lowest probability bin, where the mean predicted probability was about 0.10 and the observed proportion was about 0.33; this bin included the sparsely populated low-IgE, marked-eosinophil cell. At a chosen threshold of 0.520, the model’s confusion matrix corresponded to 74.4% accuracy, 77.0% precision, 65.2% sensitivity and 82.6% specificity.

The findings position the Bayesian network as a methodological demonstration rather than a clinical decision tool. Its principal strengths are transparent conditional probability tables, native uncertainty propagation and flexible evidence updates, while the study does not establish that using it would improve patient outcomes. Important limitations include the cross-sectional design, reliance on one historical NHANES cycle, the modest effect of eosinophils on stratification, and the inability of a binary laboratory outcome to model the full chain from allergen-specific sensitization through relevant exposure to compatible symptoms. The model also cannot distinguish allergic asthma from other asthma endotypes because the survey question records physician-diagnosed asthma without that clinical resolution. Independent external validation, prospective assessment against clinical endpoints and data linking sensitization to symptoms are needed before the framework could move beyond research use.

Subject of Research: Cross-sectional evaluation of a Bayesian network for probabilistic stratification of laboratory-defined IgE sensitization in NHANES 2005–2006 data.

Article Title: Bayesian network-based risk stratification of allergic sensitization using NHANES population data

Article References: Shayakhmetova, A., Tasbolatuly, N., Sultangaziyeva, A., Shurenov, M., Bissarinova, A., & Kurishbay, N. (2026). Bayesian network-based risk stratification of allergic sensitization using NHANES population data. Frontiers in Artificial Intelligence, 9, Article 1920823. https://doi.org/10.3389/frai.2026.1920823

Image Credits: AI Generated

DOI: 10.3389/frai.2026.1920823

Keywords: Bayesian networks, IgE sensitization, NHANES, risk stratification, model calibration, eosinophils, machine learning, uncertainty quantification, allergic sensitization, Bayesian, network-based, risk