Predicting Cow’s Milk Challenge Outcomes in Children: Multivariate Analysis of Clinical Predictors

The burden of food allergies is growing with a self-reported food allergy prevalence of 9.3% and a physician-diagnosed food allergy prevalence of 2.5% [1, 2]. Cow’s milk allergy (CMA) is one of the most common food allergies, affecting 0.4% of children, and cow’s milk (CM) is the main culprit of accidental allergic reactions and a major cause of food-induced anaphylaxis-related fatalities [1]. The major protein allergens in CM are α-lactalbumin (ALA), β-lactoglobulin (BLG), and casein (CAS).

Skin prick tests (SPT), food-specific immunoglobulin E (IgE) testing, and oral food challenges (OFCs) are often used to establish the diagnosis of food allergy. However, these tests have substantial limitations. The SPT relies on a liquid allergen extract applied onto the surface of the skin where it activates IgE antibodies on mast cells, resulting in degranulation and measurable wheal and flare formation [3, 4]. Despite being highly sensitive, SPTs have low specificity [3, 4]. Additionally, they can be affected by allergen extract quality, recent anaphylaxis, recent use of antihistamine medication, or young age, all of which can be associated with false negative tests [3, 4]. Specific IgE (sIgE) measures are generated by detecting circulating sIgE levels for a given food allergen in a blood sample and, similar to SPTs, this type of testing is highly sensitive, yet has low specificity [3, 4].

OFCs are considered the gold standard for food allergy diagnosis and assessing reactivity threshold, especially in the context of oral immunotherapy (OIT), through the administering of the food allergen in incremental doses [3, 4]. Despite being the gold standard, the OFC is time consuming, resource intensive, and exposes patients to a potentially severe allergic reaction [4, 5]. Data on factors associated with positive OFC outcomes are sparse, especially in patients with a history of physician-diagnosed anaphylaxis. We aimed to assess factors associated with a positive OFC and to generate a model to predict CM OFC outcome.

An emerging tool, Component testing, involves using purified native or recombinant allergens to measure sIgE antibody responses to individual allergenic proteins and can improve diagnostic accuracy by identifying IgE responses to specific CM proteins, such as CAS, which is associated with more persistent and severe reactions, compared to whey proteins like ALA and BLG [6].

Between April 2013 and December 2022, 111 children aged 6–18 years old followed by physician-diagnosed IgE-mediated CMA were recruited at the allergy clinics of the Montreal Children’s Hospital, Hôpital Sainte-Justine, British Columbia Children’s Hospital, and the Hospital for Sick Children to participate in CM desensitization. This was accomplished through an OIT protocol with a randomized, controlled study with a crossover design [7]. Ethics approval was granted from all participating sites, and written informed consent was obtained from the participants’ parent/legal guardian/next of kin to participate in the study.

Prior to beginning OIT, patients underwent an initial screening by single-blind placebo-controlled food challenge, with either positive (reaction) or negative (tolerance) outcomes. Eligible patients had a suggestive clinical history of IgE-mediated CMA, positive skin prick test, defined by a wheal with diameter ≥3 mm as compared to saline, and/or CM-sIgE level >0.35 kU/L, and a positive OFC. The CM used for challenge consisted of 40 mg of protein per milliliter of milk. Patients who tolerated a cumulative dose of CM greater than 150 mL (6,000 mg protein) or baked forms of milk were not eligible to participate in the study. Children with uncontrolled asthma, cardiovascular disease, severe hypertension, malignancies, autoimmune diseases, and/or severe primary and/or secondary immune deficiencies and who were on treatment with β-blockers were excluded.

Initial factors recorded included sex, age, history of asthma, eczema, allergic rhinitis, prior history of allergic reactions, history of anaphylaxis to CM, epinephrine use for CM-induced reactions, SPT wheal size, and serum sIgE levels to total CM and components ALA, BLG, and CAS. Age and SPT size were treated as both continuous and binary variables.

Total serum CM-sIgE was quantified using ImmunoCAP (Phadia 250, Thermo Fisher Scientific, Uppsala, Sweden) for 100 of the 111 subjects. Enzyme-linked immunosorbent assay (ELISA) was used to quantify ALA, BLG, and CAS-sIgE antibodies as previously described [8]. Polystyrene 96-well microplates were coated overnight at 4°C with 20 µg/mL solutions of each protein. Subsequently, plates were washed with 0.1% Tween 20 in phosphate-buffered saline and blocked with 100 µL per well of 1% bovine serum albumin for 1 h at room temperature. Patient serum samples obtained at baseline prior to OFC served as the primary antibody and were added to each well at a range of dilutions in 1% bovine serum albumin (50 µL/well) for 2 h at room temperature [8]. For detection, biotinylated polyclonal goat anti-human IgE antibody (1:20,000, 50 µL/well, 1 h at room temperature; #A80-108B, Bethyl Laboratories, Inc. Montgomery, TX, USA) was added, followed by incubation with horseradish peroxidase-streptavidin (1:3,000, 50 µL, 1 h at room temperature, Bio-Legend, San Diego, CA, USA) [8]. Optical density values were measured at 450 nm with reference at 570 nm after incubation with 3,3′,5,5′-tetramethylbenzidine substrate (Bio-Legend).

To construct a standard curve, wells were coated with anti-human IgE capture antibody (1:1,000; #A80-108A, Bethyl Laboratories Inc.) and subsequently incubated with 10-fold serial dilutions of recombinant human IgE antibody starting at 50 ng/mL (ELISA Ready-SET-Go! Kit, #88-50610-77, Thermo Fisher Scientific). Known concentrations were plotted versus optical density values at 450 nm [8]. For all assays, values were averaged over two technical replicates. Values were converted from nanograms per milliliter to kilo units per liter by dividing by a factor of 2.4 [9].

SPTs were conducted by placing a drop of commercial CM extract on the forearm followed by a scratch using a solid bore needle; saline and histamine (1 mg/mL, ALK Abello) were used as negative and positive controls, respectively. After 10 min, wheal boundaries were outlined with pen and translucent medical tape was used to transfer imprints to a paper and kept as a permanent SPT record. Wheal diameters were then measured in millimeters. Patients were instructed to abstain from using antihistamine-containing medications for at least 5 days before the procedure.

Predictors with low variance or with more than 30% missing data from either positive or negative OFC subgroups were excluded. Continuous variables were assessed for normality using QQ plots and log-transformed if non-normal. If continuous variables with a correlation >0.75 were found, only one was used for logistic regression modeling. Finally, the Random Forest algorithm was used for data imputation for remaining missing values.

Means and standard deviations are presented for quantitative data, while percentages are presented for categorical data. Differences between positive and negative challenges by each predictor were assessed using Fisher’s exact test for categorical data and unpaired Student’s t test for quantitative data.

Age and SPT were each analyzed as both dichotomous and continuous variables. Age was dichotomized so that patients aged 7 years or older were considered in the high age group, while those below 7 years old were placed in the low age group. SPT was dichotomized so that patients with SPT measures of 8 mm or greater were defined as in the high SPT group. These cut-off values were selected based on previous studies [10].

Univariate logistic regression analysis was performed to identify promising predictors (p < 0.2), before stepwise backward multivariate Firth bias-reduced logistic regression was used to create the final model. A comparison Firth logistic regression model using only SPT as a continuous predictor was also generated. Firth bias-reduced logistic regression is a variant of traditional logistic regression with more robust performance with smaller sample sizes and imbalanced outcomes [11]. We present odds ratios (OR) for each variable alongside 95% confidence intervals (CI). For continuous variables, the OR represents the increase in the odds for a positive challenge for each unit increase of that predictor. For continuous variables identified in the final model, cut-off threshold values for maximum specificity were also determined.

Discriminatory performance of the final multivariate model and the univariate SPT model were evaluated via their receiver operator characteristics curves. Further validation and generation of 95% CIs were also performed with 3-fold cross-validation with 10,000 bootstrap replicates. All analyses were performed using the open-source software R (R Core Team, 2022) and RStudio (Rstudio Team, 2022).

Only 73 (5.2%) observations were missing from the dataset: asthma (4 cases), eczema (6), allergic rhinitis (4), previous epinephrine use (22), ALA-sIgE (5), BLG-sIgE (5), CAS-sIgE (5), total CM-sIgE (11). Of these, total CM-sIgE had more than 30% missing values for negative OFC patients and was thus discarded.

Clinical and demographic profiles of patients are listed in Table 1. Among the 111 children who underwent an OFC, 103 patients had a positive reaction, while 8 tolerated the challenge. sIgE levels for ALA, BLG, and CAS were highly right-skewed and non-normal and were, therefore, log-transformed, with subsequent qualitative separation of distributions between positive and negative reactors (Fig. 1, online suppl. Fig. 1; for all online suppl. material, see https://doi.org/10.1159/000545027) [12]. There was moderate correlation between the log-transformed values (online suppl. Fig. 2). Descriptive analysis revealed significant differences between positive and negative OFC groups for continuous SPT values, previous epinephrine use, and both untransformed and log-transformed ALA-, BLG-, and CAS-sIgE (Table 1). While not significant, the difference in SPT tests ≥8 mm between groups had a p value of 0.075.

Univariate logistic regression analysis revealed that a history of asthma, continuous SPT values, previous epinephrine use, and log-transformed ALA-, BLG-, and CAS-sIgE were significantly associated with positive OFC (Table 2). Non-transformed sIgE components were not significantly associated. The final multivariate model included three significant factors: log-transformed CAS (aOR 2.4; 95% CI: 1.4–5.9; p < 0.001), SPT (aOR 1.44; 95% CI: 1.1–2.0; p = 0.002), and previous epinephrine use (aOR 6.5; 95% CI: 1.2–68.0; p = 0.03) (Table 3). The final model showed good discriminatory performance (AUC 0.928 (95% CI 0.83–0.98), with sensitivity and specificity of 0.825 and 1.00 at its optimal threshold of 0.92, respectively (Fig. 2). In comparison, the univariate model using only SPT (OR 1.44, 95% CI: 1.1–2.0; p = 0.002) had a worse discriminatory performance (AUC 0.83 (95% CI: 0.64–0.93) (Fig. 2).

By itself, a threshold log-transformed CAS value of 2.8 had a specificity and sensitivity of 1.00 and 0.641, respectively. While the total ImmunoCap values were excluded from analysis, even if their missing data were imputed and included in the model, it was removed during the stepwise backward multivariate Firth bias-reduced logistic regression.

Data regarding predictors for positive OFCs are sparse. We have conducted the largest Canadian study assessing predictive models for positive OFCs in children with severe CM allergy. Our study reveals that log-transformed CAS-sIgE and previous epinephrine use are useful in predicting OFC outcomes in pediatric patients. We have developed a model to predict true CMA with high specificity (1.00) and sensitivity (0.825). A threshold log-transformed CAS value of 2.8 was found to have a specificity and sensitivity of 1.00 and 0.641, respectively, for predicting positive OFC results. Log-transformed components seem more accurate to diagnose true CMA as compared to traditional diagnostic tests, such as SPT.

A smaller, retrospective study that aimed to determine values of CM-sIgE and ratios of CM-sIgE and its components to total IgE developed a model for prediction of OFC outcome [13]. A cut-off value of CAS-sIgE >0.95 kU/L was found to be 88.9% sensitive and 90.9% specific, and when combined with a compatible history of CMA, could accurately diagnose CMA without need for an OFC [13]. This study differs from ours in that we performed a logarithmic transformation on the data to eliminate any potential confounding effect by the lack of normality present in our dataset. Previous studies have found that the utilization of logarithmic transformation enables accurate statistical inference for immunologic data with a positive skew [12]. This had not yet been done with ALA, BLG, or CAS-sIgE values. A consequence of employing this technique is the determination of the geometric mean, which proves to be a more reliable measure of central tendency for this type of data compared to the sample mean [12]. Apart from use in allergy diagnostics, associations have been found between CM-sIgE component levels and milk OIT outcomes. Previous studies by our group found that high sIgE levels to total CM and its components are associated with a decreased likelihood of reaching the maintenance dose during OIT [8].

Not only has component testing been found to be highly predictive of the presence of CMA in the absence of OFC but it has also been found to be useful in the diagnosis of other food allergies. Recent studies underlined the deficits in allergy diagnostics, especially for peanut-allergic patients who have intermediate positive results on first-line diagnostic tests, such as the SPT or sIgE testing [14]. Increased sIgE levels for the peanut protein component Ara h 2 have been associated with increased likelihood of true peanut allergy [14, 15]. Therefore, Ara h 2 component testing might be a useful second-line test to accurately identify patients with true peanut allergy without the need for an OFC [14, 15]. High ratios of IgE/IgG4 to ovalbumin and ovomucoid in egg-allergic patients have been found to be associated with the need for treatment with epinephrine during OFC to baked and raw egg [16]. This group also developed an accurate logistic regression model that predicts baked egg reactivity and includes the interactions between IgE and IgG4 to ovalbumin and ovomucoid [16]. Allergen component testing has proven to be useful in the identification of multiple different food allergies and provides an additional measure that can serve to decrease the need for OFCs by improving accuracy of allergy diagnostic tests and models [10, 14‒16].

A recent study reported that individuals experience reproducibly stereotypic allergic reactions over time [17]. Hence, it is likely that those who experienced anaphylaxis in the past and require epinephrine are more likely to react during challenge. Indeed, it was suggested in other studies that previous use of epinephrine is a predictor of severe reactions [17, 18]. However, no study thus far has incorporated this factor into a model including component-sIgE [17, 18].

The hesitancy of some patients to undergo an OFC and lack of access to an allergist are barriers to establish true food allergy [19]. Previous use of machine learning in various clinical domains has successfully predicted patient outcomes, yet few attempts have been made to utilize it in predicting OFC outcomes [19]. The machine learning method with the highest performance in terms of AUC was learning using concave and convex kernels for CMA and peanut allergy with an AUC of 0.94 and 0.91, respectively. The Random Forest machine learning method was reported to have the highest predictive performance for egg OFCs [19]. Machine learning predictions were based on patient demographics, comorbidities, sIgE levels, SPT results, and clinical rationale for OFC administration [19]. Nevertheless, this study highlights the importance of incorporating other factors, such as log-transformed component-sIgE levels, to improve the accuracy and performance of predictive models. Adjusting machine learning and predictive modeling based on emerging research remains critical in the development of an accurate tool for the diagnosis of true food allergy, without the need for an OFC.

Our study has some potential limitations. First, we had a relatively small sample size with imbalanced outcomes. Differently skewed variables and a small sample size may affect the associations evaluated and the generalizability of findings. However, we still expect the results to be robust given the statistical measures used, and similar performance after cross-validation. Second, data imputations were made to account for missing values using a Random Forest algorithm. While multiple data imputations increase the risk of statistical bias, we minimized this bias by excluding variables with over 30% missing data from either positive or negative subgroups. Additionally, although not found to be statistically significant, more children with a negative challenge tended to be older, which could be explained by various factors, including the possibility that CMA resolves with age as some children outgrow the allergy [20]. While age was not a significant predictor in this study, future studies should investigate age as a potential predictor, which could help inform clinical decisions on when to re-challenge or monitor for CMA resolution.

In conclusion, we conducted the largest study in Canada and the first study to utilize log-transformed data in evaluating predictive models for OFC outcomes in patients with CMA. Our findings suggest that components, specifically log-transformed CAS-sIgE levels, and previous epinephrine use may be useful in predicting OFC outcomes in pediatric patients. Although not without its limitations, we believe our model may serve as a tool to establish the presence of true CMA and reduce the need for OFC. Future studies should attempt to use modeling for other food allergies and use larger sample sizes in order to accurately and reliably detect true food allergy without the need for OFCs.

This study received approval from the Research Ethics Boards of the Montreal Children’s Hospital, the British Columbia Children’s Hospital, the Hospital for Sick Children in Toronto, ON, Canada, and Hôpital Sainte-Justine. This study was a registered clinical trial (NCT03644381). Written informed consent was obtained from the participants’ parent/legal guardian/next of kin to participate in the study.

Moshe Ben-Shoshan reports consultant fees from Pfizer, ALK Abello, Bausch Health, Kaleo, Sanofi, and Food Allergy Canada, all outside the submitted work. Julia Upton reports research support/grants from Novartis, Regeneron, ALK Abello, DBV Therapeutics, CIHR, and SickKids Food Allergy and Anaphylaxis Program and fees from Pfizer, ALK Abello, Bausch Health, Kaleo, AstraZeneca, and Food Allergy Canada, all outside the submitted work. Ann. E. Clarke has received research funds from GlaxoSmithKline and honoraria from AstraZeneca, BristolMyersSquibb, and GlaxoSmithKline, all outside the submitted work. Christine McCusker has served on scientific advisory boards for Sanofi Adventis and Bausch Health Canada, all outside the submitted work. Edmond. S. Chan has received research support from DBV Technologies; has been a member of advisory boards for Pfizer, Miravo, Medexus, Leo Pharma, Kaleo, DBV, AllerGenis, Sanofi Genzyme, Bausch Health, Avir Pharma, AstraZeneca, and ALK; is on the Executive of the CSACI (Canadian Society of Allergy and Clinical Immunology); is on the Executive of the CPS (Canadian Paediatric Society) Allergy Section; and is a member of the Healthcare Advisory Board for Food Allergy Canada, all outside the submitted work. All other authors have no competing interests to declare. The lead author (Luca Delli Colli) affirms that the manuscript is honest, accurate, and a transparent account of the study being reported. No important aspects of the study have been omitted.

This study was funded by the Canadian Institute of Health Research (PJT – 185873). The funders were not involved in the research, preparation of this manuscript (study design, data collection and analysis, result interpretation, and writing of the article), or the decision to submit this article for publication.

The milk OIT study design and protocol were developed by Dr. Moshe Ben – Shoshan. Data collection and curation for this study was conducted by Luca Delli Colli, in which Liane Beaudette, Vera Laboccetta, and Danbing Ke provided assistance with patient recruitment and sample collection. The laboratory analysis on the collected samples was performed by Luca Delli Colli, Casey Cohen, and Diana Toscano-Rivero. The data analysis for manuscript one was conducted by Luca Delli Colli and Dr. Joshua Yu. The introduction, methods, and discussion were written by Luca Delli Colli. The results section, tables, and figures in manuscript was written and created by Luca Delli Colli, Dr. Joshua Yu, and Dr. Aaron Jones. The revision and editorial process of the manuscript prior to submission to the journal was performed by Dr. Derek Lanoue, Dr. Adhora Mir, Justin Sacksner, Dr. Bruce Mazer, Dr. Christine McCusker, Duncan Lejtenyi, Dr. Edmond S. Chan, Ingrid Baerg, Dr. Julia Upton, Dr. Eyal Grunebaum, Dr. Philippe Bégin, and Dr. Ann E. Clarke.

Edited by: H.-U. Simon, Bern.

All data generated or analyzed during this study are included in this article. Further inquiries can be directed to the corresponding author.