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\begin{document}

\title{Natural history of cow's milk allergy: a prospective study in children
aged 6 to 12 years}



\author[1]{Noriyuki Yanagida}%
\author[1]{Kei Kubota}%
\author[1]{Ken-ichi Nagakura}%
\author[1]{Yuki Ejiri}%
\author[1]{Sakura Sato}%
\author[1]{Motohiro Ebisawa}%
\affil[1]{Kokuritsu Byoin Kiko Sagamihara Byoin}%


\vspace{-1em}



  
  \date{June 16, 2024}


\begingroup
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\selectlanguage{english}
\begin{abstract}
\textbf{Background:} Approximately 50--90\% of children with
immediate-type cow's milk allergy (CMA) acquire tolerance by pre-school
age. We aimed to investigate the tolerance acquisition rate of CMA in
children aged 6--12 years. \textbf{Methods:} Children with CMA that
persisted until 6 years of age were included. Tolerance acquisition was
defined as either passing an oral food challenge with 200 mL of unheated
cow's milk (CM) or consuming CM of any quantity without symptoms.
Persistent CMA was defined as fulfilling neither of these criteria by 12
years of age. Children undergoing oral immunotherapy were defined as
having persistent CMA. Risk factors associated with persistent CMA were
assessed using Cox regression analysis. \textbf{Results:} Of the 123
children analyzed, 60 (49\%) had previous CM anaphylaxis, 82 (67\%)
eliminated CM from their diet, and the median CM-specific immunoglobulin
E (sIgE) level was 23.3 kU \textsubscript{A}/L at 6 years of age.
Twenty-five children (20\%) acquired tolerance by 9 years of age, and 46
(37\%) by age 12. At baseline, higher CM-sIgE levels (hazard ratio: 2.58
{[}95\% confidence interval: 1.62--4.12{]}, optimal cutoff level: 34.4
kU \textsubscript{A}/L), previous CM anaphylaxis (2.42
{[}1.24--4.69{]}), and complete CM elimination (5.18 {[}2.45--10.99{]})
were associated with persistent CMA. None of the children with CMA who
had all three risk factors (n = 26) acquired tolerance.
\textbf{Conclusion:} At least one-third of the children with CMA at 6
years of age acquired tolerance by 12 years of age. Children with CMA
who have the risk factors are less likely to acquire tolerance.%
\end{abstract}%



\sloppy


\textbf{Introduction}

Cow's milk allergy (CMA) is one of the most common food allergies in
infants, with a global prevalence of 2--3\%.\textsuperscript{1-6} In
Japan, cow's milk (CM) is the second major food allergen, with a
proportion of 21.8\% of causative foods.\textsuperscript{7}

Previous studies have reported that approximately 50--90\% of children
with CMA acquire tolerance by pre-school
age.\textsuperscript{8-10}Regarding the natural history of CMA beyond
school age, a CMA resolution rate of 97\% by the age of 15 years was
reported in a birth-cohort study from Denmark.\textsuperscript{11} A
longitudinal study in the USA reported that the CMA resolution rate was
42\%, 64\%, and 79\% by 8, 12, and 16 years of age,
respectively.\textsuperscript{9} However, these studies started
follow-up in infancy, and there are no studies on the natural history of
CMA that persist beyond school age.

Higher levels of CM-specific immunoglobulin E (sIgE), larger wheal sizes
in skin prick tests, the presence of anaphylaxis, more severe atopic
dermatitis, and coexisting bronchial asthma and allergic rhinitis have
been reported as risk factors for the persistence of CMA in
infants.\textsuperscript{8-10, 12-14} However, these factors were based
on the results of studies in which follow-up started in infancy; thus,
the risk factors associated with CMA that persists beyond school age are
unknown.

Therefore, we aimed to investigate the tolerance acquisition rate in
children with CMA persisting from the age of 6 years until the age of 12
years, as well as the factors affecting its persistence.

\textbf{Methods}

Study design and subjects

This is a single-center prospective review of the clinical records of
patients registered in the iAnet database (UMIN000013561), designed with
the cooperation of Hitachi Solutions Create.\textsuperscript{16}

Participants who were born between January 2002 and December 2005, and
first visited National Hospital Organization, Sagamihara National
Hospital before the age of 6 years with IgE-mediated CMA were included.
Patients who tolerated CM or underwent CM-OIT before the age of 6 years,
who refused to participate in this study, or who had missing clinical
information were excluded. All participants had confirmed sensitization
to CM with CM-sIgE levels \textgreater{} 0.35 kU\textsubscript{A}/L
using ImmunoCAP\textsuperscript{TM} (Thermo Fisher Scientific/Phadia,
Uppsala, Sweden).

Definitions

IgE-mediated CMA was diagnosed by either sensitization to CM and a
history of a convincing immediate-type allergic reaction to CM or
failure in a CM oral food challenge (OFC). Tolerance acquisition was
defined as either passing an OFC of consuming 200 mL of unheated CM or
CM of any quantity without allergic symptoms. Persistent CMA was defined
as fulfilling neither of these criteria by the age of 12 years. Partial
elimination was defined as being able to consume \textless{} 200 mL of
CM without allergic symptoms. Children with CMA who were enrolled in CM
oral immunotherapy (OIT) after 6 years of age were defined as having
persistent CMA.

Follow-up

Children with CMA were annually assessed using CM-sIgE and CM OFC.
According to the Japanese guidelines for food allergies, we performed
stepwise OFC.\textsuperscript{7, 16} When a child passed an OFC, we
instructed them to consume the amount of CM that was confirmed by the
OFC to be tolerated. Children with complete CM elimination were usually
requested to undergo OFCs. Children who were lost to follow-up between
the ages of 6 and 12 years were considered dropouts.

Detailed methods and eligibility criteria for enrollment in OIT at our
institution are described in the Supplementary information.

Outcomes

The primary outcome was the rate of CM tolerance acquisition by 12 years
of age when we defined children who enrolled in OIT after the age of 6
years as having persistent CMA. Secondary outcomes were the risk factors
associated with persistent CMA among the children's characteristics at
the age of 6 years, as well as immunological changes between 6 and 12
years of age. We also calculated the optimal cutoff values for
laboratory parameters associated with persistent CMA. In sub-analysis,
we estimated the rate of CM tolerance acquisition by either defining
children who enrolled in OIT after the age of 6 years as dropouts or by
factoring in the OIT results.

Statistical analysis

Values are presented as the median (interquartile range {[}IQR{]}). To
analyze the differences between the two groups, we used either the
Mann--Whitney U test or Fisher's exact test (both two-tailed).
Kaplan--Meier survival curves were generated to depict the acquisition
rate of CMA tolerance. Hazard ratios (HRs) and 95\% confidence intervals
(CIs), comparing children with factors affecting persistent CMA, were
determined based on a Cox proportional hazards model. We considered the
number of children to be sufficient to confirm the occurrence of 10 or
more tolerant events per explanatory variable.\textsuperscript{17} All
statistical analyses were performed using SPSS (version 25.0; IBM Corp.,
Armonk, USA) and GraphPad Prism version 8.0.2 (www.graphpad.com).
A\emph{p} -value of 0.05 was considered significant. Specific IgE values
to CM and casein \textless{} 0.35 kU\textsubscript{A}/L were considered
as 0.15 kU\textsubscript{A}/L, and those \textgreater{} 100
kU\textsubscript{A}/L were considered as 101 kU\textsubscript{A}/L.

Ethical considerations

This study was approved by the Institutional Review Board of the
National Hospital Organization Sagamihara National Hospital (approval
number: 2014031817). Written informed consent was obtained from the
legal guardians of all participants in accordance with the Declaration
of Helsinki.

\textbf{Results}

Patient enrollment

We enrolled 145 children who fulfilled the eligibility criteria.
Children who were lost to follow-up between the ages of 6 and 12 years
(n = 22) were also excluded; therefore, the 123 remaining children were
analyzed in this study (Figure 1).

Of the 123 children, 82 (67\%) were male, 60 (49\%) had previous
anaphylaxis due to CM, 82 (67\%) had eliminated CM completely, and the
median CM-, and casein-sIgE values were 23.3 (7.0-66.4)
kU\textsubscript{A}/L and 26.9 (5.8-72.0) kU\textsubscript{A}/L,
respectively (Table 1).

The estimated rates of tolerance acquisition of CMA in children

Twenty-five children (20\%) acquired tolerance by 9 years of age, and 46
children (37\%) by 12 years of age. Of the 77 remaining children (63\%)
who were considered to have persistent CMA, 20 (16\%) had partially
eliminated CM at the age of 12 years, 14 (11\%) had completely
eliminated CM at this age, and 34 (28\%) were enrolled in CM OIT by the
age of 12 years (Figure 2).

When we designated children who underwent OIT between the ages of 6 and
12 years as dropouts, the estimated rate of tolerance acquisition by the
age of 12 years was 58\%. When we defined tolerance acquisition as
achieving short-term unresponsiveness to 200 mL of unheated CM for
children who underwent OIT after the age of 6 years, the estimated rate
of tolerance acquisition by the age of 12 years was 50\% (Supplementary
figure 1).

Risk factors for persistent CMA

In a comparison of baseline characteristics between the tolerant and
persistent groups, statistically significant differences were observed
for the presence of coexisting atopic dermatitis, anaphylaxis to CM
before the age of 6 years, complete elimination of CM at the age of 6
years, and sIgE to CM and casein (Table 2). In both groups, the CM-sIgE
level was the highest at ages 6--7 years and then decreased annually,
except for ages 8 and 9 years in the tolerant group (Supplementary
figure 2). At all ages between 6 and 12 years, the CM-sIgE levels were
significantly higher in the persistent group than in the tolerant group.

The results of the Cox hazard model analysis are presented in Table 3.
Using the significant risk factors identified by univariate analysis,
the multivariate Cox regression analysis showed that previous
anaphylaxis to CM (adjusted HR {[}95\% CI{]}: 2.42
{[}1.24--4.69{]},\emph{p} = 0.01), complete CM elimination at the age of
6 years (adjusted HR {[}95\% CI{]}: 5.18 {[}2.45--10.99{]}, \emph{p}
\textless{} 0.001), and higher CM-sIgE levels at the age of 6 years
(adjusted HR {[}95\% CI{]}: 2.58 per ten-fold increase {[}1.62--4.12{]},
\emph{p}\textless{} 0.001) were independent risk factors for persistent
CMA.

The area under the curve for CM-sIgE levels was 0.83 (95\% CI:
0.76--0.90), and the optimal cutoff level of CM-sIgE was 34.4
kU\textsubscript{A}/L. Using this cutoff value, the sensitivity and
specificity were 60\% and 91\%, respectively.

Although there was no statistical significance, these baseline
characteristics tended to be higher in the persistent group with
enrollment in OIT than in the persistent group without enrollment in OIT
(Supplementary table 1).

Kaplan--Meier curves grouped by risk factors

Four of 50 children (8\%) with a CM-sIgE level [?] 34.4
kU\textsubscript{A}/L and 42 of 73 children (58\%) with a CM-sIgE level
\textless{} 34.4 kU\textsubscript{A}/L acquired tolerance (Figure 3A).
Twelve of 81 children (15\%) with and 34 of 42 children (81\%) without
complete CM elimination acquired tolerance (Figure 3B). Twelve of 59
children (20\%) with and 34 of 64 children (53\%) without previous
anaphylaxis to CM acquired tolerance (Figure 3C).

Figure 3D shows the estimated rates of tolerance acquisition grouped by
combining the two factors, CM complete elimination and previous
anaphylaxis.

In the absence of the three risk factors, 23 of 26 children (88\%)
acquired tolerance, whereas in their presence, none of the children with
CMA (n = 26) acquired tolerance (Supplementary figure 3).

\textbf{Discussion}

In this study, we investigated the natural history of IgE-mediated
immediate-type CMA in children aged 6--12 years. Forty-six of the 123
(37\%) children with persisting CMA until the age of 6 years acquired CM
tolerance by the age of 12 years. Furthermore, we demonstrated that
higher CM-sIgE levels, previous anaphylaxis to CM, and complete CM
elimination from the diet were independent risk factors for persistent
CMA.

It has been reported that most children with CMA acquire tolerance
during the pre-school age.\textsuperscript{1, 8-12, 18-20} Half of
Korean children with CMA develop tolerance by the age of 8.7
years.\textsuperscript{19} A Danish birth-cohort study showed that the
tolerance acquisition rates in children with CMA, including
non-IgE-mediated CMA, were 92\% and 97\% at 5 and 15 years of age,
respectively.\textsuperscript{20} However, all of these studies
initiated follow-up in infancy, making it difficult to clarify the
tolerance acquisition rate in children with CMA persisting beyond school
age. Few studies on the natural history of CMA have focused on children
beyond school age. Our data demonstrated that the tolerance acquisition
rate in children with CMA between the ages of 6 and 12 years was 37\%.
This rate is obviously higher than that for peanut allergy; however, it
seems to be lower than that for hen's egg allergy
(HEA).\textsuperscript{21, 22} A previous study reported that the rate
of tolerance acquisition for peanut allergy in children aged 4--20 years
was 21.5\%.\textsuperscript{21} Our institution reported a rate of
tolerance acquisition for HEA of 60.5\%.\textsuperscript{22} However,
children with OIT were defined as dropouts in this previous study;
therefore, their rate may be overestimated. When we defined children
with OIT as dropouts, the tolerance acquisition rate was 58\%
(Supplementary figure 1), which was similar to the results of the
previous HEA study.\textsuperscript{22} When we defined tolerance
acquisition as achieving short-term unresponsiveness to 200 mL of
unheated CM for children who underwent OIT after the age of 6 years, the
tolerance acquisition rate was 50\% (Supplementary figure 1); this is
lower than the rate of 65.2\% reported in the HEA
study.\textsuperscript{22} This difference would result from the poor
outcome of OIT to CMA compared to HEA.\textsuperscript{22} These
findings indicate that the ``real'' tolerance acquisition rate in
children aged 6--12 years with CMA might be between 37\% and 50\%. In
many previous studies, CMA persistence was not confirmed in annual
OFCs.\textsuperscript{8, 11, 12, 19} In our institution, children
usually undergo blood tests and OFCs annually, providing a more accurate
assessment of CMA tolerance.

In the present study, 88\% of patients with CMA in the absence of the
identified risk factors (higher CM-sIgE levels, previous anaphylaxis to
CM, and complete CM elimination) acquired tolerance by the age of 12
years; therefore, these children should be proactively assessed by OFCs
for their tolerance acquisition. In contrast, none of the children with
CMA presenting all three risk factors acquired tolerance by the age of
12 years (Supplementary figure 3); therefore, these children should be
considered for OIT. Previous anaphylaxis and higher CM-sIgE levels were
common risk factors identified in the present and previous studies, and
both factors contributed to difficulties in acquiring tolerance (Figure
3A and 3C). This is the first report showing that complete CM
elimination from the diet is associated with CMA persistence. The
immunomodulatory effects of consuming baked milk proteins may accelerate
the progression to tolerance of non-baked milk.\textsuperscript{23} In
addition, continuous consumption of small amounts of heated milk has
been suggested to increase the safely ingestible amount of
CM.\textsuperscript{24} These results suggest that continuous small-dose
intakes of CM may induce immunological benefits for acquiring CM
tolerance.

In the present study, CM-sIgE levels in the persistent group were
significantly higher than those in the tolerant group at all ages from
6--12 years. Interestingly, CM-sIgE levels decreased annually, not only
in the tolerant group, but also in the persistent group. In previous
studies on the natural history of CMA, the CM-sIgE level in children
with persistent allergy was reported to increase over the first 3--4
years of life, followed by a plateau, and then a gradual decrease until
the age of 18 years.\textsuperscript{9, 10} These findings indicate that
decreasing CM-sIgE levels during school age may not be associated with
CM tolerance acquisition.

This study has some limitations. First, we defined children undergoing
OIT as having persistent CMA, not as dropouts. In children who received
OIT, 95\% of the children eliminated CM completely, two-thirds had
previous anaphylaxis, and the median CM-sIgE level was 58.5
kU\textsubscript{A}/L at the age of 6; these characteristics were higher
than those in the persistent group who did not receive OIT
(Supplementary table 1). Since children with OIT should have difficulty
acquiring tolerance, we considered that children with OIT should be
defined as having persistent CMA rather than as dropouts. Second, this
study had a single-center design. Our facility is a tertiary center for
food allergies, and children with food allergies tend to be more
severely affected than the general population, which may have influenced
the study outcomes.

In conclusion, at least one-third of patients who still had IgE-mediated
CMA at the age of 6 years acquired tolerance by the age of 12 years. We
demonstrated that children with CMA whose CM-sIgE levels were higher
than the optimal cutoff value, who previously had anaphylaxis to CM, and
who eliminated CM from their diet at the age of 6 years have difficulty
acquiring tolerance by the age of 12 years. This study provides
important insights into the natural history of CMA persisting into
school age and identifies risk factors associated with persistent CMA.

\textbf{Acknowledgements}

We thank the pediatricians and nurses who were involved in the medical
care at Sagamihara National Hospital. We would like to thank Editage
(\emph{www.editage.com}) for assistance with English language editing.

\textbf{Key messages}

At least one-third of the children who had immediate-type cow's milk
allergy at the age of 6 years tolerated cow's milk by the age of 12
years. At 6 years of age, children with cow's milk allergy and higher
cow's milk-specific immunoglobulin E, previous cow's milk anaphylaxis,
and complete cow's milk elimination were less likely to tolerate cow's
milk by the age of 12 years.

\textbf{Author Contributions}

KK: Conceptualization, data curation, formal analysis, investigation,
and writing. NY: Conceptualization and supervision. YE:
Conceptualization and supervision. SS: Conceptualization and
supervision. ME: Conceptualization and supervision. KN:
Conceptualization and supervision.

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\textbf{Table 1.} Patient characteristics at the age of 6 years\selectlanguage{english}
\begin{longtable}[]{@{}ll@{}}
\toprule
& n = 123\tabularnewline
\midrule
\endhead
Male, n (\%) & 82 (67\%)\tabularnewline
Term delivery, n (\%) & 113 (97\%)\textsuperscript{*}\tabularnewline
Breast-fed, n (\%) & 95 (79\%)\textsuperscript{+}\tabularnewline
Age at the first visit to our hospital (years) & 2.3
(0.9--4.1)\tabularnewline
Atopic dermatitis, n (\%) & 96 (78\%)\tabularnewline
Bronchial asthma, n (\%) & 75 (61\%)\tabularnewline
Allergic rhinitis, n (\%) & 51 (41\%)\tabularnewline
Previous anaphylaxis to CM, n (\%) & 60 (49\%)\tabularnewline
Complete CM elimination, n (\%) & 82 (67\%)\tabularnewline
Number of food allergens, n & 2 (2--4)\tabularnewline
Total IgE (IU/mL) & 1165 (661--1985)\tabularnewline
CM-specific IgE (kU\textsubscript{A}/L) & 23.3
(7.0--66.4)\tabularnewline
Casein-specific IgE (kU\textsubscript{A}/L) & 26.9
(5.8--72.0)\textsuperscript{++}\tabularnewline
\bottomrule
\end{longtable}

CM, cow's milk. \textsuperscript{*} Missing values:
7.\textsuperscript{+} Missing values: 3. \textsuperscript{++} Missing
values: 22.

\textbf{Table 2.} Comparison of patient characteristics at the age of 6
years between the tolerant group and the persistent group\selectlanguage{english}
\begin{longtable}[]{@{}llll@{}}
\toprule
\begin{minipage}[b]{0.24\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[b]{0.24\columnwidth}\raggedright\strut
Tolerant group (n = 46)\strut
\end{minipage} & \begin{minipage}[b]{0.24\columnwidth}\raggedright\strut
Persistent group (n = 77)\strut
\end{minipage} & \begin{minipage}[b]{0.24\columnwidth}\raggedright\strut
\emph{p} value \textsuperscript{*}\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Male, n (\%)\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
35 (76\%)\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
46 (60\%)\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
0.08\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Term delivery, n (\%)\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
41 (98\%)\textsuperscript{+}\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
71 (96\%)\textsuperscript{++}\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
\textgreater{} 0.99\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Breast-fed, n (\%)\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
34 (77\%)\selectlanguage{ngerman}\textsuperscript{§}\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
60 (79\%)\textsuperscript{\#}\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
0.82\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Age at the first visit to our hospital (years)\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
2.2 (0.8--4.3)\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
2.3 (1.0--4.1)\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
0.78\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Atopic dermatitis, n (\%)\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
41 (89\%)\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
54 (70\%)\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
0.02\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Bronchial asthma, n (\%)\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
26 (57\%)\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
48 (62\%)\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
0.57\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Allergic rhinitis, n (\%)\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
21 (46\%)\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
29 (38\%)\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
0.45\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Previous CM anaphylaxis, n (\%)\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
12 (26\%)\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
47 (61\%)\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
\textless{} 0.001\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Complete CM elimination, n (\%)\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
12 (26\%)\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
69 (90\%)\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
\textless{} 0.001\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Number of eliminated foods, n\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
2.0 (2.0--3.0)\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
3.0 (2.0--4.0)\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
0.01\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Total IgE (IU/mL)\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
1105 (734--2335)\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
1285 (617--1960)\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
0.59\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
CM-specific IgE (kU\textsubscript{A}/L)\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
6.1 (2.3--17.7)\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
48.4 (13.1--94.5)\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
\textless{} 0.001\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Casein-specific IgE (kU\textsubscript{A}/L)\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
5.2 (1.4--22.1)\textsuperscript{**}\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
50.9 (21.8--99.0)\textsuperscript{++}\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
\textless{} 0.001\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

CM, cow's milk. \textsuperscript{*} Mann-Whitney U test and Fisher's
exact test (both two-tailed) were used to compare continuous and
categorical data, respectively, between groups.
\textsuperscript{+}Missing values: 4. \textsuperscript{++} Missing
values: 3.\selectlanguage{ngerman}\textsuperscript{§} Missing values: 2. \textsuperscript{\#}
Missing values: 1. \textsuperscript{**} Missing values: 9.
\selectlanguage{english}\textsuperscript{++}Missing values: 13.

\textbf{Table 3.} Analysis of risk factors at the age of 6 years for
persistent cow's milk allergy\selectlanguage{english}
\begin{longtable}[]{@{}lllll@{}}
\toprule
\begin{minipage}[b]{0.19\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[b]{0.19\columnwidth}\raggedright\strut
Crude HR \textsuperscript{+} (95\% CI)\strut
\end{minipage} & \begin{minipage}[b]{0.19\columnwidth}\raggedright\strut
\emph{p} value\strut
\end{minipage} & \begin{minipage}[b]{0.19\columnwidth}\raggedright\strut
Adjusted HR \textsuperscript{++} (95\% CI)\strut
\end{minipage} & \begin{minipage}[b]{0.19\columnwidth}\raggedright\strut
\emph{p} value\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Male, sex\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
1.86 (0.94--3.66)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
0.07\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Term delivery\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
0.60 (0.08--4.37)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
0.62\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Breast-fed\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
1.04 (0.51--2.10)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
0.92\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Age at the first visit to our hospital\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
1.04 (0.88--1.22)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
0.67\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Atopic dermatitis\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
0.35 (0.14--0.89)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
0.03\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
0.55 (0.21--1.42)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
0.22\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Bronchial asthma\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
1.30 (0.73--2.33)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
0.77\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Allergic rhinitis\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
0.78 (0.43--1.39)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
0.39\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Previous CM anaphylaxis\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
3.22 (1.66--6.21)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\textless{} 0.001\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
2.42 (1.24--4.69)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
0.01\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Complete CM elimination\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
11.24 (5.71--21.74)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\textless{} 0.001\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
5.18 (2.45--10.99)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\textless{} 0.001\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Number of eliminated foods\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
1.20 (1.00--1.43)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
0.052\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Total IgE (IU/mL)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
0.65 (3.11--1.38)\selectlanguage{ngerman}\textsuperscript{§}\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
0.27\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
CM-specific IgE (kU\textsubscript{A}/L)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
4.52 (3.02--6.76)\selectlanguage{ngerman}\textsuperscript{§}\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\textless{} 0.001\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
2.58 (1.62--4.12)\selectlanguage{ngerman}\textsuperscript{§}\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\textless{} 0.001\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

CM, cow's milk; HR, hazard ratio; CI, confidence interval. Using
Pearson's correlation analysis, the correlation coefficient between
casein- and CM-sIgE levels exceeded 0.99; therefore, the casein-sIgE
level was excluded from the Cox regression analysis.
\textsuperscript{+}Univariate Cox regression analysis.
\textsuperscript{++} Multivariate Cox regression analysis; adjusted for
the significant items in the univariate analysis. \selectlanguage{ngerman}\textsuperscript{§}
Hazard ratio per ten-fold increase in total IgE or cow's milk-specific
IgE.

\textbf{Figure legends}

\textbf{Figure 1.} Flow chart of study participant selection.

CMA, cow's milk allergy; CM-OIT, cow's milk oral immunotherapy

\textbf{Figure 2.} Kaplan--Meier analysis of the tolerance acquisition
rate in children aged 6--12 years with CMA. Patients enrolled in oral
immunotherapy after the age of 6 years were considered as having
continued elimination of cow's milk.

CMA, cow's milk allergy

\textbf{Figure 3.} Kaplan--Meier curves showing CMA tolerance from ages
6--12 years. (A) Grouped by the optimal cutoff value of CM-sIgE levels,
as determined by the receiver operating characteristic curve. (B)
Grouped by complete elimination of CM by the age of 6 years. (C) Grouped
by anaphylaxis to CM prior to the age of 6 years. (D) Grouped by
combinations of the two factors, complete CM elimination from the diet
and previous anaphylaxis to CM at the age of 6 years. Two of 45 children
(4\%) with complete CM elimination and previous anaphylaxis, 10 of 36
children (28\%) with complete CM elimination but without previous
anaphylaxis, 10 of 14 children (71\%) with partial CM elimination and
previous anaphylaxis, and 24 of 28 children (86\%) with partial CM
elimination but without previous anaphylaxis acquired tolerance (A-D)
Groups are significantly different (\emph{p} \textless{} 0.001, log-rank
test).

CM, cow's milk; CM-sIgE, CM-specific immunoglobulin E; CMA, CM allergy

\selectlanguage{english}
\FloatBarrier
\end{document}

