The JECS is a nationwide, multicenter, prospective birth cohort study and the details of the study design were reported previously [11, 12]. In brief, pregnant participants and their partners were registered between January 2011 and March 2014 at 15 research sites covering a wide geographical area of Japan. Information was mainly obtained from medical record transcripts and self-reported questionnaires. The JECS was conducted in accordance with the Declaration of Helsinki. The protocol was reviewed and approved by the Ministry of Environment’s Institutional Review Board for Epidemiological Studies and by the Ethics Committees of all the participating institutions (#100910001). Written informed consent was obtained from all participants.

In this study, we used the fixed dataset “jecs-ta-20190930”, which was released in October 2019. The dataset contains the data for 104,062 fetuses from 103,060 pregnancies until the child reached 36 months old. A total of 88,567 live-born children for whom information on sex and birthweight had been recorded and for whom data were available at 1, 6 and 12 months old were selected as participants (Fig. 1). Of these children, we excluded those who used formula specialized for CMA (e.g. extensively-hydrolyzed formula), whose reply was absent at 18, 24 and/or 36 months old and whose reply was delayed at 6, 12, 18, 24 or 36 months old. A questionnaire was regarded as ‘delayed’ when a response was received over 2 months after delivery of 6- and 12-month questionnaires and over 3 months after delivery of 18-, 24- and 36-month questionnaires. We also excluded children who had missing information on feeding habit during the 1 year of life or intake statuses of CM protein at any ages of 12 to 36 months old. After excluding these 22,999 children, data for 65,568 children remained for the analysis.

Flow chart for participant selection. CM, cow’s milk

The main exposure factor was whether a child regularly consumed CM formula during the 1 year of life, divided into 3 periods: very-early (0–3 months old), early (3–6 months old) and late infancy (6–12 months old), as reported previously [10]. In each period, an infant was defined as consuming substantially formula milk if he or she received formula milk over half of the period (for 2 or 3 months during the 3-month period of very-early and early infancy; for 4, 5 or 6 months during the 6-month period of late infancy). The validity and reliability of this definition was confirmed in the previous study [10]. Before 12 months old, unfortunately, the JECS only collected data concerning the commencement timing of dairy food but not the detailed consumption status. Since our previous study demonstrated that the main results were similar between the analyses between before and after excluding the participants who had commenced dairy foods [10], this information was not analyzed in the current study.

The primary outcome was the prevalence of CMA at 6, 12, 18, 24 and 36 months old. Inclusion criteria for CMA at 6 and 12 months old were (1) parent-reported allergic reactions of the child to CM protein, such as formula milk and dairy food; (2) no consumption of CM protein at the evaluation time; and (3) a physician’s diagnosis of food allergy, as reported previously [10]. The same criteria were used for CMA at 18, 24 and 36 months old, but limited consumption of CM protein was also acceptable under the (2) criterion. At these older ages, an additional criterion was (4) positivity of serum-specific IgE or positive skin-prick test to CM protein in clinics or hospitals, although the values of the former and the wheal sizes of the latter were unknown. Information on these criteria was obtained from the questionnaire at each age. A child was regarded as having CMA when they met all criteria at that evaluation time.

To examine the association between the periods of formula and CMA, we used logistic regression models. The regression models included the three periods of formula, as well as covariates, determining the impact of each period independently from the influence of other periods [10]. The covariates included i) sex; ii) mode of delivery (vaginal vs. Caesarean); iii) any maternal allergic disease; iv) maternal smoking during pregnancy, confirmed in the first trimester; v) maternal education level (junior high school, high school, or university or graduate school); vi) annual family income (low: < 4,000,000; middle: 4,000,000–5,999,999; high: ≥ 6,000,000 Japanese yen); vii) early eczema, occurring within the first 3 months of life and defined as an intermittent itchy rash over a period of ≥ 2 months; and viii) living with older siblings. As covariates, we also included ix) the intake statuses of CM proteins other than formula milk (e.g. pasteurized milk, cheese, etc.) before that evaluation time (e.g. in estimating the risk of CMA at 24 months old, the intake statuses of CM proteins at 12 and 18 months old were included in the model). The information on the statuses was collected using the 12-, 18-, 24- and 36-month questionnaires, which asked whether a child ordinarily consumed the proteins (versus no or limited intake) at that time. Statistical analyses were performed using the R software program, version 4.0.3. Firth’s bias reduction method was employed when separation occurred in a logistic regression analysis, using ‘logistf’ version 1.23 in the R package. We reported the adjusted relative risks (aRRs) with 95% confidence intervals (CIs) that were converted from odds ratios in an established method. [13, 14]