Data of participants in this cross-sectional study were extracted from the National Health and Nutrition Examination Survey (NHANES) in 2005–2006. NHANES is a representative survey research program to assess the health and nutritional status of American adults and children. Regular data collection of approximately 5,000 persons is carried out from 15 areas since 1999 and examines in two-year periods. NHANES 2005–2006 is the only cycle with complete questionnaires on eczema. More details of statistical data can be found on the NHANES website [14].

A total of 4,785 children and adolescents (aged < 18 years old) in the NHANES were initially included. The exclusion criteria were (1) missing information of dietary intake of vitamin E, β-carotene, vitamin C, Zn, Se or retinol, and (2) children having an answer of ‘refused,’ ‘don’t know’ or ‘missing’ for the eczema questionnaire. Finally, 2,305 of them were eligible. The NHANES survey is approved by the institutional review board (IRB) of the National Center for Health Statistics (NCHS). The participants’ legal guardians/next of kin have provided written informed consent for participation. Since all the data were de-identified and publicly available, no ethical approval of this study by the IRB of Children’s Hospital Affiliated to Capital Institute of Pediatrics was required. In addition, all study methods were carried out in accordance with relevant guidelines and regulations (declaration of Helsinki).

In NHANES, dietary antioxidants intake was collected via two 24-h dietary recalls, in which participants reported individual foods and drinks consumed during the midnight-to-midnight 24-h period prior to the in-person dietary interview. Participants under the age of 16 years old were interviewed by a proxy interviewee (typically their parents). The first dietary recall interview is collected in-person in the Mobile Examination Center (MEC), and the second interview is collected by telephone 3 to 10 days later. NHANES conducted the coding of interview data and conversion to total nutrient intakes by using the United States Department of Agriculture (USDA) Food and Nutrient Database for Dietary Studies, 5.0 (FNDDS 5.0) [15].

Data of dietary antioxidants intake including vitamin E, β-carotene, vitamin C, Zn, Se and retinol were extracted in this study. We divided the antioxidants consumption into three levels respectively according to their own quantiles: vitamin E (< 3.82, 3.82 ≤ vitamin E < 6.28, and ≥ 6.28 mg), β-carotene (< 230, 230 ≤ β-carotene < 613, and ≥ 613 mcg), vitamin C (< 35.5, 35.5 ≤ vitamin C < 96.1, and ≥ 96.1 mg), Zn (< 7.47, 7.47 ≤ Zn < 11.83, and ≥ 11.83 mg), Se (< 68.8, 68.8 ≤ Se < 104.4, and ≥ 104.4 mcg) and retinol (< 253, 253 ≤ retinol < 500, and ≥ 500 mcg).

The diagnosis of childhood eczema was according to the self-reported NHANES questionnaire. Respondents for the interviews included the following: a proxy for child aged < 6 years old; a proxy with the assistance of the child for those aged 6–8 years old; assistance of a proxy for child aged 9–11 years old; and children aged ≥ 12 years old who answered by themselves. Children and adolescents who had self-reported symptoms (an itchy rash, which was intermittently coming and going) in the last 12 months or a positive answer to the question “Has a doctor or other health professional ever told you that you have eczema?” were recognized as childhood eczema [16].

We collected variables from the NHANES database including age, gender, race, family educational background, poverty-to-income ratio (PIR), exposure to environmental tobacco smoke, insurance, maternal age, asthma, hay fever, food allergy, peanut allergy, egg allergy, milk allergy, shrimp allergy, height, weight, body mass index (BMI), cotinine, C-reactive protein (CRP), vitamin D, energy intake, polyunsaturated fatty acids (PUFA) intake, and serum immunoglobulin E (IgE) level.

The diagnoses of asthma and hay fever were both according to the NHANES questionnaires similar to that of the eczema. A positive response to both questions: “Has a doctor or other health professional ever told you that you have asthma?” and “In the past 12 months (have you/he/she) had wheezing or whistling in (your/his/her) chest?” were used to recognize asthma. Hay fever (itchy, runny, or blocked nose without a cold accompanied by red itchy eyes) was diagnosed according to the positive response for the question: “Have you had hay fever in the past 12 months?” [17]. The sensitization to common food allergens in the USA, including peanut allergy, egg allergy, milk allergy, and shrimp allergy, was assessed using serum concentrations of allergen specific IgE according to a previous study [18]. Serum samples were collected for the analyses by the Pharmacia Diagnostics Immuno CAP 1000 System (Pharmacia Diagnostics, Kalamazoo, MI, USA) [19].

Normal distribution data were expressed as mean ± standard deviation (Mean ± SD), and t test was used for comparison between groups. Skewed distribution data were expressed as median and quartiles [M (Q1, Q3)], and used rank sum test for comparison. Categorical data were expressed as frequency and constituent ratio [N (%)], and chi-square test (χ2) was used for comparison.

Univariate logistic regression analysis was used for covariates screening. Univariate and multivariate logistic regression analyses were used to explore the association between dietary antioxidants intake and childhood eczema. Model 1 was the crude model. Model 2 adjusted for age, gender, race, family educational background, PIR, insurance, asthma, hay fever, food allergy, BMI, energy intake, PUFA intake and serum IgE level. Model 3 adjusted for variables included in the Model 2 and different dietary antioxidants. Subgroup analyses of age and gender were also performed.

The evaluation index was odds ratios (ORs) with 95% confidence intervals (CIs). Two-sided P < 0.05 was considered significant. To eliminate differences results from dimension, we normalized the data [with the formula: (x-mean)/standard deviation], and the normalization can magnify the influencing of these variables on the outcome to make it more direct. Statistical analyses were performed using SAS 9.4 (SAS Institute, Cary, NC, USA). Missing data were deleted (accounting for more than 20%) or interpolated using the multiple interpolation method (accounting for ≤ 20%). The sensitive analysis of characteristics of participants before and after interpolation of missing variables is shown in Additional file 1: Table S2.