We conducted two cross-sectional surveys from September 2020 to January 2022. The first survey was performed in Beijing and Tangshan (in Hebei province) from September to December 2020, and the second in January 2022 in Pinggu district, Beijing.

According to the 2022 census data, there are approximately 21.8 million persons in Beijing and 7.7 million persons in Tangshan. There are 16 districts in Beijing and 7 districts in Tangshan. Beijing covers an area of 16,410 km², and Tangshan covers an area of 13,472 km². Per capita disposable income was 77,400 RMB in Beijing and 39,600 RMB in Tangshan.

The selection process of study participants was reported previously (14, 15). Specifically, in the first survey, study participants were consisted of preschool-aged children attending junior to senior kindergarten classes. We randomly selected 4 out of 16 districts in Beijing and 2 out of 7 districts in Tangshan by using the stratified and cluster sampling methods. In total, 5 kindergartens were selected from each district, and 30 kindergartens were included finally. In the second survey, study participants included children attending primary school or junior high school. We randomly selected 26 schools, including 8 primary schools and 18 junior high schools, in Pinggu district, Beijing. In this study, data were collected from children aged 3–14 years in 30 kindergartens and 26 schools in Beijing and Tangshan.

We collected data by self-designed questionnaires. To ensure reliability and validity, both questionnaires were separately distributed in 200 samples before formal circulation, and the reliability coefficient (alpha) was over 0.85.

We integrated the items from both questionnaires, covering four main areas as follows: (i) demographic area: age, sex, nationality, date of birth, height, weight, and food and drug allergy; (ii) fetal and neonatal area: birth body length, gestational age, delivery mode, pregnancy order, delivery order, assisted reproduction, twin birth, infancy feeding, breastfeeding duration, and time of adding solid food; (iii) lifestyle-related area: sitting time, screen time, outdoor activity time, sleep duration, fall asleep time, eating speed, number of dental caries, and weekly intake frequencies of sweet food, night meals, and fast food; (iv) family-related area: parental age, parental weight, parental height, parental education, and family income. Body mass index (BMI) was calculated as weight divided by height squared (kg/m²).

The questionnaires were generated by the “Wenjuanxing” website.¹ As an online platform in China, the “Wenjuanxing” can yield a unique QR code for each questionnaire. The QR code can be recognized by smartphones and was sent to the parents or guardians by teachers-in-charge via the “WeChat” social media application. The “Wenjuanxing” platform automatically integrated data from individual questionnaires as an Excel spreadsheet, which can be downloaded for analysis.

Before the distribution of questionnaires, healthcare physicians and teachers-in-charge selected in this survey from all schools and kindergartens were trained to be familiar with the survey procedures and each item in the questionnaires. During the survey, healthcare physicians and teachers-in-charge can help parents or guardians of participating children to fill out questionnaires. At the end of the survey, data were downloaded into a Microsoft Office Excel™ spreadsheet from the “Wenjuanxing” platform and were strictly checked by our trained staff. Healthcare physicians and teachers-in-charge were requested to contact the parents or guardians of participating children to resupply or confirm information that was obviously abnormal in the questionnaires. Body weight (to the nearest 0.1 kg) and height (to the nearest 0.1 cm) were measured by healthcare physicians.

Child malnutrition included stunting, underweight, and wasting. In this study, we adopted the WHO criteria to define child malnutrition. Specifically, the 2006 WHO Child Growth Standard (16) defined stunting, underweight, and wasting for children aged 0–5 years (0–60 months), and the 2007 WHO growth reference for school-aged children and adolescents (17) defined stunting and wasting for children aged 5–19 years (61–228 months). The nutritional status of a child was evaluated by the Z-score, which was calculated using the deviation of the value of a child from the median of the reference population, divided by the standard deviation of the reference population. According to the WHO criteria, we defined stunting, underweight, and wasting based on two age stages: (i) children aged 36–60 months: stunting was defined as a height-for-age Z-score (HAZ) less than −2 standard deviations (SDs), underweight as weight-for-age Z-score (WAZ) of less than −2 SDs, and wasting as weight-for-height Z-score (WHZ) less than −2 SDs; (ii) children aged 61–180 months: stunting was defined as a height-for-age Z-score (HAZ) less than −2 standard deviations (SDs) and BMI for age Z-score (BMIZ) less than −2 SDs.

Delivery modes included vaginal delivery and cesarean section. Gestational age was recorded in months, and birth between 37 and 42 gestational weeks was regarded as full-term birth. Birth body length (to the nearest 0.1 cm) was reported by the parents or guardians of participating children. Pregnancy order and delivery order meant the times of pregnancy and bearing birth, respectively.

Infancy feeding included pure breastfeeding, partial breastfeeding, and non-breastfeeding. Breastfeeding duration and time of adding solid food were recorded in months. Some lifestyle-related factors, including sitting time, screen time, and outdoor activity time recorded in hours, were calculated as the sum of time spent on workdays × 5 and weekends × 2 divided by 7. In this survey, sitting time included screen time, and screen time referred to the amount of time spent on screen-related behaviors such as watching TV and playing computer games (18). Sleep duration included time for a lunch break. Eating speed was calculated as the average of breakfast, lunch, and dinner. Sweet food refers to food with sweet taste (such as bread cakes and desserts), and fast food is defined as food with high energy and low nutrition, such as hamburger and pizza. Night meal refers to food eaten within 2 h before bedding. We investigated the weekly intake frequency, which was classified as every day, often (3–5 times), occasional (1–2 times), and none, of sweet food, fast food, and night meals.

Parental BMI was calculated from self-reported weight and height. Family education referred to the highest educational level of parents and was categorized as master’s degree or above, bachelor’s degree, and high school degree or below. Family income (RMB per year) was categorized as ≥300,000, 100,000–300,000, and < 100,000.

Data were analyzed using STATA software version 16.0 (Stata Corp, College Station, TX, United States) and R programming environment (version 3.5.2). Study power was calculated using PS (Power and Sample Size Calculations) software version 3.0.

We assign values to categorical variables, as shown in Supplementary Table S1. The possible biases arising from different kindergartens and schools were assessed by the intraclass correlation coefficient (ICC). In theory, ICC can be used to quantify observed differences within and between clusters (19).

To reduce the influence of potential bias and confounding, we adopted 1:4 propensity score matching (PSM) between the malnutrition and control groups. Continuous variables are expressed as mean (standard deviation), in the case of no deviation from normal distribution based on the Skewness and Kurtosis tests, and as median (interquartile range). Categorical variables are expressed as count (percent). Between-group comparisons of variables were performed using the t-test, χ² test, or rank-sum test, where appropriate. The variance inflation factor (VIF) was calculated to assess multiple collinearities.

To identify statistically significant risk factors for child malnutrition, logistic regression analyses were conducted before and after considering age, sex, twins and infancy feeding, birth length, pregnancy order, and delivery order. Effect-size estimates are expressed as odds ratio (OR) and 95% confidence interval (CI).

After adding significant factors associated with child malnutrition to the basic model, prediction performance was appraised from both calibration and discrimination aspects. From the calibration aspect, Akaike information criterion (AIC) and Bayesian information criterion (BIC) were used to observe how closely the prediction probability, by adding significant factors, reflected the actual observed risk and global fit of the modified risk model, and the calibration curves for different models provide another form of visualization. From the discrimination aspect, the receiver operating characteristic (ROC) curve of both models was also presented to observe the discrimination capability of identified significant factors. The net benefits of this addition were also inspected by decision curve analysis (DCA).

In the first survey from September to December 2020, questionnaires were distributed to the parents or guardians of 10,441 children. In the second survey in January 2022, 11,633 questionnaires were sent. We pooled data from both surveys and strictly reviewed the validity of the survey data. Finally, 18,503 questionnaires were deemed eligible for inclusion. In this study, the prevalence of child malnutrition was 10.93% (n = 2022), and stunting, underweight, and wasting were 1.34% (n = 248), 11.22% (n = 563), and 9.77% (n = 1808), respectively.

The baseline characteristics of participating children are shown in Table 1 and Supplementary Table S2. The ICCs for all factors under the study were all relatively low (<0.01), indicating a low probability of clustering within kindergartens or schools and a lower likelihood of differences in surveyed items (Supplementary Table S3).

Multiple collinearities revealed by variance inflation factor (VIF) indicated that no multiple collinearities existed between different variables (Supplementary Table S4).

As shown in Table 1, baseline variables were selected based on clinical relevance or with a p-value of less than 0.05 on univariate analyses. After adjusting for age, gender, twins and infancy feeding, birth length, pregnancy order, and delivery order, seven factors, namely, family education (OR, 95% CI, p: 1.52, 1.40 to 1.67, <0.001), family income (1.23, 1.16 to 1.30, <0.001), fast food intake frequency (1.14, 1.06 to 1.21, <0.001), night meals intake frequency (1.09, 1.04 to 1.15, <0.001), eating speed (1.01, 1.01 to 1.02, <0.001), maternal BMI (0.97, 0.95 to 0.99, <0.001), and paternal BMI (0.97, 0.96 to 0.98, <0.001) were found to be associated with the significant risk of child malnutrition, as shown in Table 2.

The power to detect significance when estimating the risk for child malnutrition was over 80% for the above comparisons.

We constructed both the basic model and full models to assess the prediction performance of seven significant factors identified above. The full model included all variables, and the basic model included all variables with the exception of seven significant factors. The prediction performance of both models was assessed from calibration and discrimination aspects, and the difference between the basic model and full model was compared. Significant improvement was observed in the prediction accuracy of the full model relative to that of the basic model (Table 3). In addition, the DCA plot showed that the net benefits gained by adding seven significant factors to the basic model were obvious (Figure 1).

The ROC curves are shown in Figure 2, and calibration curves are shown in Supplementary Figure S1. As revealed by the area under the receiver operating characteristic (AUROC) curve, both models differed significantly in discrimination (p < 0.001).

Some limitations should be acknowledged for this study. First, in this study, all participating children were enrolled from Beijing and Tangshan, which are two economically developed cities; hence, extrapolation of our findings to the other areas should be made with caution. Second, data derived from questionnaires filled by parents or caregivers cannot exclude the possibility of recall bias. Third, some socioeconomic data were unavailable for us, such as parental employment. Fourth, the causality of potential risk factors with child malnutrition cannot be addressed due to the cross-sectional design.