This cross-sectional study was conducted on a sample of 3975 children and adolescents (1793 boys) aged 6 to 17 years old, attending public and private schools in Santa Cruz do Sul located in Southern Brazil. The data used in this study is derived from a cohort, where the initial sample was recruited in 2004. The population density of students from all regions of the city was considered to determine the number of participants included in the research. From a total of fifty schools with 20,380 schoolchildren, twenty-five schools were randomly selected to form a representative sample of the city, encompassing schools from different regions of the municipality. All students from these 25 schools were invited to participate in the cohort study, which was divided into multiple phases: Phase I (2004–2005), Phase II (2007–2009), Phase III (2011–2012), Phase IV (2014–2015), and Phase V (2016–2017). For the present study, data from Phase IV and V were considered.

The study was managed in accordance with Resolution 466/2012 of the National Health Council of Brazil, follows the guidelines of Helsinki declaration [30], and received approval from the ethics committee of University of Santa Cruz do Sul (Approval No. 4,278,679). Prior to participation, the parents or legal guardians of the schoolchildren provided signed consent forms.

Variables

Evaluations took place from 2014 to 2017 in the facilities of the University of Santa Cruz do Sul, conducted by a team of trained researchers. For assessments involving questionnaires, parents provided assistance for children under the age of 10 in answering the questions.

Sleep time

Sleep time was evaluated through the following questions: “What time do you go to sleep during the week and the weekend?” and “What time do you get up during week and weekend?. These questions were used in previously published paper [31]. To calculate the total sleep time, the questions referring to the week and the weekend were averaged. Sleep time classification was performed according to National Sleep Foundation’s reference values for short time, adequate time and long sleep time (≤ 8 h, 9–11 h and ≥ 12 h for individuals 6–13 years, and ≤ 7 h, 8–10 h and ≥ 11 h for teenagers 14–17 years old, respectively) [32], being recategorized in two categories, adequate and inadequate sleep time (short and long sleep).

Adiposity indicators

Weight and height measurements were obtained using an anthropometric scale equipped with a stadiometer (Filizola®). BMI was calculated by dividing the weight (kilograms) by the square of the height (meters). The body fat percentage was evaluated through the measures of tricipital and subscapular folds, evaluated using a Lange® capilar (Beta Technology Inc, Houston, TX) and then applying the Slaughter et al.’s Eq. [33]. In addition, the obesity information of the parents was obtained through a self-reported questionnaire, where both the mother and father were asked to indicate their obesity status (presence or absence). Information regarding the perception of parents obesity was obtained by a self-reported questionnaire, in which there was a table where mothers/fathers could indicate the presence of cardiac, pulmonary, or circulatory diseases before the age of 55 years. Obesity was one of the included diseases. The questionnaire was sent via the children, to be answered by their parents. The possible answers were yes and no.

Lifestyle

A self-reported questionnaire was used to evaluate the lifestyle, encompassing five components related to individual well-being [34]: nutrition, PA, preventive behavior, relationships, and stress control. Nutrition included the following questions: (a) Your daily diet includes at least 5 servings of fruits and vegetables; (b) You avoid eating fatty foods (fatty meat, fried foods) and sweets; (c) You eat 4 to 5 varied meals a day, including a full breakfast. Physical activity considered the following questions: (a) You perform at least 30 min of moderate/intense physical activity, continuously or cumulatively, 5 or more days a week; (b) At least twice a week, you perform exercises involving strength and muscle stretching; (c) In your day-to-day life, do you walk or cycle as a means of transport and, preferably, use the stairs instead of the elevator. Preventive behavior was evaluated by questions: (a) You know your blood pressure, your cholesterol levels and try to control them; (b) You do not smoke and do not drink alcohol (or drink in moderation); (c) You respect traffic rules (as a pedestrian, cyclist or driver), if you drive, always wear your seat belt and never drink alcohol. Relationships included the questions: (a) You seek to cultivate friends and is satisfied with your relationships; (b) Your leisure includes meetings with friends, group sports activities, and participation in associations or social entities; (c) You seek to be active in your community, feeling useful in your social environment. Stress control considered the following questions: (a) You set aside time (at least 5 min) every day to relax; (b) You maintain a discussion without changing yourself, even when contradicted; (c) You balance the time dedicated to work with the time dedicated to leisure. All questions had the following options for the responses: never, sometimes, often, and always. The questionnaire was answered by the adolescents, and for children under the age of 10, parents provided assistance in answering the questions.

Physical activity levels

Physical activity levels were obtained by self-reported questionnaire through the following questions: “Do you usually practice any sport/physical activity?” (yes, or not); “How many times a week and hours/minutes per day do you practice this sport/physical activity”. Thus, the total time (in minutes per week) spent on sports or physical activity was calculated by summing the responses. This value represents the individual’s physical activity levels per week.

Natural food consumption

To evaluate natural food consumption, the frequency of food intake in a typical week was assessed using a self-reported questionnaire. The questionnaire included the consumption of various natural foods such as fruits, natural fruit juice, potatoes, beans and rice, fish, beef, green salads (lettuce or other), and vegetables (tomatoes, carrots, green beans, cauliflower, etc.). Participants were provided with five response options: never, one time a week, two or three times a week, four to six times a week, and daily.

Physical fitness

Physical fitness was evaluated according to the protocols of Projeto Esporte Brasil (PROESP-Br) [35].

Cardiorespiratory fitness

Cardiorespiratory fitness (CRF) was evaluated using the six-minute walking and running test. The schoolchildren were instructed to complete as many laps as possible, either running or walking, within a six-minute time frame. The test was conducted on an outdoor athletic track, with markings every 10 m to accurately measure the distance covered (meters). The number of laps completed was recorded, and for those who were unable to complete a full lap, the additional distance covered was also noted. CRF was then determined by multiplying the number of laps by the total distance covered (meters) [35].

Muscle strength

Abdominal strength was evaluated through the sit-up test, which consisted of determining the sit-ups performed during one minute (repetitions). Upper limb strength was evaluated using a measuring tape fixed to the floor (meters). Participants were seated with their legs together, leaning their body against the wall. They were instructed to flex their arms and throw a medicine ball. Two attempts were made, and the longest distance achieved was recorded as the measurement for upper limb strength (meters) [35].

Agility and speed

Agility was measured using the square test, which involved placing cones at the four corners of a square. The participant started from a designated point and moved towards the diagonally opposite cone, then proceeded to the cone on their left, diagonally to the next cone, and finally moved towards the last cone to complete the test. Participants were required to move at their maximum speed and touch each cone. Speed was evaluated by timing (seconds) the children and adolescents as they ran a distance of 20 m as quickly as possible. The best time recorded from two attempts was used for both the agility and speed assessments [35].

Cardiometabolic risk indicators

To assess systolic blood pressure (mmHg), the auscultatory method was employed, utilizing a sphygmomanometer and a stethoscope in accordance with the recommendations outlined in the VII Guidelines of the Brazilian Society of Cardiology (2016) and [36]. Two measures were performed after five minutes of rest, and the lowest result was considered for systolic blood pressure. Waist circumference (centimeters) was obtained in the narrowest part of the trunk between the last rib and the iliac crest [37], using an inelastic tape with a resolution of 1 mm (Cardiomed®, Brazil).

Triglycerides (mg/dL), total cholesterol (TC) (mg/dL), high-density lipoprotein cholesterol (HDL-C) (mg/dL), and fasting glucose(mg/dL) were evaluated through a blood sample collection after 12 h of fasting. Blood collection was realized by morning and used serum samples and commercial kits (DiaSys Diagnostic Systems, Holzheim, Germany), performed on Miura 200 automated equipment (I.S.E., Rome, Italy).

The clustered metabolic risk score (cMetS) considered the summing z-scores of each factor risk (waist circumference, systolic blood pressure, triglycerides, TC/HDL-C ratio, and fasting glucose) divided by five. To calculate sex and age-specific standardized z-scores were considered according to an international reference [38] for each risk factor with the following equation: z-score = ([X - X̅]/SD); where X is the measured continuous value of the risk factor; X̅ is the predicted mean calculated for the cMetS risk factor using the sex- and age-specific international reference equation; and standard deviation (SD) is the international SD for the specific each risk factor. Before calculating z-scores, TC/HDL-C ratio and triglycerides were log-transformed using the natural logarithm because of their skewness.

Parental education level

The determination of parental education level consisted of a self-reported question, in which parents should indicate their level of education, according to the following options: Illiterate/Incomplete Elementary Education (up to 3rd Grade), Complete Elementary Education/Incomplete Elementary Education, Complete Middle School/Incomplete High School, Complete High School/Incomplete Higher Education, Complete Higher Education.

Statistical analysis

Based on the objectives of the present study and previous literature [39, 40], we developed a structural equation model (Fig. 1) to examine the complex relationships between parental obesity and cardiometabolic risk factors in children and adolescents with both inadequate and adequate sleep time, considering the aforementioned variables. Within this model, lifestyle, PA levels, natural food consumption, and physical fitness were considered interconnected mediators. The latent constructs presented in Fig. 1 were defined as follows: parental obesity, lifestyle habits (nutrition, PA, preventive behavior, relationships, and stress control); natural food consumption (fruits, natural fruit juice, potatoes, beans and rice, fish, beef, green salads, and vegetables; physical fitness (CRF, abdominal strength, agility, speed, and upper limb strength); Cardiometabolic risk factors (cMetS), and adiposity indicators [BMI, and body fat percentage]).

Based on these primary aspects, the data were evaluated using structural equation models (SEM) with a split file for two classifications based on sleep time (adequate and inadequate). In addition, considering a discrepant of theoretical consistency in primary results to the model for inadequate sleep time children, we input an alternative model for this group, with a correction to the parental education level.

The direct and indirect effects are estimated based on the beta (β) values of standardized variables, to be possible to measure the factorial load importance of each variable included in the model. The goodness-of-fit criteria used to compare the groups are as follows [29]: CMIN/DF: This criterion measures the ratio of the chi-square statistic (CMIN) to the degrees of freedom (DF). It assesses the disparity between the observed and expected covariance matrices. A lower CMIN/DF value indicates a better fit, with a value close to 1 being desirable. IFI (Incremental Fit Index): IFI compares the proposed model with a null model to measure the improvement in fit. It ranges from 0 to 1, with values closer to 1 indicating a better fit. TLI (Tucker-Lewis Index): TLI also compares the proposed model with a null model and quantifies the degree of improvement in fit. Similar to IFI, TLI ranges from 0 to 1, with values above 0.90 indicating a better fit. FMIN: This criterion represents the minimum discrepancy between the observed and predicted covariance matrices. A lower FMIN value indicates a better fit. RMSEA (Root Mean Square Error of Approximation): RMSEA measures the discrepancy between the predicted model and the population covariance matrix, considering the model’s complexity. It provides an index of how well the model fits the data, with a lower RMSEA value (close to 0) indicating a better fit. Values below 0.05 are often considered good. AIC (Akaike Information Criterion): AIC is a measure of model fit those accounts for model complexity. It balances goodness of fit with model complexity, with lower AIC values indicating a better fit. BIC (Bayesian Information Criterion): Similar to AIC, BIC considers both goodness of fit and model complexity. It penalizes more complex models and provides a measure of relative fit. Lower BIC values indicate a better fit. By applying these criteria, we can determine if the groups with adequate or inadequate sleep time are statistically the most suitable to be represented by the proposed SEM [29] (Figs. 1 and 2, and 3). The statistical program used for the analysis was IBM AMOS version 21.0.

Fig. 1

Theoretical model proposal to determine the relationship between parental obesity and cardiometabolic risk factors in children and adolescents, considering the mediator role of health indicators accordingly to sleep time