Over the past 40 years, the number of 5- to 19- year- old children and
adolescents suffering from obesity has increased tenfold globally (it was 11 million in 1975 and increased to 124 million in 2016). From 1985 to 2014, the prevalence of overweight and obesity in Chinese students aged 7 to 18 years increased from 1.11% to 12.1%, and 0.13% to 7.3%, respectively.  A number of studies have demonstrated that children with excess body fat have increased cardio-metabolic risk factors (CMRFs). [2,3] Excess body fat in children was also related to cardiovascular diseases in adulthood. [4-9] Therefore, in order to slow the development of cardio-metabolic diseases in adulthood, early identification of children and [10,11] adolescents with CMRFs is of great importance. 
As one of the most commonly used obesity assessment indicators, body mass index (BMI) is based on the finding that body weight is proportional to height squared in adults.
However, as children and  adolescents are still in the growth and developmental stage, their weight is not proportional to their height squared, which undercuts the validity of BMI. Furthermore, during puberty, adiposity tends to increase with growth and development due to the influence of sex hormones.  Consequently, these increases in fat mass rather than lean mass from childhood causes the annual increase of BMI. [15,16] Therefore, Cole  recommended that BMI could be used for preschool children and adults, but mentioned that it is not appropriate for children in early puberty as it tends to assess tall or physically advanced children as being overweight. Using BMI-  z score can also lead to an over-diagnosing problem, eventually causing wasteful healthcare expenditure. Besides, available BMI cutoff values are age- sex-, and ethnic-specific, limiting the comparison among studies and challenging their use in normal families and clinical practice. [14,17,19,20] 
A recent study highlighted the usefulness of tri-ponderal mass index (TMI),
which is calculated by weight/height  3 (kg/m 3), and suggested it as a better indicator that could replace BMI in children and adolescents. Peterson et al found that in  adolescents, TMI was more stable with age, more accurate in estimating body fat percentage, and was simpler to use compared with BMI. Some studies have compared the effectiveness of TMI and BMI in identifying CMRFs in adolescents, reporting TMI as a better predictor. However, Ashley-Martin [14,22-25] et al, Wu  et al, and Gomes [27,28] et al claimed that TMI was not significantly superior to BMI in predicting CMRFs. 
In many previous studies, subjects were
adolescents, while children <7 years of age have been paid less attention. This resulted in a lack of relevant data on the capabilities of BMI and TMI for assessing clustered CMRFs. Furthermore, neither BMI nor TMI can provide the information on fat distribution, waist-to-height ratio (WHtR) ≥ 0.5 as a rapid assessment of excess abdominal fat, in both adults and children, can provide the information about abdominal fat.  A previous study found that combined use of WHtR and stratified BMI could further specify CMRFs.  Apart from that, the study of Wang  et al found that the combination of TMI and WHtR did not improve the accuracy of screening for CMRFs. 
Based on previous studies,
we hypothesized that the distribution of TMI in children aged 3 to 17 years would remain stable and would show good screening ability for CMRFs. Therefore, the aim of this study was to: (1) assess the stability of TMI in relation to age in Chinese children aged 3 to 17 years; (2) compare the abilities of BMI and TMI to identify CMRFs; and (3) evaluate whether the combined use of TMI and WHtR could improve the ability to recognize CMRFs.  Methods
This study has been approved by the Institutional Review Board and Ethics Committee of Capital Institute of Pediatrics, China (No. SHERLL 2015031). All participants and/or their parents or guardians provided written informed consent before initiation of the study.
Study design and participants
All data used in the current study came from two previous cross-sectional studies. For kindergarten children, in a study exploring blood pressure in preschool children, data were obtained by typical sampling from 382 participants who were recruited from four kindergartens in Chaoyang District, Beijing, China, between January to July 2018. The inclusion criteria were: (1) aged between 3 years and 6 years; (2) parents or guardians provided written informed consent. The exclusion criteria were: (1) basic information was incorrect and cannot be corrected; (2) missing data on age, height, weight, waist circumference (WC), and blood pressure; (3) self-reported hypertension-related diseases, such as diabetes, thyroid disease, etc; (4) family history of hypertension, diabetes, and kidney disease. For elementary, middle, and high school students, in a study exploring effects of dietary salt intake on hypertension and target organ damage in children and
adolescents, data were collected by a stratified cluster sampling from 1207 participants who were recruited in one elementary school, one junior high school, and one high school in Chaoyang District, Beijing, China, between 2015 and 2016. The inclusion criteria were: (1) aged between 6 years and 17 years; (2) participants and/or their parents or guardians provided written informed consent. The exclusion criteria were: (1) basic information was incorrect and cannot be corrected; (2) menstrual period girls; (3) self-reported medical conditions (eg, cardiovascular disease, diabetes, and other organic diseases); (4) history of kidney disease; (5) history of blood transfusion and major surgery within 6 months.
For the present study, the inclusion criteria for participants were: (1) aged between 3 years and 17 years; (2) participants and/or their parents or guardians provided written informed consent. The exclusion criteria were: (1) basic information was incorrect and cannot be corrected; (2) missing biochemical or anthropometric data; (3) self-reported medical conditions (eg, cardiovascular disease, diabetes, and other organic diseases); (4) history of cardiovascular disease, diabetes, and kidney disease; (5) family history of hypertension, diabetes, and kidney disease.
Anthropometric measurements, which included body weight, height, WC, systolic blood pressure (SBP), and diastolic blood pressure (DBP), were collected by trained staff following standard procedures. Body weight, height, and WC were measured following technical standards for physical examination for students (GB/T 26343-2010). Body height and weight were measured by scales (RGZ-120, China) without shoes and in light clothing after overnight fasting. Standing height was defined to the nearest 0.1 cm, and body weight was measured to the nearest 0.1 kg. WC was measured to the nearest 0.1 cm at a point midway between the lowest rib and the iliac crest in a horizontal plane using non-elastic tape. Height, weight, and WC were measured twice for each student, and the mean of two measurements was used in the analysis. SBP and DBP were measured on the right upper arm with appropriate cuff size by Omron HBP1100 electronic blood pressure monitor (OMRON, Dalian, China) while subjects were seated and after a 5-min rest. The measurement was repeated three times, and the mean of three measurements was used in the analysis.
A fasting blood sample was collected by trained examiners after a 12 h overnight fast. In order to make sure the participants were adhering to the 12 h overnight fast, a briefing session was held before the start of the study, and all guardians were informed in advance to collect fasting blood samples from children. They were also informed of all precautions and test indicators, and the paper version of the notice was provided at the same time as the informed consent. The day before the blood collection, the staff reminded the guardians of corresponding requirements, and the school teachers were asked to inform the students again. Serum levels of total cholesterol (TC), triglyceride (TG), high-density lipoprotein cholesterol (HDL-C), low-density lipoprotein cholesterol (LDL-C), and fasting plasma glucose (FPG) were measured by the Capital Institute of Pediatrics Laboratory (China National Accreditation Service for Conformity Assessment [CNAS] ISO-15189) with strict quality control.
BMI was calculated as a weight to height squared (kg/m
2), while TMI was calculated as a weight to height cubed (kg/m 3); other weight/height n ( n = 1–4, increments of 0.5) were calculated as weight/height n (kg/m n). BMI was converted to age-sex-standardized values according to 2007 World Health Organization (WHO) growth standard and 2009 Chinese standard, respectively. WHtR was the ratio of WC (cm) to height (cm). [32,33] Questionnaire variables
A standardized questionnaire was used to collect comprehensive information of participants and their parents, including basic demographic information of the research subjects (name, sex, date of birth, ethnicity, grade, etc), children's birth and feeding status, children's diet and living habits, children's physical activity and sleep habits, personal disease history (hypertension, diabetes, kidney disease, etc), family history of hypertension, and information on parents and other family members (height, weight, education level, and history of smoking and drinking).
Definitions of outcomes
The following CMRFs were evaluated
: (1) hypertension, which was defined as SBP and/or DBP ≥ the 95th percentile for a given sex and age group [34,35] ; (2) impaired fasting glucose (IFG), which was defined as FPG ≥ 5.6 mmol/L  ; (3) abnormalities in any of the following indicators were defined as dyslipidemia  : (a) TC ≥ 5.2 mmol/L; (b) TG ≥ 1.1 mmol/L for 0 to 9 years old children and TG ≥ 1.5 mmol/L for 10 to 18 years old children; (c) LDL-C ≥ 3.4 mmol/L; (d) HDL-C ≤ 1.0 mmol/L; (4) abdominal obesity was defined as WC ≥ the 90th percentile of the same sex and age group.  Clustered CMRFs were defined as meeting three or more of the four items of hypertension, dyslipidemia, impaired fasting glucose, and abdominal obesity. [39,40]  Statistical analysis
Considering the impact of growth and development on children and
adolescents, height, weight, and WC significantly differed among 3- to 6-year-old, 7- to 12-year-old, and 13- to 17-year-old participants. Besides, considering the sampling procedure and participants’ educational status, included pre-school children were aged 3 to 6 years, primary school children were aged 7 to 12 years, and middle and high school students were aged 13 to 17 years. Thus, all the participants in the current study were divided into three groups according to age for subsequent statistical analysis, namely, 3 to 6 years old, 7 to 12 years old, and 13 to 17 years old.
General characteristics of the population were described according to age groups. For comparisons of continuous variables among groups, one-way analysis of variance or Kruskal-Wallis test for variables with normal or skewed distribution were used, respectively. For the differences in CMRFs prevalence among different age groups, the chi-squared test was used. Line graphs with an error bar were chosen to present the fluctuation of weight/height
n in relation to age in participants of different sex. Line graphs showed that weight/height 2.5 and weight/height 3 were more stable than others, considering previous findings, which suggested that weight/height 2.5 performed equally to TMI in identifying CMRFs, and TMI was more convenient for practical application. Therefore, only BMI and TMI were included in the subsequent statistical analysis. 
Partial correlation analysis was used to evaluate the relationship among anthropometric and biochemical indicators (adjusted for age and sex). Three different logistic regression models were used to evaluate associations of BMI and TMI with CMRFs; ORs and 95% confidence intervals (CIs) were separately calculated. Model 1 was a crude model, while model 2 was adjusted for age and sex; potential confounding factors adjusted in model 3 were sociodemographic variables (age, sex, ethnic groups, and social-economic status), lifestyle characteristics (passive smoking), and family history of hypertension. AUCs and 95% CIs were used to assess the abilities of BMI and TMI in identifying CMRFs. We also examined whether a significant difference existed between the AUCs of TMI and BMI, when BMI was set as the reference. The AUCs were defined as follows: fail (0.5–0.6), poor (0.6–0.7), fair (0.7–0.8), good (0.8–0.9), and excellent (0.9–1.0).
Overweight and obesity were separately set as the cutoff values to evaluate and compare the accuracy of these indicators in distinguishing CMRFs. When overweight was set as the cutoff value, thresholds were obtained according to the following standards: (1) 1 ≤ body mass index World Health Organization (BMI-WHO) < 2, based on the 2007 WHO growth standards
; (2) BMI-China were classified by age- and sex-specific thresholds for overweight in Chinese pediatric population  ; (3) 85th age- and sex-specific BMI percentiles ≤ BMI < 95th age- and sex-specific BMI percentiles; (4) 85th sex-specific TMI percentiles ≤ TMI < 95th sex-specific TMI percentiles. When obesity was set as the cutoff value, thresholds were obtained as follows: (1) BMI-WHO ≥ 2  ; (2) BMI-China were classified by age- and sex-specific thresholds for obesity in Chinese pediatric population  ; (3) BMI ≥ 95th age- and sex-specific BMI percentiles; (4) TMI ≥ 95th sex-specific TMI percentiles. Non-parametric receiver operating characteristic analyses were used to calculate the false positive rate (FPR), false negative rate (FNR), and total misclassification rate (TR) of each indicator. BMI-WHO was set as a reference, and statistical differences in TRs of each indicator were also compared. Finally, the ORs (adjusted for age and sex) and TRs of combined using TMI percentiles and WHtR were also calculated. 
All the data were analyzed by IBM SPSS Statistics 25.0 (SPSS Inc., Chicago, IL, USA) and RStudio4.0.5 for Windows64 (RStudio, Boston, USA). FPRs, FNRs, and TRs for screening clustered CMRFs by four indicators in different age groups were drawn by GraphPad prism 9.0.0 for Windows (GraphPad Software, USA). All reported
P values were two-sided and P < 0.05 was considered statistically significant. Results
Demographic characteristics of participants
adolescents aged 7 to 17 years, two cases were excluded because of missing data related to height, weight, and biochemical data. Therefore, 1587 subjects aged 3 to 17 years were included. Among the total population, 50.8% ( n = 806) were boys, and 48.2% ( n = 781) were girls; the mean ± standard deviation (SD) of age was 10.3 ± 4.1 years. All the baseline demographic characteristics and the prevalence CMRFs of the subjects are presented in Table 1. The total prevalence of clustered CMRFs was 2.6%, 3.2%, and 7.0% in 3 to 6 years old, 7 to 12 years old, and 13 to 17 years old, respectively ( P < 0.01).
Table 1 -
Baseline demographic characteristics and the prevalence of CMRFs by age.
3–6 years (
n = 458) 7–12 years (
n = 636) 13–17 years (
n = 493) Statistical value
5.3 ± 1.0
10.0 ± 1.7
15.4 ± 1.2
113.8 ± 8.0
141.9 ± 12.1
166.5 ± 8.5
20.4 ± 4.8
39.1 ± 12.9
61.7 ± 15.3
53.0 ± 5.6
64.5 ± 11.3
73.3 ± 11.5
100.6 ± 11.9
113.8 ± 13.0
118.5 ± 11.6
58.2 ± 10.5
66.7 ± 10.3
66.2 ± 7.5
0.47 ± 0.04
0.45 ± 0.06
0.44 ± 0.06
2) 15.62 ± 2.20
18.99 ± 4.04
22.12 ± 4.57
3) 13.76 ± 1.89
13.37 ± 2.51
13.29 ± 2.71
4.2 ± 0.8
4.5 ± 0.8
4.3 ± 0.7
0.7 (0.6, 0.9)
0.7 (0.6, 1.0)
0.8 (0.6, 1.0)
1.5 ± 0.3
1.5 ± 0.3
1.4 ± 0.3
2.5 ± 0.6
2.4 ± 0.7
2.4 ± 0.7
4.8 ± 0.3
5.0 ± 0.3
5.2 ± 0.7
Data are presented as mean ± standard deviation or
n (%). Statistical value: continuous variables with a normal distribution were F-values, continuous variables with a skewed distribution were H-values, and categorical variables were represented by chi-square values. BMI: Body mass index; FPG: Fasting plasma glucose; HDL-C: High-density lipoprotein cholesterol; IFG: Impaired fasting glucose; LDL-C: Low-density lipoprotein cholesterol; TMI: Tri-ponderal mass index; TC: Total cholesterol; TG: Triglyceride; WHtR: Waist-to-height ratio; Clustered CMRFs: Satisfy three or more of the four items of hypertension, dyslipidemia, impaired fasting glucose, and abdominal obesity. Stability with age
To compare the stability of the distribution of TMI and BMI in children aged 3 to 17 years, we calculated mean ± SD of TMI and BMI in children aged 3 to 17 years to compare their stability. The mean TMI were 13.57 ± 2.50 (kg/m
3) in boys and 13.34 ± 2.33 (kg/m 3) in girls, and means BMI were 19.31 ± 4.72 (kg/m 2) in boys and 18.66 ± 4.35 (kg/m 2) in girls. Furthermore, Figure 1 shows the age-specific means and SDs of weight/height n, kg/m n ( n = 1–4, increments of 0.5) in 3- to 17-year-old participants. This line graph shows that weight/height 2.5 and TMI performed more stable than BMI in both sexes as age increased. However, as mentioned in the Methods section, we only included BMI and TMI in the follow-up analysis due to previous research results and ease of practical application. Figure 1:
n, kg/m n ( n = 1–4, increments of 0.5) for boys (A) and girls (B) aged 3 to 17 years. Correlations among anthropometric and biochemical indicators
After adjusting for age and sex, the correlation coefficients among anthropometric indicators and biochemical indicators, listed in Supplementary Table 1,
, revealed that BMI-WHO, BMI, TMI, and WHtR had strong correlation with each other ( https://links.lww.com/CM9/B202 P < 0.001), while all of them were significantly associated with SBP, DBP, TG, HDL-C, and LDL-C ( P < 0.001). ORs of TMI and BMI for CMRFs
The ORs and 95% CIs of BMI and TMI in relation to single or clustered CMRFs of all the participants are listed in
Table 2. Each unit increase in TMI represented an increased risk of hypertension, dyslipidemia, abdominal obesity, and clustered CMRFs; the ORs and 95% CIs for TMI were 1.19 (95% CI: 1.10–1.19), 1.13 (95% CI: 1.06–1.20), 3.15 (95% CI: 2.73–3.64), and 1.48 (1.30–1.68), respectively, which was higher than for BMI, whose ORs and 95% CIs ranged from 1.08 (95% CI: 1.04–1.13) to 2.98 (95% CI: 2.58–3.44). However, both the ORs and 95% CIs of BMI and TMI for IFG were not statistically significant. We also calculated associations within each age group, finding that the ORs of IFG was not statistically significant in any of the three age groups, while in adolescents aged 7 to 17 years, the ORs for clustered CMRFs were higher in TMI than in BMI [Supplementary Table 2, ]. https://links.lww.com/CM9/B202
Table 2 -
Association between BMI, TMI, and CMRFs in all the participants (OR [95% CI]).
1.10 (1.07, 1.12)
1.06 (1.03, 1.08)
1.09 (1.04, 1.13)
1.50 (1.40, 1.52)
1.26 (1.20, 1.33)
1.17 (1.14, 1.21)
1.08 (1.05, 1.12)
1.00 (0.95, 1.05)
2.90 (2.58, 3.25)
1.29 (1.22, 1.37)
1.14 (1.10, 1.19)
1.08 (1.04, 1.13)
0.97 (0.90, 1.04)
2.98 (2.58, 3.44)
1.30 (1.20, 1.41)
1.24 (1.18, 1.30)
1.11 (1.06, 1.17)
0.97 (0.89, 1.05)
2.99 (2.67, 3.35)
1.47 (1.34, 1.61)
1.24 (1.18, 1.30)
1.14 (1.06, 1.17)
0.98 (0.90, 1.06)
3.01 (2.68, 3.36)
1.46 (1.33, 1.59)
1.19 (1.12, 1.26)
1.13 (1.06, 1.20)
0.93 (0.83, 1.04)
3.15 (2.73, 3.64)
1.48 (1.30, 1.68)
Model 1: crude model; Model 2: adjusted for age and sex; Model 3: adjusted for age, sex, ethnic groups, social economic status, passive smoking, and family history of hypertension.
∗ P < 0.001.BMI: Body mass index; CI: Confidence interval; CMRFs: Cardio-metabolic risk factors; Clustered CMRFs: Satisfy three or more of the four items of hypertension, dyslipidemia, impaired fasting glucose, and abdominal obesity; TMI: Tri-ponderal mass index; IFG: Impaired fasting glucose; OR: Odds ratio. AUCs of TMI and BMI for CMRFs
The AUCs of BMI and TMI for single or clustered CMRFs are listed in
Table 3. Results showed that the AUCs of TMI for hypertension, dyslipidemia, and abdominal obesity increased with increasing age, while this was not the case for BMI. In the group with all participants, both TMI and BMI demonstrated good ability in identifying clustered CMRFs, that is, 0.85 (95% CI: 0.80–0.89, P < 0.05) for BMI and 0.83 (95% CI: 0.78–0.88, P < 0.05) for TMI, while the AUCs for clustered CMRFs did not significantly differ between two regardless of age group or inclusion of all participants. The AUCs of TMI reached 0.64 (95% CI: 0.61–0.67, P < 0.05) and 0.92 (95% CI: 0.91–0.94, P < 0.05) for hypertension and abdominal obesity, respectively, and were significantly higher than BMI, which had AUCs of 0.61 (95% CI: 0.58–0.64) for hypertension and 0.85 (95% CI: 0.82–0.87) for abdominal obesity, respectively. Also, there was no statistically significant difference for dyslipidemia between TMI and BMI. For IFG, AUC values for TMI and BMI could not be compared due to the low prevalence of IFG in the 3- to 6-year-old group. However, the ability of TMI to identify IFG was not significantly better than BMI in the 7 to 12 and 13 to 17 age groups, and the screen capability of TMI for IFG in 3 to 17 age group was only 0.49 (95% CI: 0.43–0.55, P < 0.05), which was significantly lower than that for BMI (AUC: 0.65, 95% CI: 0.60–0.70, P < 0.05).
Table 3 -
Area under curve (AUCs) of BMI and TMI for CMRFs in 3 to 17 children.
P value AUC
P value AUC
P value AUC
0.65 (0.59, 0.72)
0.60 (0.55, 0.65)
0.73 (0.67, 0.79)
0.61 (0.58, 0.64)
0.57 (0.51, 0.64)
0.63 (0.59, 0.68)
0.71 (0.65, 0.78)
0.64 (0.61, 0.67)
0.51 (0.40, 0.62)
0.55 (0.50, 0.60)
0.65 (0.59, 0.71)
0.57 (0.53, 0.61)
0.50 (0.39, 0.60)
0.55 (0.50, 0.60)
0.66 (0.60, 0.72)
0.58 (0.54, 0.62)
0.79 (0.74, 0.85)
0.61 (0.50, 0.72)
0.51 (0.44, 0.58)
0.65 (0.60, 0.70)
0.94 (0.91, 0.97)
0.50 (0.38, 0.61)
0.51 (0.44, 0.57)
0.49 (0.43, 0.55)
0.90 (0.87, 0.93)
0.95 (0.94, 0.97)
0.96 (0.95, 0.98)
0.85 (0.82, 0.87)
0.88 (0.84, 0.91)
0.93 (0.91, 0.95)
0.95 (0.93, 0.97)
0.92 (0.91, 0.94)
0.93 (0.84, 1.00)
0.84 (0.78, 0.91)
0.82 (0.75, 0.89)
0.85 (0.80, 0.89)
0.89 (0.80, 0.98)
0.85 (0.79, 0.91)
0.81 (0.74, 0.88)
0.83 (0.78, 0.88)
Data are shown as n (95% CI).
∗ P < 0.001. † P < 0.01. ‡ P < 0.05.BMI: Body mass index; CMRFs: Cardio-metabolic risk factors; IFG: Impaired fasting glucose; clustered CMRFs: Satisfy three or more of the four items of hypertension, dyslipidemia, impaired fasting glucose, and abdominal obesity; Ref: Reference; TMI: Tri-ponderal mass index. –: Not available.
Furthermore, we compared whether the AUCs of TMI for identifying CMRFs were significantly different among three age groups. For hypertension and dyslipidemia, there was no significant difference between 3 to 6 years and 7 to 12 years, but the AUCs of TMI in the 13 to 17-year-old group were significantly higher than those in the 3 to 6-year-old and 7 to 12-year-old groups. For IFG, there was no significant difference between 7 to 12-year-old and 13 to 17-year-old groups. For abdominal obesity, the AUCs of TMI were significantly higher in the groups of 7 to 12 years and 13 to 17 years than in the 3 to 6 years group; however, there was no significant difference between the groups of 7 to 12 years and 13 to 17 years. For clustered CMRFs, AUCs of TMI were not significantly different between 3 to 6 years, 7 to 12 years, and 13 to 17 years.
FPRs, FNRs, and TRs of each indicator in different thresholds
We set overweight and obesity as the screening threshold, respectively, and evaluated the capability of BMI-WHO, BMI-China, BMI, and TMI to identify subjects with cardio-metabolic risks. The FPRs, FNRs, and TRs of each indicator in different age groups are shown in Supplementary Table 3,
When overweight was set as the cutoff value, BMI-China had the highest FPRs for clustered CMRFs among four indicators in all the age groups, ranging from 25.0% (95% CI: 19.5–31.2%) to 40.2% (95% CI: 36.3–44.2%), while the other three indicators showed satisfied FPRs that ranged from 11.9% (95% CI: 9.1–15.3%) to 16.1% (95% CI: 11.5–21.5%). In addition, BMI-China had the lowest FNRs and highest TRs for clustered CMRFs among four indicators in all the age groups. With the thresholds changed from overweight to obesity, the FPRs and TRs of four indicators dropped in each group; however, the FNRs dramatically increased [
Figure 2]. We set BMI-WHO as a reference and compared whether there were significant differences of TRs among the other three indicators with BMI-WHO. We found that regardless of whether overweight or obesity was used as the screening threshold, there was no significant difference in the TRs of TMI and BMI-WHO in each age group [Supplementary Table 3, ]. For instance, when using obesity as the threshold, the TRs of TMI and BMI-WHO in children aged 3 to 6 years were 6.5% (95% CI: 3.8–10.7%) and 9.1% (95% CI: 5.9–13.8%), respectively, while in 7 to 12-year-old and 13 to 17-year-old participants, the TRs of TMI were 7.3% (95% CI: 5.5–9.7%) and 11.2% (95% CI: 8.7–14.5%), which was higher than BMI-WHO of 5.4% (95% CI: 3.8–7.5%) and 9.0% (95% CI: 6.7–12.0%), respectively; no significant differences were observed between these two indicators in each group. https://links.lww.com/CM9/B202 Figure 2:
FPRs (A,B), FNRs (C,D), and TRs (E,F) of identifying clustered CMRFs by four indicators in different age groups when setting overweight or obesity as thresholds. When overweight is used as the diagnostic threshold, division criteria of each anthropometric index are as follows: (1) 1 ≤ BMI-WHO < 2, based on the 2007 WHO growth standards; (2) BMI-China: according to age- and sex- specific thresholds of overweight based on 2009 BMI curves for Chinese pediatric population; (3) BMI: 85th age- and sex-specific BMI percentiles ≤ BMI < 95th age- and sex-specific BMI percentiles; (4) TMI: 85th sex-specific TMI percentiles ≤ TMI < 95th sex-specific TMI percentiles. When obesity is used as the diagnostic threshold, division criteria of each anthropometric index are as follows: (1) BMI-WHO≥2, based on the 2007 WHO growth standards; (2) BMI-China: according to age- and sex- specific thresholds of obesity based on 2009 BMI curves for Chinese pediatric population; (3) BMI: BMI≥95th age- and sex-specific BMI percentiles; (4) TMI: TMI≥95th sex-specific TMI percentiles. BMI-WHO: Body mass index World Health Organization; Clustered CMRFs: Satisfy three or more of the four items of hypertension, dyslipidemia, impaired fasting glucose, and abdominal obesity; FPR: False positive rate; FNR: False negative rate; TMI: Tri-ponderal mass index; TR: Total misclassification rate.
Combined use TMI and WHtR for identifying CMRFs
Considering that WHtR can provide information about abdominal obesity, we calculated the TRs and ORs of the combined use of TMI and WHtR in discriminating CMRFs [Supplementary Table 4,
]. In the group that included all the participants, compared with using TMI alone, the ORs of combined usage of WHtR were increased to 8.06 (95% CI: 4.69–13.85) for https://links.lww.com/CM9/B202 P 85 of TMI+ WHtR, and 4.42 (95% CI: 2.17–8.99) for P 95 of TMI+ WHtR. TRs of clustered CMRFs were 13.3% (95% CI: 11.5–15.2%) at P 85 of TMI+ WHtR, and 8.2% (95% CI: 6.8–9.8%) at P 95 of TMI+ WHtR, which were significantly lower than the use of TMI percentiles alone that were 15.6% (95% CI: 13.7–17.7%) at P 85 and 8.6% (95% CI: 7.2–10.3%) at P 95, respectively. However, observations were not consistent within each age group. Discussion
In the current study, TMI performed well in identifying abdominal obesity and clustered CMRFs. Also, its screening abilities increased with increasing age. However, TMI showed poor ability in identifying hypertension, and it failed to recognize dyslipidemia and IFG. Compared with BMI, it showed similar ability in screening hypertension, dyslipidemia, and clustered CMRFs. TMI performed significantly better in abdominal obesity, but it was inferior to BMI in IFG. Considering that TMI is more stable with the increase of age between different sexes, is easier to use, and can evaluate body fat more accurately,
we suggest that it can be used in children and [14,22] adolescents for screening of abdominal obesity and clustered CMRFs. It should be used with caution in screening for hypertension, and we do not recommend TMI screening for dyslipidemia and IFG.
In the present study, 7 to 17-year-old participants were split into two groups, that is, 7 to 12-year-old and 13 to 17-year-old groups. Also, among all the CMRFs, only in 7 to 12-year-old participants showed that TMI was significantly better than BMI (
P < 0.05) in discriminating hypertension. The AUCs of these two indicators were similar for other CMRFs. Yet, we also calculated AUCs in all subjects aged 7 to 17 years, finding that TMI was significantly superior to BMI in identifying hypertension, dyslipidemia, and abdominal obesity, which was consistent with the studies of Peterson et al and Wang  et al in children and  adolescents. However, Wang et al demonstrated that TMI had better screening capability for IFG than BMI in the Chinese population (  P < 0.05), while in our population, TMI was not correlated to FPG, ORs were not significant in logistic regression models, and AUCs also showed that TMI failed to identify IFG. A recently published paper evaluated the ability of TMI to identify insulin resistance in Brazilian overweight adolescents aged 12 to 18 years and compared with BMI. Their findings found that TMI was not superior to BMI in its accuracy and capacity to predict insulin resistance. Nonetheless, in the present study, TMI performed well in identifying abdominal obesity, and correlation analysis showed a strong relationship between TMI and WHtR (  r = 0.882, P < 0.001), which is one of the most important central adiposity measures. The association between TMI and central adiposity measures may potentially contribute to using TMI for prediction of CMRFs in type 2 diabetes mellitus patients. Therefore, association between TMI and IFG needs to be further studied. [27,43]
TMI showed limited ability in identifying dyslipidemia in the current study, which was consistent with Wang
et al while Ashley-Martin  et al found that AUCs of TMI in identifying TC, TG, and HDL-C ranged from 0.62 (95% CI: 0.57, 0.67) to 0.68 (95% CI: 0.64, 0.73), which were higher than our results. Also, for younger participants aged 3 to 6 years, TMI did not show significantly better capability than BMI in screening abdominal obesity, which was inconsistent with the conclusions of Nascimento  et al . 
In addition to comparing the screening power of BMI and TMI for CMRFs in children aged 3 to 17 years, we also compared whether there is a significant difference in the screening ability of TMI for CMRFs among different age groups. For hypertension, dyslipidemia, and IFG, TMI showed the highest screening capacity in children aged 13 to 17 years. However, since AUC values of IFG for 3 to 6-year-olds are not available, we only compared the ability of TMI to screen for IFG in children aged 7 to 12 years and 13 to 17 years, and the results showed no significant difference. The ability of TMI to screen abdominal obesity in 7 to 17-year-old children is significantly better than that in 3 to 6-year-old-children. In addition, the ability of TMI to screen for clustered CMRFs did not differ significantly among the three age groups.
To compare the accuracy among indicators in distinguishing CMRFs, we used overweight and obesity as thresholds separately, after which we calculated FNRs, FPRs, and TRs. Interestingly, for clustered CMRFs, BMI-China showed the highest FPRs and TRs and lowest FNRs among four indicators in each age group, which may be due to age- and sex-specific BMI thresholds in 2009 BMI growth curves that were divided at intervals of 0.5 years in Chinese pediatric standards. TMI, BMI, and BMI-WHO showed similar accuracy for clustered CMRFs but fluctuated among age groups.
Studies from different countries have confirmed the stability of TMI in the pediatric population,
including ours. In the present study, the diagnostic thresholds of TMI in distinguishing overweight and obesity were 16.22 kg/m [14,24,26,44,45] 3 and 18.33 kg/m 3 in boys, and 15.55 kg/m 3 and 17.90 kg/m 3 in girls, separately. This was slightly different from the results of Peterson et al and Ashley-Martin  et al, which may be due to the different nationalities and ages of the participants. Nascimento  et al evaluated the ability of TMI in screening abdominal obesity in preschool children, recommending 16.5 kg/m  3 as the cutoff value, irrespective of the sex and age of preschool children. However, considering that the use of TMI as a screening indicator is to enable early identification of overweight and obese children, and early prevention of future metabolic and cardiovascular diseases, more attention should be paid to sensitivity. Therefore, the author suggested that the threshold can be advanced to 14.0 kg/m 3, which means the sensitivity is close to 100%. Still, Ashley-Martin  et al demonstrated that although TMI was more stable than BMI in children and  adolescents, its value still fluctuated in a small range with age. Shim suggested that sex- and age-specific TMI should be used. Therefore, specific cutoff values of TMI for the identification of overweight and obese children still need to be calculated among different nations and larger scale populations. Further, another limitation of using TMI is that, like BMI, it cannot distinguish fat mass from muscle mass.  
The strengths of this study are the following: first, we demonstrated the distribution of TMI in the 3 to 17-year-old population according to sex and age, revealing satisfied stability compared with BMI. Second, by setting overweight and obesity as separate screening thresholds, we compared the diagnostic accuracy (FPRs, FNRs, and TRs) among two indicators (BMI and TMI) and two standards (2007 WHO growth standard and 2009 BMI curves for Chinese children and
adolescents) in different age groups. Third, we not only compared the ability of four indicators to screen individual CMRFs, namely, hypertension, dyslipidemia, IFG, and abdominal obesity, but also evaluated clustered CMRFs.
There are also several limitations in the present study. First, the cross-sectional design of this study cannot infer the causality of associations between anthropometric indices and CMRFs, and therefore, we cannot examine whether TMI or BMI can predict future CMRFs. Second, all the participants in our study are living in a specific city in China, which limits the applicability of our results to other populations. Third, confounding factors such as participants’ diet and living habits, physical activity, and sleep were not included in the logistic regression models. Fourth, only one person in the 3 to 6-year-old group suffered from IFG, which may reduce the robustness of the results in this age group.
In children and
adolescents aged 3 to 17 years, TMI performed equally well or even better than BMI in discriminating hypertension, abdominal obesity, and clustered CMRFs. However, it failed in identifying dyslipidemia and IFG. The discriminative ability of TMI with each single CMRFs increased with age. In addition, compared with BMI, TMI became stable with age in both sexes and was easier to use. Therefore, TMI may be used as a surrogate for BMI in screening for obese-related CMRFs in children and adolescents. Funding
The present study was supported by a grant from The Special Fund of the Pediatric Medical Coordinated Development Center of Beijing Hospitals Authority [No. XTCX201813].
Conflicts of interest
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