In this study of Copenhagen schoolchildren aged 7 years, 10 years and 13 years born between 1930 and 1996, we derive for the first time the optimal height powers needed to standardise childhood FM and FFM, and demonstrate how they vary across birth cohort groups, by sex and age (within birth cohort groups), and by ethnic groups (for those born in the 1990s). The findings are also complemented by results demonstrating the variation in the optimal height powers needed to standardise childhood weight by birth year, sex and age.

For FM, FFM, and weight, the optimal height powers at 7 years and 10 years increased with birth year and were typically higher for girls compared to boys. At 13 years the height powers for all three markers initially increased with birth year before declining for those born in the more recent birth cohort groups. This decline was more marked for FM and weight compared to FFM. Furthermore, for children born in the 1990s, we observed that a greater power was needed to standardise all three markers for height for South Asian children compared to White European and Black children, albeit with low levels of precision accompanying the estimates.

These changes in the sex- and age-specific optimal powers by birth year, particularly for weight and FM, are largely explained by the much greater variation in these markers in recent birth cohort groups compared to the earlier birth cohorts. Moreover, differences observed in the optimal powers for all three markers by sex, age, and ethnicity, within birth cohort groups, can be explained by both differences across these subgroups in the variability (i.e. spread) of the markers, and their correlations with height, both of which contribute to the estimation of the optimal height powers required for standardisation.

Several studies have investigated the suitability of BMI as a height-independent marker of childhood adiposity and the optimal height power required to standardise weight for height in childhood [4, 6, 9, 19,20,21]. Most investigated how the power varied by childhood age. The study by Johnson et al. [6], while primarily investigating the differences in the power by age across the life course, also explored differences by birth year, primarily for 11-year-olds, within several historic and contemporary UK birth cohorts. Our results are generally consistent with those of Johnson et al, which found that the height power needed to standardise weight increased with birth year amongst 11-year-olds. The height powers amongst boys were estimated at 2.44 for those born in 1946, 2.61 for those born in 1958, and 3.11 for those born in 2001 and amongst girls at 2.58, 2.69, and 3.12 for those born in 1946, 1958, and 2001, respectively [6]. The same study found that amongst 10-year-old UK children born in 1970, the height powers were estimated to be 2.20 and 2.36 for boys and girls respectively [6], estimates which were lower than those observed in our study among Copenhagen children (boys: 2.75, girls: 2.83), which may be explained by the UK study containing children born only in 1970 as opposed to our results being for those born in 1970–79. Another study conducted in the 1970s with weight and height measurements of 7-year-old US children (i.e. those born in the late 1960s) [19] also found estimates of the height power similar to those of our study. Our findings pertaining to the age- and sex-specific differences in the height power for weight were also largely consistent with a study of children from Hong Kong who were born in the 1970s [4], and a study of Japanese children born in the 1980s and 1990s [21].

Far fewer studies have investigated the optimal height powers for FM and FFM, and their variability by age and sex, with no studies investigating changes in the powers over time. Our earlier studies based on UK children born in the 1990s and early 2000s estimated the height power to standardise FM to be approximately four for 7-year-olds and at least five for 10-year-olds [22, 23], which although slightly higher, are generally consistent with those of the current study. Furthermore, a study of 7-year-old children in the UK-based Millennium Cohort Study born in 2000 estimated the height powers for FM to be 3.88 and 4.31 amongst boys and girls respectively, and for FFM to be 2.43 for both boys and girls [24]. These results are consistent with our findings for children of the same age born between 1990 and 1996.

The key strengths of this study are the extremely large sample size of children with measured weights and heights, which allowed optimal height powers to be estimated with high levels of precision within sub-groups, and the time span of the cohort which contains childhood surveillance data across several decades spanning across the time periods both before and during the rise of the childhood obesity epidemic. Data from the CSHRR are currently available on children measured until 2011 and therefore we were not able to include very recent measurements on children from Copenhagen. However, the variability in the optimal height power observed at each of the ages for birth years 1930–1996, covering both the periods before and during the childhood obesity epidemic, highlights the difficulties of using a uniform power of height to standardise both weight and FM. Additionally, given that the CSHRR contains almost every schoolchild in Copenhagen, Denmark born between 1930 and 1996, representativeness is strong [15]. Weight and height were measured by trained physicians and nurses in a consistent manner, thus reducing the risk of measurement error. Whilst the results of this study pertaining to FM and FFM rely on the validity and accuracy in FFM estimation from the prediction equation, its high accuracy has previously been documented within several childhood settings across a range of birth years from the late 1960s onwards [16,17,18, 25, 26]. The prediction equation models the relationship between the included predictors and log-transformed FFM, which are unlikely to change by birth year, thus indicating the suitability of the equation also for the earlier birth years used in this study. FM estimates obtained from the prediction model have also been shown to be as accurate as those from dual-energy X-ray absorptiometry and bioelectrical impedance [18]. Limitations of this study include missing ethnicity information on children measured prior to the late 1990s onwards and thus for the estimation of childhood FFM and FM, ethnic origins were presumed to be White European. This is unlikely to have impacted the estimation of the height power in the earlier birth cohort groups, due to the low levels of immigration to Denmark in this time period [15], though estimates from the 1970–79 and 1980–89 birth cohorts may have been affected by potential misclassification of ethnic origins. Moreover, information on genetic and socioeconomic factors to explain ethnic differences was not available so we could not assess its effects on the findings.

Height-standardised indices of weight and FM, as they remain correlated with height to varying degrees by sex, age, birth year and ethnic groups, have a different meaning within each of these groups making them difficult to interpret accurately. Given that the rationale for the standardisation of body size markers for height is to allow for meaningful comparisons within- and between individuals, this represents an important challenge. For example, the correlation between BMI and height amongst 7-year-old boys was 0.14 for those born in the 1930s but was 0.30 for boys born in the 1990s. That implies that the amount of variation in BMI explained by height was 2% in 7-year-old boys born in the 1930s but was 9% for boys born in the 1990s, highlighting the changing meaning of BMI for children born in the two different time periods, before and after the emergence of the obesity epidemic, and thus the difficulty in drawing comparisons across individuals of the same sex and age based on widely used height-standardised body size indices. Moreover, current definitions of weight status groups (underweight, healthy weight, overweight or obesity) are based upon reference values of childhood BMI, which (as demonstrated in these findings) uses an inaccurate fixed height power of 2 to standardise weight for all children irrespective of their sex, age and birth year. This is problematic as it is likely that the use of any index adopting a fixed height power to define these groups (e.g. BMI) will result in incomparable groups due to the variability in the relationship between BMI and height across subgroups. Adopting different height powers for each subgroup of sex, age and birth year would not be feasible for clinical or public health practice as this would essentially mean different adiposity markers are adopted for each subgroup of the childhood population. While some studies have suggested that body size indices should not be completely height-independent [9, 27], the issue of variability over birth years (and by sex, age, and ethnicity) in the correlation between such indices and height would remain a concern even if this were the case.

While there is a need for a shift in childhood adiposity assessment away from weight-based markers and towards fact-based assessment, particularly in light of the World Health Organisation’s recent definition of obesity as “excessive fat accumulation that presents a risk to health” [2], our results suggest that indices of FM may well be prone to the same limitations of poor height-standardisation as weight-for-height indices such as BMI. Therefore, alternative methods for taking account of height for epidemiological analyses are needed. One alternative to forming such body size indices would be to retain the original childhood body size marker (e.g. FM or weight) and take account of height in the modelling process for the analyses of interest, for example, by assessing height-adjusted mean levels of childhood FM or weight, quantifying trends over time in childhood FM or weight stratified by levels of height (e.g. quintiles), or quantifying cross-sectional or longitudinal associations between childhood FM or weight and short- or long-term outcomes of interest, adjusting for/ stratified by height.

Future work will seek to investigate alternative approaches to interpreting FM- or weight-based assessments on an individual level, such as in clinal practice, namely whether childhood FM (along with weight, height, sex and other demographics) can be used to obtain an accurate probability of an individual developing adiposity-related health conditions in the short- and long-term. If so, such risk probabilities could be used for improved interpretation of an individual’s FM level which is indicative of associated health risks.