Observed and predicted ages at peak height velocity in soccer players

The purpose of the study was to evaluate predicted maturity offset (time before age at PHV) and age at PHV (chronological age [CA] minus maturity offset) in a longitudinal sample of 58 under-13 club level soccer players in central Portugal for whom ages at PHV were estimated with the SITAR model. Two maturity offset prediction equations were applied: the original equation which requires CA sitting height, estimated leg length, height and weight, and a modified equation which requires CA and height. Predicted maturity offset increased, on average, with CA at prediction throughout the age range considered, while variation in predicted maturity offset and ages at PHV within CA groups was considerably reduced compared to variation in observed ages at offset and at PHV. Predicted maturity offset and ages at PHV were consistently later than observed maturity offset and age at PHV among early maturing players, and earlier than observed in late maturing players. Both predicted offset and ages at PHV with the two equations were, on average, later than observed among players maturing on time. Intra-individual variation in predicted ages at PHV with each equation was considerable. The results for soccer players were consistent with similar studies in the general population and two recent longitudinal studies of soccer players. The results question the utility of predicted maturity offset and age at PHV as valid indicators of maturity timing and status.


Introduction
Predicted maturity offset, defined as time before peak height velocity (PHV) [1,2], and estimated age at PHV, i.e., chronological age (CA) minus predicted offset, are widely used as estimates of maturity status (state of maturation at the time of observation) and/or timing (age at which a specific maturational event occurs) in studies of youth athletes and to a lesser extent in studies youth physical activity and fitness [3][4][5][6]. The original sex-specific equations require CA, sitting height, estimated leg length, height and weight [1], while the modified equations [2] require CA and height (both sexes) or sitting height (boys). Validation studies of the original equations in three independent longitudinal series, the Wroclaw Growth Study [7,8], the Fels Longitudinal Study [9] and the Cracow Growth Study [10], and of the modified equations in two of the samples [10,11] have indicated major limitations of the predictions in both males and females. The validity of the prediction equations has also been questioned in longitudinal samples of female artistic gymnasts [12] and soccer players [13,14], but sample sizes in longitudinal samples tend to be limited and to some extent select as they are limited to athletes who have persisted in the respective sports [15]. Similarly, cross-sectional studies of tennis [16] and soccer [17] players have questioned maturity status classifications based on the original prediction equations [1] relative to classifications based on skeletal age.
Current interest in the application of the maturity offset prediction equations in samples of youth athletes is considerable [3][4][5][6]. Predictions based on the original and modified equations, however, depend upon CA and body size at prediction, have reduced variation relative to observed ages at PHV, and have major limitations with early and late maturing youth as defined by observed ages at PHV [7][8][9][10][11]. The latter are problematic as advanced (early for CA) or delayed (late for CA) maturity status is often of major concern in developmental studies of youth athletes [15].
In the context of the preceding, the purpose of the present study is to evaluate predicted maturity offset and derived ages at PHV with the original [1] and modified [2] equations in a sample of 58 soccer players for whom age at PHV was determined from longitudinal height records. The study specifically considers variation in the predictions in three contexts: (i) relative to actual maturity offset and observed age at PHV at each observation, (ii) among players differing in the timing of observed age at PHV, and (iii) within individual players.

Research design and procedures
The data set for the present study was extracted from the Coimbra Soccer Longitudinal Project [18]. This project was conducted according to the standards established by the declaration of Helsinki [19], and formal approval was obtained from the University of Coimbra Sports Sciences and Physical Education Board Signed institutional agreements were also obtained from the Presidents of the respective clubs. All players were registered with the Portuguese Soccer Federation. Male players 11-14 years of age were recruited from five clubs in the Midlands of Portugal; the initial sample included 159 players [20]. Written consent was obtained from parents or legal guardians of the participants who were informed that contribution to the study was voluntary and that they could withdraw from the study at any time. All observations were completed at the Biokinetics Laboratory of the Coimbra University Stadium.

Sample
According to the Portuguese Soccer Federation, male soccer players were grouped as infantiles (aged 11-12 years, n = 87) and initiates (aged 13-14 years, n = 72). The analysis in the current study is limited to under-13 players (U13) who were measured annually in December for four or five years (n = 59). CAsat baseline ranged from 10.98 to 12.94 years. The heights of one player were not successfully modeled; consequently, the final sample was composed of 58 players. All players were of European ancestry, except one. Participants trained and competed September through May. They had a median of 3 years of soccer experience at baseline (range: 2-6 years). The clubs had 3-5 training sessions per week (each about 90-120 minutes) and usually one game, mainly on Saturdays.

Anthropometry
Participants wore shorts and a t-shirt; shoes were removed. Height and sitting height were measured to the nearest 0.1cm using, respectively, a stadiometer (Harpenden 98.603, Holtain Ltd, Croswell, UK) and a table (Harpenden sitting height table, model 98.607, Holtain Ltd, Crosswell, UK). Body weight was measured to the nearest 0.1 kg using a scale (SECA 770, Hanover, MD, USA). The heights, sitting heights and weights of players who continued at the respective clubs were subsequently measured on an annual basis. Measurements were made by a single observer (MJCS). Intra-observer technical errors of measurement for height, sitting height and weight were 0.27 cm, 0.31 cm and 0.47 kg, respectively [19].

Age at PHV
The longitudinal height records were fit with the Superimposition by Translation and Rotation (SITAR) model [21][22][23][24] to derive an age at peak height velocity for each player. As noted, the heights of one player were not successfully modeled; the estimated age at PHV for the player was outside of the empirical data range and was inconsistent with his advanced skeletal maturity status at observations one and three. Mean age at PHV for the remaining 58 players was 13.60±0.85 years, with a range from 11.89 to 15.49 years [25].

Predicted maturity offset
Maturity offset, defined as time before PHV, was predicted at each observation for the 58  Leg length was estimated at each observation as standing height minus sitting height. The need to multiply the weight by height ratio by 100 was overlooked in the original report [1]; in some publications using the equation, it is not clear if the adjustment was applied. Maturity offset was also predicted at each observation with a modified equation for boys that incorporated age and height [2]: Maturity offset ðyearsÞ ¼ À 7:999994 þ ð0:0036124 � ðCA � HeightÞÞ Eqð2Þ The equation with age and height was selected for evaluation as it is increasingly used [26][27][28][29][30][31]. Standard errors for the original [1] and modified [2] equations were, respectively, 0.592 and 0.542 year. Predicted maturity offset and predicted age at PHV with the respective equations are subsequently labelled in the text, tables and figures as Mirwald and Moore, respectively.

Predicted age at PHV
Predicted age at PHV was estimated as CA minus predicted maturity offset at each observation for individual players with the respective equations.

Observed maturity offset
Observed or actual maturity offset at each observation was estimated as CA at prediction minus observed age at PHV based on the SITAR model.

Analyses
Descriptive statistics were calculated at each observation for CA and actual offset, for predicted maturity offset and age at PHV, and for the difference of predicted age at PHV minus observed age at PHV with the two prediction equations. The players were also classified as advanced (early), average (on time) or delayed (late) maturing relative to the mean and standard deviation for age at PHV (SITAR) in the total sample. Average was defined as an age at PHV within ±1 SD of the mean age at PHV for the total sample of 58 players (13.60±0.85 years); delayed was a PHV >14.45 years and advanced was a PHV <12.75 years.
Linear mixed-effect models with the data grouped by subjects (random effects) were used with a maximum-likelihood estimator to evaluate the variance structure of the dependent variable, i.e., the differences between observed and predicted ages at PHV. Separate analyses were done for predictions with the Mirwald and Moore equations. The difference of the dependent variable from zero (so-called unconditional means model) was initially tested. In the second step, the effect of predictions at observations 1-5 (as a time variable) on the dependent variable at the population level (fixed effect) and at the intra-individual level (i.e., random slopes model, or unconditional growth model) were tested. Note that the term growth in the statistical context refers to the general change in a dependent variable with a time variable; it does not refer to growth in the biological sense. Finally, maturity status was added as a fixed factor to test the effect of variation in maturity timing on the predictions. The model was run separately for predictions with the Mirwald and Moore equations in the R-software [22] with the help of the nlme statistical package [32].
Weighted Deming regression using the jackknife procedure [33] was used to compare observed age at PHV estimated with the SITAR model (i.e., the reference) with predicted ages at PHV at each observation based on the two equations. The weighted Deming procedure considers both x (observed age at PHV) and y (predicted age at PHV) as subject to measurement error whereas simple regression permits only the y variable to have an associated error. With the weighted Deming regression, systematic differences between x and y are indicated by the intercept, while proportional differences are indicated by the slope.
Many applications of the equations use predicted maturity offset to classify youth as pre-PHV, at/circa/mid-PHV, or post-PHV using a band of -0.5 to +0.5 year to define the interval at PHV [29,[34][35][36][37][38][39][40][41]; a band of -1.0 to +1.0 year is used less often [42][43][44][45][46]. On the other hand, some studies do not report the specific cut-offs that were used [47][48][49]. The standard errors of the prediction equations, 0.592 and 0.542 year, also approximate the narrow cut-offs used in many studies. Thus, the number and percentage of predicted ages at PHV with each equation within ±0.5 year of observed age at PHV at each observation were estimated for players of contrasting maturing status and for the total sample.

Results
Descriptive statistics for CA at prediction, observed and predicted maturity offset, predicted ages at PHV and the difference of predicted age at PHV minus observed age at PHV (the reference for comparison) with the original (Mirwald) and modified (Moore) equations in the soccer players are summarized in Table 1. Observed and predicted maturity offset increase linearly, on average, across the five observations. Predicted offset with the Moore equation is similar to actual offset at observation one but is then less than actual offset at subsequent observations. Predicted maturity offset with the Mirwald equation is less than actual offset and predicted offset with the Moore equation across the five observations.
Corresponding trends in predicted ages at PHV and the difference of predicted minus observed ages at PHV parallel those for maturity offset. Standard deviations for predicted maturity offset and ages at PHV with both equations are consistently lower than corresponding standard deviations for observed offset and age at PHV across the five observations. Variability is reduced more so with the Moore compared to the Mirwald equation.
Results of the mixed effects model indicate significant differences between observed and predicted ages at PHV with the Mirwald equation (F = 40.95; p<0.001) and also with the Moore equation (F = 9.39; p<0.01). Details of the analytical protocol and results are summarized in S1 Table. The differences between observed and predicted ages at PHV with the respective equations at each observation increase significantly with subsequent observations with the Mirwald (F = 22.81; p<0.001) and the Moore (F = 172.97; p<0.001) equations, although the 95% confidence intervals indicate that the difference at observation 1 for the Moore equation is not different from zero.
Intercepts based on weighted Deming regressions for the two prediction equations are well above zero at each observation, indicating that the methods differ significantly by a constant error (Table 2). Estimated slopes for each regression are <1.0, indicating significant proportional differences between predicted ages at PHV with each equation and observed age at PHV. Overall, the results indicate systematic error for predicted ages at PHV. Descriptive statistics for the three maturity groups are summarized in Table 3. Sample sizes and ages at PHV of players in each maturity timing group were as follows: advanced, n = 8, 12.30±0.27 years; average, n = 38, 13.50±0.51 years; delayed, n = 12, 14.76±0.27 years.
Results of the mixed-effects model comparing the three maturity groups indicate that maturity status as a fixed factor has a significant effect on the dependent variable (predicted ages at PHV) with both the Mirwald (F = 36.85, p<0.001) and the Moore (F = 51.28, p<0.001) equations. By inference, predicted ages at PHV differ relative to observed age at PHV in each group. However, the interaction between observation and maturity group is significant for the Mirwald equation (F = 5.39, p = 0.005) and indicates different slopes of change in predicted ages at PHV with consecutive observations in the maturity groups. The latter reflects the trend in differences between predicted and observed ages at PHV for the Mirwald equation which are not significant except at observation 1. In contrast, the interaction term is not significant for the Moore equation.
In the context of the results of the mixed-effects model, differences between predicted and observed ages at PHV are significant and positive across the five observations among players advanced in maturity timing (i.e., early ages at PHV). The predicted ages at PHV are consistently later observed ages at PHV.
Results are similar for players maturing on time (average), i.e., predicted ages at PHV with the two equations are later than observed age at PHV. Across the five observations, the differences between predicted and observed ages at PHV with each equation are significant, Table 3. Sample sizes and descriptive statistics (mean ± standard deviation) for chronological age (CA) at prediction, observed maturity offset and predicted maturity offset, predicted ages at PHV and the difference of predicted age at PHV minus observed ages at PHV (criterion) with the original (Mirwald) and modified (Moore) equations at each observation in players classified as advanced, average and delayed based on observed ages at PHV † . although predicted age at PHV with the Moore equation at observation one approaches that for observed age at PHV. Among late maturing players, in contrast, differences between predicted and observed ages at PHV for the Mirwald equation are not significant except at observation one, while differences between predicted and observed ages at PHV for the Moore equation are significant at each observation. The differences between predicted and observed ages at PHV with the Mirwald equation are also smaller than corresponding differences with the Moore equation.
Predicted ages at PHV (y-axis) for individual players with the Mirwald and Moore equations are illustrated relative to their respective observed ages at PHV (x-axis) in Figs 1 and 2, respectively. Intra-individual variation in predicted ages at PHV is considerable and ranges of predicted ages are reduced with the Moore equation. Relatively few predicted ages approximate observed ages at PHV in early and late maturing players.
Across the five observations (Table 4)

Discussion
The 58 players comprising the present study was larger than samples in five other longitudinal studies of European youth soccer players, 8 to 33 players [25]. Results of the application of the maturity offset prediction equations in the longitudinal series of Portuguese youth soccer players were consistent with recent studies of English [13] and Dutch [14] soccer players. The study of English players was limited to the Mirwald et al. [1] equation, while that of the Dutch players considered the original and modified [2] equations in addition to an equation which predicted a maturity ratio [50]. Although the three studies varied in design, scope and focus, the results were consistent in highlighting major limitations of predicted maturity offset and predicted age at PHV in longitudinal samples of soccer players. Applications of the original and modified equations in the longitudinal series of Portuguese youth soccer players were also consistent with validation studies of the maturity offset prediction equations in three longitudinal series of youth spanning late childhood through adolescence, one in the U.S. [9] and two in Poland [10,11]. The three studies and the present study of soccer players used similar analytical methods and noted several major limitations of the prediction equations.
First, predicted maturity offset increased, on average, with CA at prediction throughout the age range considered in each study. In the study of soccer players, mean predicted ages at PHV based on the Moore equation increased, on average, with CA, while those based on the Mirwald equation increased from observation one to two, changed negligibly through observation four and then increased to observation five. The age-related trend probably reflects the predictors comprising each equation which increase, on average, with CA. The preceding is apparent in the correlations between predicted maturity offset and predicted age at PHV with CA, height, sitting height, estimated leg length and weight at each observation for the Mirwald equation and with CA and height with the Moore equation (Table 5). For predicted maturity offset, correlations within each CA group range from moderately high to high; correlations are highest for sitting height and tend to be lowest for estimated leg length. For predicted age at PHV, correlations are relatively low and positive for CA, but are negative and moderate to high for the anthropometric variables. Within an age group, taller and heavier players tended to have an earlier predicted age at PHV.
Second, variation in predicted maturity offset and ages at PHV within CA groups was consistently reduced compared to variation in observed ages at offset and at PHV. Variation was reduced more so with the Moore compared to the Mirwald equation. Third, predictions varied with maturity status defined by observed age at PHV. Predicted maturity offset and ages at PHV were consistently later than observed maturity offset and age at PHV among early maturing boys, and earlier than observed in late maturing boys. By inference, maturity status defined by observed age at PHV influenced predicted ages at PHV in both early and late maturing boys. It should be noted, however, that Moore et al. [2, p. 1761] cautioned that "Our sample was not large enough to rigorously assess variation in prediction error due to early-and late-maturing children". This caution, however, is overlooked in applications of the equations. In contrast to early and late maturing youth, predicted ages at PHV appeared to be reasonably accurate for average maturing boys within approximately ±1 year of observed PHV. Unfortunately, the maturity status and/or timing of individuals is not ordinarily known in studies applying the prediction protocols.

Table 5. Correlations at each observation between predicted maturity offset and predicted APHV (CA-predicted maturity offset) with chronological age (CA), height (Ht), sitting height (SitHt), estimated leg length (LegLt) and body weight (Wt) for the Mirwald equation and with CA and
Fourth, intra-individual variation in predicted ages at PHV with each equation was considerable in the present sample of soccer players and in each of the longitudinal studies. Ranges of predicted ages at PHV were reduced with the Moore compared to the Mirwald equation.
The dependency of predicted maturity offset upon CA and body size at prediction merits attention. Means for predicted maturity offset are plotted relative to means for CA and height in the present study and in samples of male soccer players extracted from the literature [13,38,43,46,[51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68][69] are illustrated in Figs 3 and 4. The means plotted in the figures were limited to studies using the Mirwald equation, as it was more widely used in studies of soccer players. Predicted maturity offset increased linearly with CA and with height at prediction. The plotted means were largely based on one or two year CA groups, although several were based on players spanning age ranges of three or more years. Studies reporting maturity offset by relative age categories within an age group and studies classifying players across variable age ranges as pre-, at/circa-or post-PHV based on predicted offset were not included in the graphs. In the former, players born early in the year were, on average, older and taller than those born later in the year, while in the latter, CA and height systematically increased from pre-, to at/circa-to post-PHV groups (see above). Given the trends, studies applying predicted maturity offset as a maturity indicator beg the following question: Is predicted maturity offset an indicator of time before age at PHV or is it an indicator of CA and size at prediction? By inference, the validity of predicted maturity offset as an indicator of the time before or after PHV can be questioned.
The preceding has implications for studies using predicted maturity offset as an indicator of maturity status among youth athletes in soccer and other sports. Predicted maturity offset is used most often to classify youth as pre-, at-/circa-and post-PHV, although mean CAs, heights and weights show, on average, a clear gradient across the respective maturity groups. Many studies simply compare the three groups with analysis of variance without controlling for the variation in CA and body size among groups [31,35,36,40,70]. It is also unclear as to how CA-related variation in predicted offset or ages at PHV was addressed in studies applying the prediction equations in short-term longitudinal studies [71][72][73].
Although studies of youth athletes do not ordinarily indicate the ethnic composition of samples, the issue of ethnic variation is relevant as the maturity offset prediction equations were developed and validated on samples of European ancestry. The original Mirwald equation [1] requires sitting height and estimated leg length, while one of the Moore equations [2] for boys requires age and sitting height. Of potential relevance, population variability in the proportions of sitting height and estimated leg length to standing height is reasonably well established [74,75]. American youth of European (White), African (Black) and Hispanic ancestry, for example, vary in the proportions of sitting height and estimated leg length [76,77]. The proportions of the Portuguese youth soccer players in the present study, as reflected in the sitting height-height ratio, were, on average, generally similar to those for American White and Hispanic youth, but different from American Black youth who have proportionally longer lower extremities. This trend was also noted in a recent study of soccer players in which players of non-European ancestry were taller with a lower sitting height/height ratio, i.e., proportionally longer legs, than players of European ancestry [13].
Results of the current study also have practical implications for those working with youth athletes. The interval of PHV is central to the Long Term Athlete Development (LTAD) model for youth athletes [78,79], which calls for identifying youth of contrasting maturity status, i.e., early, average or late maturing. The LTAD, however, does not specify the method for doing so other than suggesting the monitoring of estimated growth velocities; the latter, however, have limitations over the short term. Estimated increments over short intervals (3-4 months), however, must be interpreted with care; they must be adjusted for the interval between measurements and evaluated relative to factors which influence short term estimates of growth ratespecifically measurement errors (both inter-and intra-observer), diurnal variation and perhaps seasonal variation [80]. Nevertheless, application of predicted maturity offset in this context has the potential for misclassification and thus implications for player development. Those using predicted maturity offset per se or variations of the method to identify when players enter and exit the interval of the adolescent growth spurt should employ these methods with caution. If predicted offset is used to inform training design and prescription, it is essential that variation in chronological age at prediction and error associated with the prediction equations be considered. Perhaps additional or alternative methods might be used as a complement, for example, percentage of predicted adult stature attained at the time of observation. As noted above, the utility of estimated velocities of growth in height based on short term height increments has limitations.
The inability of the maturity offset prediction methods to effectively differentiate between early and late maturing youth implies that they should not be used to group players by maturity status as in bio-banding [81], or to adjust fitness and performance scores to accommodate individual differences in maturation [70,82]. As age at PHV is over-estimated in early and under-estimated in late maturing youth, the majority of these players will likely be categorised as being on time and some will be grouped in equivalent bands. Similarly, maturity associated adjustments to performance or fitness scores in early and late maturing boys will, by virtue of these biases, be attenuated and regress towards a common mean.

Conclusions
Results of the study of applying maturity offset prediction equations to the sample of Portuguese soccer players were consistent with similar studies of soccer players and of the general population. Predicted maturity offset increased, on average, with CA at prediction throughout the age range considered. Variation in predicted maturity offset and ages at PHV within CA groups was consistently reduced compared to variation in observed ages at offset and at PHV. Predictions also varied with maturity status defined by observed age at PHV; predicted maturity offset and ages at PHV were consistently later than observed maturity offset and age at PHV among early maturing boys, and earlier than observed in late maturing boys. And, intraindividual variation in predicted ages at PHV with each equation was considerable and ranges of predicted ages at PHV were reduced more with the Moore compared to the Mirwald equations.
Supporting information S1 Table. Mixed effects linear models analysis of differences between predicted ages at PHV with the Mirwald (S1A Table) and Moore equations (S1B Table) and observed age at PHV based on the SITAR model, and likelihood ratio tests for differences between two consecutive models (S1C Table). (DOCX)