Using SITAR (SuperImposition by Translation and Rotation) to estimate age at peak height velocity in Avon Longitudinal Study of Parents and Children

Puberty is a time of substantial biological and psychological changes. One of the hallmarks of puberty is a rapid growth spurt, however its timing varies between individuals. The impact of pubertal timing on later health outcomes has been of interest in life course epidemiology, however its measurement can be challenging. Age at peak height velocity (aPHV) offers an objective measure of pubertal timing without having to rely on physical examination or self-report. We describe the derivation of aPHV estimates in Avon Longitudinal Study of Parents and Children (ALSPAC) offspring, using Superimposition by Translation And Rotation (SITAR) mixed effects growth curve analysis. ALSPAC is a rich source of phenotypic and genotypic data and given the importance of pubertal timing for later health outcomes, these data offer an opportunity to explore the determinants and consequences of aPHV.


Introduction
Puberty is a period of significant biological and psychological changes in human development. One of its hallmarks includes a rapid growth spurt, the timing and speed of which varies between individuals, with marked sexual dimorphism.
The relationship of pubertal timing with adverse health outcomes in later life has been investigated previously 1 . For example, previous studies reported an association between late menarche and increased risk of osteoporosis 2 , whereas early pubertal timing has been found to be related to higher risk of obesity and cardiovascular disease in both men and women 3 . Thus, investigating the influences of pubertal timing and understanding its relationship with later health outcomes is of great public health importance. While clinical assessment remains the gold standard for the assessment of pubertal status, this is difficult to achieve in large-scale studies. Self-reported puberty measures lack reliability 4,5 , and may be unpopular with study participants, potentially leading to large amounts of missing data. Another measure, age at peak height velocity (aPHV) provides an objective and non-invasive assessment of pubertal status.
The Avon Longitudinal Study of Parents and Children (ALSPAC) is a longitudinal birth cohort, which was established in the 1990s in the South West of England 6 . ALSPAC is a rich source of data, including phenotypic and genetic data collected for the mothers, fathers and children.
This paper describes the application of Superimposition by Translation And Rotation (SITAR) mixed effects growth curve model (described previously by Cole et al. 7 ) for analysis of height in puberty and estimating aPHV in ALSPAC offspring which resulted in a new dataset being generated. Previous studies have shown this to be a suitable method for estimating aPHV 8 , even with fairly sparse data 9 .

Methods
ALSPAC recruited a total of 14,541 pregnant women with expected delivery date between 1 st April 1991 and 31 st December 1992. Of these pregnancies, 69 have no known birth outcome, and of these 14,472 pregnancies, 195 were twin, 3 were triplet and 1 was quadruplet accounting for 14,676 known foetuses. These pregnancies resulted in 14,062 live births of which 13,988 children were alive at 1 year of age 6 .
In order to increase sample size additional recruitment took place when the children were on average 7 years old (Phase II) and again between age 8 -18 years (Phase III) resulting in a total of 15,247 enrolled pregnancies, of which 14,701 were alive at 1 year of age. For more details regarding eligibility and recruitment please refer to Boyd et al. 6 . These children have been followed up from birth (those recruited during Phases II and III were followed up from the time they joined the study) and data collection included questionnaires and clinical assessments. For the purpose of estimating age at PHV, only height measurements obtained by trained fieldworkers during assessment clinics were used. These clinics encompassed 'children in focus clinics' (CIF) to which a random 10% subsample of children were invited between the ages of 2 and 5 years, and six assessment clinics in late childhood (between age 7 and 13 years) to which all enrolled children were invited, three further assessment clinics in adolescence (ages 13, 15 and 17 years) to which all enrolled participants were invited. These data were restricted to include height measurements collected when the children were between 5 to 20 years of age which resulted in a total of 61,290 height measurements available for 10,236 participants of whom 5,099 were female and 5,137 were male. To maximise accuracy of the estimate of aPHV, these data were further restricted to include individuals with at least one height measurement for the following time periods: 5 to <10 years, 10 to < 15 years and 15 to 20 years (representing the pre-, peri-and post-pubertal periods for the majority of children). A total of 46,246 height measurements for 5,707 individuals (3,019 females, 2,688 males) were available for SITAR analysis.
SITAR is a mixed effects shape-invariant growth curve model, consisting of a mean growth curve along with three transformations (size, tempo and velocity), used to describe how each individual differs from the mean curve. The three SITAR parameters are size, reflecting up/down shift from the mean curve; tempo, reflecting left/right shift (on the age scale) which corresponds to the relative timing of puberty based on aPHV, and velocity reflecting stretching/shrinking of the age scale and hence describing differences in the rate at which individuals pass through puberty. For a detailed description of the method please refer to Cole et al. 7 .
Following initial cleaning of height data (at least one height measurement available at each of the time periods: 5-<10 years, 10-<15 years and 15-20 years), as described above, the data were uploaded into R for further cleaning. Firstly, outliers with velocity exceeding 4 SDs in absolute value from the median for the dataset were removed (using velout and zapvelout functions; for more details see sitar package documentation in R 10 ), and initial SITAR model was subsequently fitted, for males

Amendments from Version 1
We considered reviewers comments and revised our manuscript accordingly. The following changes have been made: selection criteria for participant selection clarified (see 3 rd and 5 th paragraph of methods section), utility of SITAR measures highlighted (1 st paragraph of dataset validation section), units have been added to Figure 2 and Figure 3 and numerical discrepancy regarding final number of heights available corrected.

REVISED
and females separately, in R version 3.4.1. Secondly, standardized residuals exceeding 4 in absolute value were removed leaving a total of 45,065 height measurements for 5,707 individuals available for analysis with an average of 8 measurements (range 1-10 measurements) available per participant (see Figure 1 for details regarding participant recruitment). Of male and female participants in the final model, 32 (1.2%) and 18 (0.6%) had less than three height measurements, respectively.

Dataset validation
The final SITAR model was fitted with 5 degrees of freedom, for males and females separately, and it explained 98% and 98.3% of variance in the dataset for males and females, respectively. Mean aPHV (SD) was 13.6 (0.9) for males ( Figure 2) and 11.7 (0.8) for females ( Figure 3) and these estimates are similar to those reported in the literature 11,12 . The rich phenotype data available in ALSPAC provides unique opportunity to explore an extensive range of both determinants and consequences of aPHV; the aPHV variable could further be utilised as a confounder or mediator in a wide range of analyses. However, it needs to be noted that any findings may not generalise to non-white populations owing to >90% of sample being of White ethnic origin. Table 1 shows mean and SD of additional variables that were estimated, which include: size (cm) (negative values indicating smaller whereas positive taller children and zero represents the mean), tempo (years) (negative values indicating early puberty, positive late puberty and zero represents the mean), velocity (years) (measure of intensity, positive values indicating short growth spurt, zero corresponding to mean velocity) along with peak velocity (cm) which measures the intensity of the pubertal growth spurt and aPHV measures its timing.

Ethical approval and consent
Ethical approval for the study was obtained from the ALSPAC Ethics and Law Committee and the Local Research Ethics Committees, full details of the approvals obtained are available from the study website (http://www.bristol.ac.uk/alspac/researchers/ research-ethics/). Written informed consent was obtained from parents, and children were invited to give consent where appropriate. Study members have the right to withdraw their consent for elements of the study or from the study entirely at any time.

Figure 2. Mean growth curve (solid line) and velocity (dashed line) plots estimated by SuperImposition by Translation and Rotation
(SITAR) for males. Vertical dotted line represents mean age at peak height velocity.

Data availability
ALSPAC data access is through a system of managed open access. The steps below highlight how to apply for access to the data included in this data note and all other ALSPAC data. The dataset generated in this data note has been deposited within the ALSPAC data resource and is linked to ALSPAC project number B2325. Please quote this number to request required variables which have been described in this dataset (size, tempo, velocity, aPHV and peak velocity).

Please read the ALSPAC access policy (PDF, 627kB)
which describes the process of accessing the data and samples in detail, and outlines the costs associated with doing so.
2. You may also find it useful to browse our fully searchable research proposals database, which lists all research projects that have been approved since April 2011.
3. Please submit your research proposal for consideration by the ALSPAC Executive Committee using the online process. You will receive a response within 10 working days to advise you whether your proposal has been approved.
If you have any questions about accessing data, please email alspac-data@bristol.ac.uk.
The ALSPAC data management plan describes in detail the policy regarding data sharing, which is through a system of managed open access. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.  Frysz and colleagues provide a valuable Data Note, describing the calculation of age at peak height velocity and associated parameters using the SITAR technique (reference 7 in the paper) in the ALSPAC cohort. This technique reduces the complex information inherent in longitudinal measures of anthropometry to a smaller number of biologically-interpretable parameters. The authors have clearly reported the methods used and we anticipate that the availability of these new growth parameters, alongside the information provided in this Data Note, will add significant value to the ALSPAC dataset as an epidemiological resource for the study of timing of puberty.

Grant information
We noted that the authors have removed outliers with velocity exceeding 4SDs which appears to be a reasonable method of dealing with clear measurement error. However, it leads to questions as to whether there were any individuals with velocity below -4SDs, or size or tempo parameters below -4SDs or above +4SDs. Why did the authors only remove those with velocity exceeding 4SDs?
The analyses in this paper were restricted to participants with at least one height measurement in the time periods 5 to <10 years, 10 to <15 years and 15 to <20 years. Could the authors describe why they chose these age brackets? Also, the Methods of the paper could clarify that the assessment clinics in late childhood and adolescence are were not restricted to the 10% 'children in focus' sample; currently the description is somewhat ambiguous.
Once the SITAR parameters of size, tempo and velocity have been calculated, two further variables have been created for each individual; 'peak height velocity' and 'age at peak height velocity'. It would be helpful if the authors could state specifically that these have been generated since age at peak height velocity is likely to be the output of greatest utility to future analysts using these data. There is also potential confusion within the manuscript that 'peak height velocity' and 'age at peak height velocity' both sound rather similar to the SITAR 'velocity' parameter -the authors might clarify that they are separate variables. In Table 1, the units for peak velocity should presumably be cm/year. Also, it would be useful if all three of the axes in Figures 2 and 3 had units added.
We noted two numerical discrepancies within the paper. Firstly the text describes 14,541 pregnant women recruited to the ALSPAC study, whereas 14,676 enrolled foetuses are shown in Figure 1; this difference doesn't appear to be attributable to multiple births. Secondly, the numbers of male and female measurements available for SITAR modelling in Figure 1 do not add to the total number of measurements (i.e. 20,849 + 24,216 ≠ 40,037).
The paper describes how 46,246 height measurements were available before considering potential The paper describes how 46,246 height measurements were available before considering potential measurement error. Outliers were removed with absolute velocity exceeding 4SDs and after initial model fitting those with absolute standardised residuals exceeding 4SDs were also removed. This left 40,037 height measurements available for SITAR modelling, a reduction of 13%. Since 0.006% of a normal distribution lies below -4SDs or above 4SDs, this is a surprising reduction in number of measurements, even in the context of a significant amount measurement error; a comment on this would be helpful.
The abstract ends with a helpful allusion to the opportunities afforded by these new measures available in the ALSPAC study. It would enhance the paper if the end of the Methods section could similarly describe how these measures might be used in the future. In particular the rich phenotype data available in ALSPAC provides the opportunity to consider an extensive range of both determinants and consequences of age at peak height velocity; the age at peak height velocity variable could further be utilised as a confounder or mediator in a wide range of analyses.
In addition we note the following minor points of wording: The second line of the second column of page 3 would better read "between the ages of 2 and 5 years".
Similarly, the ninth line of the second column of page 3 might be better worded "To maximise accuracy of the estimate of aPHV,".

Are the datasets clearly presented in a useable and accessible format? Yes
No competing interests were disclosed. Competing Interests:

Referee Expertise: Statistics, epidemiology
We have read this submission. We believe that we have an appropriate level of expertise to confirm that it is of an acceptable scientific standard.
Author Response 10 Dec 2018 , University of Bristol, UK

Monika Frysz
We noted that the authors have removed outliers with velocity exceeding 4SDs which appears to be a reasonable method of dealing with clear measurement error. However, it leads to questions as to whether there were any individuals with velocity below -4SDs, or size or tempo parameters below -4SDs or above +4SDs. Why did the authors only remove those with velocity exceeding 4SDs?
We thank the referee for their helpful comments.

We thank the referee for their helpful comments. Prior to final SITARmodelling the data were uploaded into R and examined for outliers. Both velocity outliers and standardized residuals exceeding 4 SDs in absolute value were removed (as previously described by Cole et al [1]) -this has now been clarified in the manuscript. Individuals with size or tempo parameters below -4SDs or above +4SDs were not excluded.
The analyses in this paper were restricted to participants with at least one height measurement in the time periods 5 to <10 years, 10 to <15 years and 15 to <20 years. Could the authors describe why they chose these age brackets? Also, the Methods of the paper could clarify that the assessment clinics in late childhood and adolescence are were not restricted to the 10% 'children in focus' sample; currently the description is somewhat ambiguous.
The time periods 5 to <10 years, 10 to <15 years and 15 to <20 years were select to represent at least one pre-pubertal, one peri-pubertal, and one post-pubertal measurement for most children. Thank you for your comment re 'children in focus clinics' sample-the assessment clinics in late childhood and adolescence were not restricted to the 10% 'children in focus' sample. The sentence has now been edited to add clarity: These clinics encompassed 'children in focus clinics' (CIF) to which a random 10% subsample of children were invited between the ages of 2 and 5 years, and six assessment clinics in late childhood (between age 7 and 13 years) to which all enrolled children were invited, three further assessment clinics in adolescence (ages 13, 15 and 17 years) to which all enrolled participants were invited.
Once the SITAR parameters of size, tempo and velocity have been calculated, two further variables have been created for each individual; 'peak height velocity' and 'age at peak height velocity'. It would be helpful if the authors could state specifically that these have been generated since age at peak height velocity is likely to be the output of greatest utility to future analysts using these data. There is also potential confusion within the manuscript that 'peak height velocity' and 'age at peak height velocity' both sound rather similar to the SITAR 'velocity' parameter -the authors might clarify that they are separate variables. In Table 1, the units for peak velocity should presumably be cm/year. Also, it would be useful if all three of the axes in Figures 2 and 3 had units added.

Thank you for your comments. We have now updated the manuscript and edited the table and figures.
We noted two numerical discrepancies within the paper. Firstly the text describes 14,541 pregnant women recruited to the ALSPAC study, whereas 14,676 enrolled foetuses are shown in Figure 1; this difference doesn't appear to be attributable to multiple births. Secondly, the numbers of male and female measurements available for SITAR modelling in Figure 1 do not add to the total number of measurements (i.e. 20,849 + 24,216 ≠ 40,037).  195 were twin, 3 were triplet and 1 was quadruplet). The total number of height measurements for both males and females has now been corrected in the main body of text and in the flow chart.
The paper describes how 46,246 height measurements were available before considering potential The paper describes how 46,246 height measurements were available before considering potential measurement error. Outliers were removed with absolute velocity exceeding 4SDs and after initial model fitting those with absolute standardised residuals exceeding 4SDs were also removed. This left 40,037 height measurements available for SITAR modelling, a reduction of 13%. Since 0.006% of a normal distribution lies below -4SDs or above 4SDs, this is a surprising reduction in number of measurements, even in the context of a significant amount measurement error; a comment on this would be helpful.
Thank you for your comments regarding the final number of heights available for SITAR modelling. We can confirm that the number of heights has now been corrected. The final sample available for SITAR modelling was 45,065 (not 40,037), a reduction of 2.6%.
The abstract ends with a helpful allusion to the opportunities afforded by these new measures available in the ALSPAC study. It would enhance the paper if the end of the Methods section could similarly describe how these measures might be used in the future. In particular the rich phenotype data available in ALSPAC provides the opportunity to consider an extensive range of both determinants and consequences of age at peak height velocity; the age at peak height velocity variable could further be utilised as a confounder or mediator in a wide range of analyses.

Thank you for your useful comments regarding the opportunities afforded by a generation of pubertal measures in ALSPAC. We have edited the manuscript accordingly:
The rich phenotype data available in ALSPAC provides unique opportunity to explore an extensive range of both determinants and consequences of age at peak height velocity; the age at peak height velocity variable could further be utilised as a confounder or mediator in a wide range of analyses.
In addition we note the following minor points of wording: The second line of the second column of page 3 would better read "between the ages of 2 and 5 years". Similarly, the ninth line of the second column of page 3 might be better worded "To maximise accuracy of the estimate of aPHV,".
Thank you for your comments. We confirm that the manuscript has been edited. SITAR, a recently developed modelling approach by Tim Cole , has been used increasingly in longitudinal studies to describe secular and population trends in childhood growth and pubertal development using skeletal development (Tanner RUS score) and aPHV in both poorly-and well-resourced communities . Its advantages are that it assesses each individual's curve against the mean curve and is able to determine the size (amplitude of change), tempo (the timing of the onset of change) and velocity (rate of change) of each individual curve in relation to the mean curve. It is also robust with missing data. Cole in a paper published this year assessed the interval required between height measurements in individual adolescent children to optimize the determination of aPHV . Cole concluded that height measurements need not be taken more frequently than biennially to obtain an accurate assessment of the average aPHV.
The reviewers have a few minor comments, which might help to provide further clarity on the participants included in the cohort. The authors describe the recruitment of participants from the ALSPAC cohort and the inclusion criteria for height measurements to be included into the database used for this particular aspect of the study. It is however unclear if black or Asian children were included in the analytical cohort sample. The reason for this comment is that data are available to suggest the age of pubertal development and aPHV in black children may differ from that of white children living in both well-and poorly-resourced countries . Thus their inclusion might have influenced the mean values of aPHV obtained and the subsequent comparisons with other cohorts.
The inclusion of an individual into the SITAR study required that at least one height measurement was available at each of three different time periods, 5-<10 years, 10-<15 years and 15-20 years. Yet in their analysis of the average number of measurements available per individual, the average is given as 8 with a range from 1-10. It is unclear how children with only one measurement were included based on the criteria for inclusion given above. It is possible that the authors meant that the participants included had at least one measurement in any of the age bands.
In the second paragraph of the Methods section, line 3, Phase II is referred to as being between age 8 -18 years. We believe this should be Phase III.

Are the datasets clearly presented in a useable and accessible format? Yes
No competing interests were disclosed.

Competing Interests:
We have read this submission. We believe that we have an appropriate level of expertise to confirm that it is of an acceptable scientific standard.
Author Response 10 Dec 2018 , University of Bristol, UK

Monika Frysz
The reviewers have a few minor comments, which might help to provide further clarity on the participants included in the cohort. The authors describe the recruitment of participants from the ALSPAC cohort and the inclusion criteria for height measurements to be included into the database used for this particular aspect of the study. It is however unclear if black or Asian children were included in the analytical cohort sample. The reason for this comment is that data are available to suggest the age of pubertal development and aPHV in black children may differ from that of white children living in both well-and poorly-resourced countries . Thus their inclusion might have influenced the mean values of aPHV obtained and the subsequent comparisons with other cohorts. the small proportion of individuals from ethnic minorities in this sample, this is unlikely to have influenced estimates reported in our manuscript. A comment regarding generalisability has also been added to the manuscript: However, it needs to be noted that any findings may not generalise to non-white populations owing to >90% of sample being of White ethnic origin.
The inclusion of an individual into the SITAR study required that at least one height measurement was available at each of three different time periods, 5-<10 years, 10-<15 years and 15-20 years. Yet in their analysis of the average number of measurements available per individual, the average is given as 8 with a range from 1-10. It is unclear how children with only one measurement were included based on the criteria for inclusion given above. It is possible that the authors meant that the participants included had at least one measurement in any of the age bands.
The inclusion criteria described (at least one height measurement available at each of the time periods: 5-<10 years, 10-<15 years and 15-20 years) applied to a sample selected prior to SITAR modelling. These data were further cleaned, following the initial fitting of the model, and outliers with velocity and standardized residuals exceeding 4 were removed. As a result, individual height measurements were removed (rather than individual participants). Of males and females included in the final sample, 32 (1.2%) and 18 (0.6%) had less than 3 height measurements, respectively.
In the second paragraph of the Methods section, line 3, Phase II is referred to as being between age 8 -18 years. We believe this should be Phase III.
Thank you for your comment -the manuscript has now been edited.
No competing interests were disclosed. Competing Interests: