{"paper_id":"1bf38bfc-eb45-4d96-bfb0-22b130ab76e3","body_text":"Correction of LMS Parameter Errors in Published Noonan Syndrome Growth Charts | medRxiv /* */ /* */ <!-- <!-- /*! * yepnope1.5.4 * (c) WTFPL, GPLv2 */ (function(a,b,c){function d(a){return\"[object Function]\"==o.call(a)}function e(a){return\"string\"==typeof a}function f(){}function g(a){return!a||\"loaded\"==a||\"complete\"==a||\"uninitialized\"==a}function h(){var a=p.shift();q=1,a?a.t?m(function(){(\"c\"==a.t?B.injectCss:B.injectJs)(a.s,0,a.a,a.x,a.e,1)},0):(a(),h()):q=0}function i(a,c,d,e,f,i,j){function k(b){if(!o&&g(l.readyState)&&(u.r=o=1,!q&&h(),l.onload=l.onreadystatechange=null,b)){\"img\"!=a&&m(function(){t.removeChild(l)},50);for(var d in y[c])y[c].hasOwnProperty(d)&&y[c][d].onload()}}var j=j||B.errorTimeout,l=b.createElement(a),o=0,r=0,u={t:d,s:c,e:f,a:i,x:j};1===y[c]&&(r=1,y[c]=[]),\"object\"==a?l.data=c:(l.src=c,l.type=a),l.width=l.height=\"0\",l.onerror=l.onload=l.onreadystatechange=function(){k.call(this,r)},p.splice(e,0,u),\"img\"!=a&&(r||2===y[c]?(t.insertBefore(l,s?null:n),m(k,j)):y[c].push(l))}function j(a,b,c,d,f){return q=0,b=b||\"j\",e(a)?i(\"c\"==b?v:u,a,b,this.i++,c,d,f):(p.splice(this.i++,0,a),1==p.length&&h()),this}function k(){var a=B;return a.loader={load:j,i:0},a}var l=b.documentElement,m=a.setTimeout,n=b.getElementsByTagName(\"script\")[0],o={}.toString,p=[],q=0,r=\"MozAppearance\"in l.style,s=r&&!!b.createRange().compareNode,t=s?l:n.parentNode,l=a.opera&&\"[object Opera]\"==o.call(a.opera),l=!!b.attachEvent&&!l,u=r?\"object\":l?\"script\":\"img\",v=l?\"script\":u,w=Array.isArray||function(a){return\"[object Array]\"==o.call(a)},x=[],y={},z={timeout:function(a,b){return b.length&&(a.timeout=b[0]),a}},A,B;B=function(a){function b(a){var a=a.split(\"!\"),b=x.length,c=a.pop(),d=a.length,c={url:c,origUrl:c,prefixes:a},e,f,g;for(f=0;f<d;f++)g=a[f].split(\"=\"),(e=z[g.shift()])&&(c=e(c,g));for(f=0;f<b;f++)c=x[f](c);return c}function g(a,e,f,g,h){var i=b(a),j=i.autoCallback;i.url.split(\".\").pop().split(\"?\").shift(),i.bypass||(e&&(e=d(e)?e:e[a]||e[g]||e[a.split(\"/\").pop().split(\"?\")[0]]),i.instead?i.instead(a,e,f,g,h):(y[i.url]?i.noexec=!0:y[i.url]=1,f.load(i.url,i.forceCSS||!i.forceJS&&\"css\"==i.url.split(\".\").pop().split(\"?\").shift()?\"c\":c,i.noexec,i.attrs,i.timeout),(d(e)||d(j))&&f.load(function(){k(),e&&e(i.origUrl,h,g),j&&j(i.origUrl,h,g),y[i.url]=2})))}function h(a,b){function c(a,c){if(a){if(e(a))c||(j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}),g(a,j,b,0,h);else if(Object(a)===a)for(n in m=function(){var b=0,c;for(c in a)a.hasOwnProperty(c)&&b++;return b}(),a)a.hasOwnProperty(n)&&(!c&&!--m&&(d(j)?j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}:j[n]=function(a){return function(){var b=[].slice.call(arguments);a&&a.apply(this,b),l()}}(k[n])),g(a[n],j,b,n,h))}else!c&&l()}var h=!!a.test,i=a.load||a.both,j=a.callback||f,k=j,l=a.complete||f,m,n;c(h?a.yep:a.nope,!!i),i&&c(i)}var i,j,l=this.yepnope.loader;if(e(a))g(a,0,l,0);else if(w(a))for(i=0;i (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0];var j=d.createElement(s);var dl=l!='dataLayer'?'&l='+l:'';j.src='//www.googletagmanager.com/gtm.js?id='+i+dl;j.type='text/javascript';j.async=true;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-P4HH5NV'); Skip to main content Home About Submit ALERTS / RSS Search for this keyword Advanced Search Correction of LMS Parameter Errors in Published Noonan Syndrome Growth Charts View ORCID Profile Joseph H Chou doi: https://doi.org/10.1101/2025.07.29.25332354 Joseph H Chou 1 Mass General Brigham for Children, Newborn Medicine Harvard Medical School , Boston MA MD PhD Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Joseph H Chou For correspondence: jchou2{at}mgh.harvard.edu Abstract Full Text Info/History Metrics Data/Code Preview PDF Abstract Growth reference curves were recently published by Cappa et al 2024 for children with Noonan Syndrome, including the LMS parameters which should allow calculation of expected values at any centile. However, closer inspection revealed significant problems with the LMS parameters, including calculated values that diverged to infinity or to imaginary numbers. In this brief report, I describe issues found, recalculate the LMS parameters based on the provided expected centile values, and quantify the improvement in performance and identify where the greatest discrepancies were found between the published and re-estimated LMS values. It is hoped that the Cappa et al will provide updated and corrected parameters to allow more confident use of this important clinical resource. Introduction Growth reference curves for Noonan Syndrome were recently developed from a 15-year single center study of 190 participants, including charts for four measures (height velocity, weight, height, and BMI) for males and females 1 . The supplementary materials included expected values at a number of centiles as well as LMS parameters to mathematically recreate the curves at arbitrary centiles 2 . During assessment of an electronic calculator created to facilitate use of these charts, some of the charts exhibited significant discrepancies between the expected values and values and those calculated from the LMS parameters. This short technical brief describes the issues discovered and re-estimates LMS parameters from the reported centile data. Methods Source data was obtained from the Supplementary Tables S1a through S1h 1 and included for each measure, sex, and age the LMS parameters as well as expected measure values at the 3 rd , 10 th , 25 th , 50 th , 75 th , 90 th , and 97 th centiles. The LMS method 2 allows calculation of measurement values X for any given L, M, S, and Z value. The parameters represent the Box-Cox power transformation for normalization of skew (L), the median value (M), and the coefficient of variation (S). Of note a Z score of 0 should represent the median (50 th percentile), as can be seen from the equations ( Figure 1 ). Download figure Open in new tab Figure 1. Calculation of growth measurement X from parameters L, M, S, and Z Those same equations can also be used to re-estimate the LMS parameters, given values of X and Z. To estimate the three LMS parameters, a minimum of three points would be required – seven X / Z pairs were available (from the seven expected centiles) for each LMS parameter. Regression estimation of the LMS parameters was performed using the minpack.lm R package for non-linear least squares regression 3 . Some convenience functions for LMS calculations were taken from the peditools R package 4 . Results Discrepancies calculating values from LMS The eight growth chart curves at the seven centile values were recreated by using the published LMS parameters ( Figure 2 see also Supplementary Materials for larger versions of each panel). While most of the calculated values (red dots) were coincident with the expected centile values (black lines), there were discrepancies seen with the male BMI and weight curves, with the 97 th percentile male BMI curve approaching infinite (and then imaginary) BMI after 17 years, indicating likely problems with the LMS parameters themselves. Less dramatic but clearly visible, the 90 th percentile male BMI and higher percentile male weight curves all showed calculated values diverging away from the expected values. Download figure Open in new tab Figure 2. Discrepancies between reported and calculated values. The reported values for the 3rd, 10th, 25th, 50th, 75th, 90th, and 97th percentile curves are in black; red dots are calculated from the published LMS values; blue dots are calculated from the re-estimated LMS values. By the definition of the LMS parameterization ( Figure 1 ), a Z score of 0 should be identical to the M parameter. Plotting the difference between the M parameter and the reported 50 th percentile for each chart and both genders at all ages revealed internal inconsistencies, most notable for the male BMI and weight curves at higher ages, but also with the female height velocity curve, also at higher ages ( Figure 3 ). Download figure Open in new tab Figure 3. Difference between the reported 50th percentile value and the M parameter, which should be identical. Recalculation of LMS parameters based on reported centile values Assuming that the reported centile values for all the curves were accurate (clearly, the male BMI curve approaching infinity was not accurate), the LMS parameters were re-estimated by least squares nonlinear regression from the seven available X / Z values from the centile curves, for all curves, ages, and sexes. Recreated growth curves The re-estimated LMS values were then used to recreate each of the percentile curves; the blue dots of the calculated values from the re-estimated LMS values now nearly precisely recreate the reported centile values ( Figure 2 ). Quantification of improved prediction The mean absolute error (MAE) and maximum absolute error from the reported percentile values were also calculated for each of the calculated X values from both the originally published and the re-estimated LMS values ( Table 1 ). For all charts, the re-estimated LMS parameters were non-inferior to the published LMS parameters at reproducing the expected values. View this table: View inline View popup Download powerpoint Table 1. Differences between reported values and values calculated from the published ( calc ) vs re-estimated ( est ) LMS values. The mean absolute value of the difference (MAE) and the maximum absolute of the differnece (MAX) are reported. The male BMI discrepancies from the published LMS values could not be calculated because of non-real number results. Comparison of published and re-estimated LMS parameters The difference between the published LMS and the re-estimated LMS parameters was visualized ( Figure 4 ). As expected, the greatest differences were seen in the plots with the greatest discrepancies seen in Figure 2 (red dots), but interestingly, the issues were not consistent for which LMS parameters were predominantly affected: the male BMI L, M, and S parameters; male weight L and M parameters; and female height velocity S parameters seemed to change most when re-estimated. Download figure Open in new tab Figure 4. Differences between published and estimated LMS parameters. Discussion The work of Cappa et al. addresses an important clinical need of evaluating expected growth outcomes in children with Noonan Syndrome, but there were significant inconsistencies between values calculated from the published LMS parameters and the expected percentile values, which compromise the clinical utility of these growth charts. Most critically, the male BMI curve parameters produced mathematically impossible values (infinity and imaginary numbers) at higher ages and percentiles, with similar but less extreme divergence with the male weight curve. The M parameter diverged significantly from the 50th percentile values for male BMI and weight curves at higher ages, with milder divergence for the female height velocity curve. To address these issues, nonlinear regression was used to independently estimate LMS parameters from the published expected percentile values in the supplementary materials. The re-estimated LMS parameters predicted the expected percentiles with substantially improved accuracy. Given that growth charts are clinical tools that could directly impact patient care decisions, I believe it is important to bring these data inconsistencies to the attention of the medical community. Incorrect LMS parameters could lead to misinterpretation of growth patterns in children with Noonan syndrome. I attempted to contact the corresponding author via email in December 2024 and February 2025 to discuss these findings, but received no response. My hope is that the authors consider providing corrected supplementary materials to ensure the clinical utility and accuracy of this important resource. Data Availability All data produced in the present study are available upon reasonable request to the authors Supplementary Materials R code to estimate LMS parameters Download figure Open in new tab Download figure Open in new tab Download figure Open in new tab Example of estimate_LMS_parameters() usage Starting data Download figure Open in new tab View this table: View inline View popup Download powerpoint Convert to long format and percentiles to Z scores Download figure Open in new tab View this table: View inline View popup Download powerpoint View this table: View inline View popup Download powerpoint Estimate LMS parameters Download figure Open in new tab View this table: View inline View popup Download powerpoint Individual plots Individual plots from each panel from Figure 2 . Discrepancies between reported and calculated values. The reported values for the 3 rd , 10 th , 25 th , 50 th , 75 th , 90 th , and 97 th percentile curves are in black; red dots are calculated from the published LMS values; blue dots are calculated from the re-estimated LMS values. Download figure Open in new tab Download figure Open in new tab Download figure Open in new tab Download figure Open in new tab Re-estimated LMS parameters Tables of recalculated L, M, and S growth chart parameters for females and males with Noonan Syndrome (NS) for height velocity, weight, height, and body mass index (BMI), derived from published estimates at the 3rd, 10th, 25th, 50th, 75th, 90th, 97th centiles. View this table: View inline View popup Table. Height velocity (cm/year) for females with NS: Estimated M, S, L parameters from centile values by age (3rd, 10th, 25th, 50th, 75th, 90th, 97th) View this table: View inline View popup Table. Height velocity (cm/year) for males with NS: Estimated M, S, L parameters from centile values by age (3rd, 10th, 25th, 50th, 75th, 90th, 97th) View this table: View inline View popup Table. Weight (kg) for females with NS: Estimated M, S, L parameters from centile values by age (3rd, 10th, 25th, 50th, 75th, 90th, 97th) View this table: View inline View popup Table. Weight (kg) for males with NS: Estimated M, S, L parameters from centile values by age (3rd, 10th, 25th, 50th, 75th, 90th, 97th) View this table: View inline View popup Table. Height (cm) for females with NS: Estimated M, S, L parameters from centile values by age (3rd, 10th, 25th, 50th, 75th, 90th, 97th) View this table: View inline View popup Table. Height (cm) for males with NS: Estimated M, S, L parameters from centile values by age (3rd, 10th, 25th, 50th, 75th, 90th, 97th) View this table: View inline View popup Table. BMI (kg/m²) for females with NS: Estimated M, S, L parameters from centile values by age (3rd, 10th, 25th, 50th, 75th, 90th, 97th) View this table: View inline View popup Table. BMI (kg/m²) for males with NS: Estimated M, S, L parameters from centile values by age (3rd, 10th, 25th, 50th, 75th, 90th, 97th) Footnotes Add full R code for the LMS estimation function (including an example of use) to the Supplementary Materials References 1. ↵ Cappa M , d’Aniello F , Digilio MC , et al. Noonan Syndrome Growth Charts and Genotypes: 15-Year Longitudinal Single-Centre Study . Hormone Research in Paediatrics . Published online July 22, 2024 : 1 – 13 . doi: 10.1159/000540092 OpenUrl CrossRef 2. ↵ Cole TJ . The LMS method for constructing normalized growth standards . European Journal of Clinical Nutrition . 1990 ; 44 ( 1 ): 45 – 60 . OpenUrl PubMed Web of Science 3. ↵ Elzhov TV , Mullen KM , Spiess AN , Bolker B . Minpack.lm: R Interface to the Levenberg-Marquardt Nonlinear Least-Squares Algorithm Found in MINPACK, Plus Support for Bounds .; 2023 . https://CRAN.R-project.org/package=minpack.lm 4. ↵ Chou JH , Roumiantsev S , Singh R . PediTools Electronic Growth Chart Calculators: Applications in Clinical Care, Research, and Quality Improvement . Journal of Medical Internet Research . 2020 ; 22 ( 1 ): e16204 . doi: 10.2196/16204 OpenUrl CrossRef PubMed View the discussion thread. Back to top Previous Next Posted August 06, 2025. Download PDF Data/Code Email Thank you for your interest in spreading the word about medRxiv. NOTE: Your email address is requested solely to identify you as the sender of this article. Your Email * Your Name * Send To * Enter multiple addresses on separate lines or separate them with commas. 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