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An EHR-based framework for modeling growth curves and constructing growth centile charts for genetic disorders.

Growth modeling is central to human genetics, as deviations from typical growth can signal an underlying disorder. In this cohort study, we developed a generalizable framework for generating growth charts across genetic conditions using electronic health records (EHR). Leveraging 22 years of longitudinal EHR data from 452,470 patients across 15 genetic conditions and unaffected individuals, we generated sex- and condition-specific growth charts using Generalized Additive Models for Location, Scale, and Shape, and quantified differences in size, timing, and intensity using SuperImposition by Translation and Rotation (SITAR). SITAR-derived growth parameters showed strong concordance with established annotations in OMIM and Orphanet, and identified previously unreported growth patterns. We stratified cystic fibrosis by CFTR functional class and observed greater growth impairment in individuals with homozygous minimal-function variants compared to those with residual function. This framework provides a generalizable approach for leveraging EHR data to refine genotype-phenotype relationships and enable continuous updating of growth charts across genetic conditions.

Journal Article

Practical application of generic growth theory and the significance of the growth curve parameters.

The generic growth curve is developed by plausibility arguments based on simple growth models. Parameters of the generic curve include the maximum size, maximum specific growth rate, and a dimensionless velocity constant which can be related to metabolic efficiency in the case of nutrient-limited growth. Parameter estimates are obtained from estimates of the size and time at the point of inflection, the size and time at any other arbitrarily selected point, and the maximum size. Parameter estimates thus obtained and used as initial estimates in nonlinear least squares analysis often give rapid convergence to a minimum error mean square. [For the growth of Escherichia coli K-12 in liquid medium, the generic curve could be simplified to a form containing only three parameters: the maximum specific growth rate, the maximum size, and the time required to reach maximum size. When the bacteria were inhibited by the addition of increasing amounts of the lactoperoxidase antimicrobial factor, there was no significant change in viable counts or maximum specific growth rate, but the time required to reach maximum growth increased linearly with increasing amounts of added antimicrobial factor.] Analysis of growth in terms of the generic growth curve can be a powerful technique for finding relationships which may not be apparent from qualitative consideration of the data.

Biometry

Standard growth curves for achondroplasia.

Standard growth curves for achondroplasia, the most common form of short-limbed dwarfism, have been constructed based on measurements of height, growth velocity, upper and lower segment, and head circumference in 400 achondroplastic dwarfs. These standard curves provide the basis to assess normal growth in these individuals, to aid in the determination of superimposed disorders, and to assess any growth accelerating therapy.

Achondroplasia

A comparison of early fetal growth curves.

The curves of the growth of the maximum fetal diameter and the biparietal diameter before 20 weeks of gestation, measured by ultrasound and derived from a New Zealand population, are presented. They are compared with other published growth curves and reveal that in the New Zealand population there is a greater variation from the mean. In the case of the maximum fetal diameter there is a significantly lower mean after 10 weeks of gestation.

Female

Growth curve of an experimental solid tumor following radiotherapy.

Because it has long been recognized that the growth of most untreated tumors is well described by Gompertzian or exponential growth curves but that the growth of treated tumors has never been well characterized mathematically, we developed and applied an equation that, while not dependent on restrictive assumptions or unmeasurable variables, was nevertheless capable of describing perturbed as well as unperturbed growth. For the 3964A rat hepatoma, a functional relationship between dose level of radiotherapy and growth-curve response was derived and used for predictive purposes. An implied relationship between tumor size and sensitivity to therapy and some clinical implications were examined.

Animals

[The problems that arise when making and using an intra-uterine growth curve (author's transl)].

The author analyses the different intra-uterine growth curves that are described in the literature and shows how in use as reference norms they have a restricted value. The author draws attention to the fact that no other author cited in the literature has used an objective method to control the gestational age of the fetus when making curves. The author demonstrates that in 17.3 p. 100 of cases the gestational age has to be corrected when making his own growth curve and this is done by measuring the bi-parietal diameter early in the pregnancy. He studies the repercussions of this high figure of non-correspondence with the dates at different levels of the curve and the percentage of infants defined as hypotrophic, macrosomic or post-mature.

Female

Growth curves and stabilization of fresh vaccine cultures of the Clemson University strain of Pastuerella multocida.

Growth curves at 37 C for the Clemson University strain of Pasteurella multocida were about the same in either brain-heart-infusion broth or in a recently developed broth called "special broth TV". Counts in both broths were usually greater than 1 x 10(9) viable bacteria per ml. With the addition of 5 g of dried skim milk to each 100 ml of broth culture in the stationary phase of the growth curve, only a slight decrease in viable counts occurred over the next 7 to 14 days when held at 4 C. Such stabilization of broth cultures of P. multocida gives added flexibility to the use of fresh cultures as a live oral turkey cholera vaccine.

Bacterial Vaccines

Analysis of the human growth curve.

Mathematical techniques are well suited to analysis of growth data. In the past there has been much emphasis on the mathematical description of shape and changes of shape as exemplified by the allometric equation. More recently these methods have been less popular and shape analysis has been handled largely by modern multivariate statistical methods. In contrast, there has been an increasing interest in fitting models to size data, related to time. Many such functions have been described; some for small parts of the growth curve and others for the whole growing period. More recently single, non-linear functions have been developed and their properties and use are now described.

Adolescent

Growth curves of anaerobic bacteria in solid media.

Simple pour plate and spectrophotometric techniques for the evaluation of growth curves of several anaerobic bacteria on solid media are described. Three basic patterns of anaerobic growth were observed. The curves obtained were very reproducible when studied on separate occasions. The curves obtained by spectrophotometric measurement were comparable to those obtained by the pour plate method, especially when a large bacterial inoculum was used. Limitations in the interpretation of the results are discussed. The methods and principles reported could provide the basis for the determination of bacterial growth on solid media using other organisms and different experimental conditions.

Agar

A randomization test for comparison of groups of growth curves with different polynomial design matrices.

Well defined methods for comparing mean polynomial growth curves exist when subjects are measured at identical times, modeled with polynomials of identical degree and when multivariate normality of the measurements can be assumed. Relaxing these conditions creates problems solved here for the special case of a completely randomized design by developing a randomization test which is both practical and interval specific. The procedure is applied to longitudinal data from a study of human growth.

Adolescent

Growth curve changes associated with long-term selection for body weight in Japanese quail.

Four quail lines were utilized to investigate growth patterns in quail. Three of these lines (P, T and S) had previously undergone long-term selection for high 4-week body weight, while line C was maintained as a nonselected control. Quail progeny from generation 37 and 38 breeders were fed diets containing 28% and 20% protein. Within each trial, the diet/line treatments were replicated 3 times with 12 quail per subclass. Body weight measurements suggested that the growth of all lines was best approximated by the logistic growth curve model. When fed a 28% protein diet the age at maximum growth (point of inflection) of selected lines was 4 to 6 days earlier than the corresponding age of controls. Similar rates of gain after 4 weeks of age between selected and control lines suggested that mechanisms influenced by selection for 4-week body weight in quail operate only during the period prior to the age at selection with little or no residual effect.

Analysis of Variance

[The growth curves of enterobacteriaceae and the estimation of L-forms under the influence of cephalosporin antibiotics].

The antibacterial effectiveness of cephalothin, cefazolin, cephacetrile and cephradine was investigated on growing cultures of Klebsiella pneumoniae recording the growth curves with a biophotometer. Thereby cefazolin has a greater antibacterial activity than the other cephalosporins. By raising the dose to 100 microgram/ml after initial bactericidal effect a second growth phase was observed. Phase microscopic observation showed that this was caused by an increasing number of L-forms. This phenomenon could be observed with two other strains and seems to be a strain-specific characteristic. It occurs only using cephalosporins and isotonic nutrient media. The medical importance of the described ability of some bacteria as a factor of pathogenicity is discussed.

Cefazolin

Growth curves, microscopic morphology, and subcultures of beta-lactamase-positive and -negative Haemophilus influenzae under the influence of ampicillin and cefamandole.

In contrast to the results obtained with ampicillin, the minimum inhibitory concentrations of cefamandole against Haemophilus influenzae were within the same range (0.5 to 1.5 mug/ml) whether or not the strains were beta-lactamase producers. The minimum bactericidal concentrations were somewhat higher for beta-lactamase-positive strains (6.4 mug/ml) than for negative strains (1.2 mug/ml). In a culture with high initial microbial density, monitored by recording optical densities, the addition of 10 mug of cefamandole per ml brought about rapid lysis of a beta-lactamase-negative strain. Observation of a beta-lactamase-positive strain revealed, in the early part of the growth curve, absence of lysis and an increase of biomass similar to that observed in a drug-free control curve. In contrast to the results obtained with ampicillin, the culture consisted uniformly of spherical forms, probably in the process of division, which were capable of generating colonies. When the microbial density exposed to cefamandole was increased still further, persistent bacillary forms were observed, and after 24 h hydrolysis had eliminated every trace of microbiologically active cefamandole.

Ampicillin

A critical analysis of the double and triple logistic growth curves.

Recently a model of human growth from the age of one year to maturity, based on two logistic terms, has been proposed. The originators of the model claim that it provides biologically meaningful parameters, and allows total growth to be partitioned into a pre-pubertal and an adolescent component. More recently, they have suggested an improved model, with three logistic terms, which gives a better fit. While the double logistic model gives an adequate fit to the observed height curve, differentiating it leads to a height velocity curve which differs considerably from the observed velocity curve. The triple logistic model gives an excellent fit to both the attained height and height velocity curves. Both models, however, imply a considerable time interval during which both the pre-pubertal and adolescent components are simultaneously contributing to growth, a situation that is difficult to justify biologically. The double model should therefore be discarded, and the triple logistic model considered to be of descriptive, rather than of interpretative, value.

Adolescent

A new nonparametric technique for constructing percentiles and normal ranges for growth curves determined from longitudinal data.

A new nonparametric method is proposed for the construction of percentile curves and normal ranges which can be used to classify an individual's growth, velocity, and acceleration of growth dynamically over a time interval selected for its biological importance. Although the procedure requires longitudinal data, it is not necessary that all subjects be measured at identical times. Unlike classic static methods it does not provide percentile curves that are typical of no one. The median curve is the actual curve of the most "central" individual. The method is applicable to growth curves of any form with a general computer program already available for many forms. The technique is demonstrated for growth in weight curves smoothed by high degree polynomials.

Adolescent

A new family of mathematical models describing the human growth curve.

A new family of mathematical functions to fit longitudinal growth data is described. All members derive from the differential equation dh/dt = s(t). (h1-h) where h1 is adult size and s(t) is a function of time. The form of s(t) is given by one of many functions, all solutions of differential equations, thus generating a family of different models. Three versions were compared. All were superior to previously described models. Model 1, in which s(t) was defined by ds/dt = (s1 - s)(s - s0) was especially accurate and robust, containing only five parameters to describe growth in stature from age two to maturity. Derived "biological" parameters such as Peak Height Velocity were very consistent between these three members of the family but, in some cases, differed signficantly from previous estimates.

Body Height