A PC program for computing confidence bands for average and individual growth curves (original) (raw)
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Growth chart curves do not describe individual growth biology
American Journal of Human Biology, 2007
Growth reference tables present statistical distributions of size for age of individuals within a sample or population. As summaries of phenotypic variability at the group level, they document that individuals grow by different rates during similar time frames. The data are commonly fitted by mathematical functions to produce the convex curves of percentile distributions useful for infant and childhood growth monitoring. In this form, the growth chart appears to be a frame of reference for judging how well an individual infant/child is progressing through time by comparison with peers across ages. This has led to the assumption that individuals should track in these channels during growth. The interpolated lines between the statistical distributions of size for age at the level of the population do not, however, represent how individuals grow. Growing is an individual process characterized by nonlinear episodic saltatory increments that result in shifting size relationships among similarly aged peers over short time intervals. Data from a prospective, longitudinal study of infants illustrate the poor performance of growth chart curves as representations of individual growth. Clarification of the paradigms supporting perceptions of normal growth patterns is useful both practically and theoretically: growth chart patterns have important clinical sequelae when this informs feeding recommendations. Further characterization of individual growth patterns will contribute to increased understanding of both individual growth biology and the nature of adaptability. Am. J. Hum. Biol.
Rao's polynomial growth curve model for unequal-time intervals: a menu-driven GAUSS program
International journal of bio-medical computing, 1991
For lack of alternatives, longitudinal data are often analyzed with cross-sectional statistical methods, for instance, t-tests, ANOVA and ordinary least-squares regression. Appropriate statistical software has been generally unavailable to investigators using serial records to study growth and development or treatment effects. In an earlier paper (Schneiderman and Kowalski, Am. J. Phys. Anthropol., 67 (1985) 323-333.) we described a suitable method, Rao's polynomial growth curve model (Rao, Biometrika, 46 (1959) 49-58), and provided an SAS computer program for the analysis of a single sample of complete longitudinal data. This method included the computation of an average polynomial growth curve, its 95% confidence band, its coefficients and corresponding confidence intervals. The present paper extends this method to accommodate a sample with observations made at unequal time-intervals. Significant improvements in the accessibility, operation and user-friendliness of the program...
An interactive computer program for the analysis of growth curves
Computers and Biomedical Research, 1987
An interactive FORTRAN program, MUDIFT, is presented. This program was designed to perform a multivariate distribution-free significance test for the comparison of growth curves. Such a test, not assuming functional forms of individual growth, has proved useful when the variety of observed growth curves was too broad to be represented by the family of growth functions and when there were incomplete observations. A numerical example illustrates the use of MUDIFI to analyze serial data pertaining to the measurable solid tumors in 20 mice treated with liposome incorporated muramyltripeptide phosphatidylethanolamine and a control group of 30 mice. The tumor volumes were recorded weekly for 10 weeks following initial entry into the research protocol. The test hypothesis was whether the tumors grew slower in the treated group than in the control group. The test statistic, an asympotically x2 statistic, was 7.312 with df = 2, which was significant at (Y = 0.05. o 1987 Academic Press. Inc. I This project has been funded at least in part with Federal funds from the Department of Health and Human Services, under Contract Number NOl-CO-23912 with Information Management Services, Inc. The contents of this publication do not necessarily reflect the views or policies of the Department of Health and Human Services, nor does mention of trade names, commercial products, or organizations imply endorsement by the U.S. Government.
Implementation of Hills' growth curve analysis for unequal-time intervals using GAUSS
American Journal of Human Biology, 1989
Longitudinal data are widely regarded as the most efficient and informative type of data with which to investigate growth. Paradoxically, appropriate statistical methods for analyzing longitudinal data have been unavailable; with the exception of a computer program for executing Rao's (Biometrika 46:49-58,1959) one-sample polynomial growth curve analysis (Schneiderman and Kowalski, Am. J . Phys. Anthropol. 67:323-333,1985) and another applying the Preece-Baines function (Brown and Townsend, Ann. Hum. Biol. 9~495-505, 1982), no programs for analyzing longitudinal data are generally available to the scientific community. Whereas much of the pediatrically oriented work has involved fitting growth curves for individual children, the concern here is the estimation of growth trends for populations. An adequate understanding of average tendencies is a prerequisite to understanding the growth of individuals. The present paper implements Hills' analysis, which is formally equivalent to Rao's but uses finite differences instead of orthogonal polynomials. This method is suitable for data collected at unequal time points and generates explicit measures of velocity and acceleration. The polynomial specification of the curve that best fits the data is also determined with this method. An additional advantage of this approach is that it is conceptually simpler than the classic model of Rao. An application of this method is given using the same craniofacial growth data as in our earlier (1985) paper for comparabil-
grofit: Fitting Biological Growth Curves with R
The grofit package was developed to fit many growth curves obtained under different conditions in order to derive a conclusive dose-response curve, for instance for a compound that potentially affects growth. grofit fits data to different parametric models and in addition provides a model free spline method to circumvent systematic errors that might occur within application of parametric methods. This amendment increases the reliability of the characteristic parameters (e.g.,lag phase, maximal growth rate, stationary phase) derived from a single growth curve. By relating obtained parameters to the respective condition (e.g.,concentration of a compound) a dose response curve can be derived that enables the calculation of descriptive pharma-/toxicological values like half maximum effective concentration (EC50). Bootstrap and cross-validation techniques are used for estimating confidence intervals of all derived parameters.
Demystifying LMS and BCPE methods of centile estimation for growth and other health parameters
Indian Pediatrics, 2014
Lambda-Mu-Sigma and Box-Cox Power Exponential are popular methods for constructing centile curves but are difficult to understand for medical professionals. As a result, the methods are used by experts only. Non-experts use software as a blackbox that can lead to wrong curves. This article explains these methods in a simple non-mathematical language so that medical professionals can use them correctly and confidently.
Canadian Journal of Fisheries and Aquatic Sciences, 2007
A way to explicitly incorporate ageing error into the estimation of von Bertalanffy growth function (VBGF) parameters using a random effects (RE) modeling framework is presented. This RE framework also accounts for the effects of selectivity on growth curve estimation by characterizing the distribution of true ages derived from multiple age reads using either an exponential or gamma distribution. Simulation testing across four life histories is used to compare the RE approach with standard nonlinear (SNL) approaches that use the primary, average, or median ages in growth estimation. Sensitivity tests compare the effects of assumed length and ageing error, selectivity, and recruitment variability on the estimation of growth curve parameters. Results support the use of the RE method using a gamma distribution over the SNL methods because RE method estimates of VBGF growth parameters were more precise across life histories and sensitivity trials. This general approach can be applied and expanded to other growth models. Applications demonstrate that the results from RE methods may differ in biologically important ways to those obtained from SNL approaches.
Automatic analysis of longitudinal growth data on the website willi-will-wachsen.de
HOMO - Journal of Comparative Human Biology, 2003
Many disorders of child development can only be treated successfully when they are detected early. Thus, child development should be checked periodically. Usually, a few parameters are sufficient to check whether or not a child is developing normally in terms of growth. By making such checks publicly available on the website: willi-will-wachsen.de the authors hope to provide a tool which helps the automatisation of simple check procedures and thereby detect with less effort more children with growth disorders.
Examining Growth with Statistical Shape Analysis and Comparison of Growth Models
Journal of Modern Applied Statistical Methods, 2012
Growth curves have been widely used in the fields of biology, zoology and medicine for assessing some measurable trait of an organism, such as height, weight, area or volume. In statistical shape analysis, a size measure is obtained using the geometrical information of an object as opposed to linear measurements. The performances of commonly used non-linear growth curves are compared by using centroid size as a size measure in a simulation study. An example is provided on the relationship between centroid size of the cerebellum and disease duration in multiple sclerosis patients.