Average Growth Curve Research Articles

An evaluation of infants' growth in the Kingdom of Nepal.

The His Majesty's Government/Japan International Cooperation Agency Primary Health Care Project began in April 1993 in collaboration with the Saitama Prefectural Government, for the purpose of improving the health status of the people in model districts of the Kingdom of Nepal. Growth monitoring is one of the basic methods that defines the health and nutritional status of children. Anthropometric indices were measured in 759 children in the Bhaktapur district. We used the World Health Organization prototype growth chart and national growth standard for Japanese children (1990) to analyze the growth data. We found that the average bodyweight growth curve of children up to 4 months of age followed the 50th percentile reference curve. For children of 5-12 months of age, there was a delay in bodyweight gain and the growth curve reached the 3rd percentile curve. For children more than 1 year old, the growth curve moved below the third percentile curve. Catch-up growth did not occur before the children reached 5 years of age. The main causes of catch-up growth being hampered were chronic undernutrition and inadequate nutritional balance. As this was the first opportunity to evaluate infant growth in this district, the first important consequence of the results was to analyze the causes of growth faltering and failure-to-thrive in Nepalese children. Even more important, was the need to give appropriate counseling on improving feeding and other health-related practices, and the most important consequence of all was to instruct Nepalese health workers that utilizing the growth charts is an integral part of health care.

Application of theoretical growth functions for Mongolian oak (Qurcus mongolica)

Four alternative functions are used for fitting tree height and diameter growth models for mongolian oak. (Quercus mongolica Fisch. et Turcz.). The data set includes 1250 random trees and 755 dominant trees coming from 510 temporary plots. The resultsshow that the Richards function is the best model for predicting height. diameter at breast height (DBH) and dominant height from age. The average growth curve of dominant height is used as a guide curve for the construction of a site index table which is partially validated using an independent data set. The Mitscherlich function is the best model for estimating height and dominant height from DBH.

Growth curve models with non-stationary errors

The estimation of growth curves has been extensively studied in both parametric and stationary situations. In this paper we propose the use of a transformation of the time scale that can produce non-stationary covariance structure, with stationarity as a special case. First, we estimate the parameters of the covariance structure using nonlinear least squares, and with these estimators we estimate the average growth curve non-parametrically. We conduct Monte Carlo studies to assess the influence of the number of subjects and the number of observations per subject on the estimation. © 1998 John Wiley & Sons, Ltd.

Kernel regression estimates of growth curves using nonstationary correlated errors

We study the nonparametric estimation of the average growth curve under a very general parametric form of the covariance structure that allows for monotone transformation of the time scale. We also investigate the properties of optimal bandwidth selection methods and compare the results with those obtained under stationarity.

九州北東部沿岸におけるアオギスの年齢と成長

The age and growth of the blue whiting, Sillago parvisquamis, were examined, based upon the ring marks on scales of 248 individuals caught in the coastal waters of Buzen sea (north eastern Kyushu, Fukuoka and Oita Prefecture) from 1992 to 1996. The relationship between the radius of scale (R) and the total length of the fish (T. L.) was shown by the formulae: ??, T. L.=76.576R+24.008, ??, T. L.=70.192R+32.691. Examination of marginal increment of scale showed that the ring mark formed twice in a year, in June and October. The ring mark in June was considered to be a real ring as the spawning season of this fish extends from May to July. The average growth curve was shown by the formulae: ?? : Lt=332.532 [1-exp{0.642(t+0.256)}] ?? : Lt=288.609 [1-exp{-0.577(t+0.479)}]Lt, total length at age; t, age.

Galena lead isotopic variations in a Mesozoic–Cenozoic Andean arc, Antarctic Peninsula

The Antarctic Peninsula magmatic arc was the site of Andean-type subduction from at least Silurian times to the late Cenozoic. Hydrothermal galenas from eight localities in accretionary complex, arc volcanic sequences and plutonic rocks along a strike length of 1100 km have restricted 206 Pb/ 204 Pb, 207 Pb/ 204 Pb and 208 Pb/ 204 Pb compositions (18.628–18.734, 15.599–15.673 and 38.441–38.689 respectively) plotting on crustal average growth curves. The local geological setting, and comparison with Andean leads, suggest that the major source reservoir was isotopically homogeneous sedimentary rocks forming the late Palaeozoic–Triassic accretionary complex. The lead data suggest that old continental basement is absent at least as far south as 65°S. Galenas from a large (13 × 2 km) epithermal vein system on Hurd Peninsula fall in three populations: a main isotopically homogenous array (18.643, 15.647 and 38.503, 2σ = 0.020, 0.020 and 0.050, n = 33) interpreted as a large hydrothermal system that extracted homogenous leads from early Triassic turbidites. Two smaller sub-populations, with more radiogenic 206 Pb/ 204 Pb, are associated with mid- to late Cretaceous intrusive rocks, and may represent either local contributions of magmatic lead or younger hydrothermal episodes. In western Graham Land, two localities associated with mantle-derived mafic intrusions of Cenozoic age have low 207 Pb/ 204 Pb and 208 Pb/ 204 Pb ratios indicating addition of some mantle-type lead.

Extension of the Carter-Yang polynomial growth curve model to allow unique times of measurement for subjects

A PC program extending the procedure due to Carter and Yang (Commun Stat: Theory Methods, 8 (1986) 2507–2526) to allow unique times of measurement for subjects is described, illustrated and made available. Given longitudinal observations on each of N subjects comprising a single group, this program determines the lowest degree polynomial in time adequate to fit the average growth curve (AGC); estimates this curve and provides confidence bands for the AGC, and confidence intervals for the corresponding polynomial regression coefficients; and so-called prediction intervals which, with a given level of confidence, will contain the growth curve of a ‘new’ subject from the same population of which the N subjects constitute a random sample. Two kinds of missing data are accommodated. First, in the context of studies planned so that subjects will be measured at identical times and, second, in unstructured studies where subjects may present with their own, unique times of measurement.

Analysis of longitudinal data in craniofacial research: some strategies.

Although it is generally acknowledged that longitudinal data provide the most information on growth and development and other time-dependent phenomena, such data are often analyzed by conventional (cross-sectional) statistical methods. This widespread practice ignores the distinctive characteristics (e.g., covariance structure) of longitudinal data and may yield misleading results. The purpose of this article is to present some strategies and make available computer programs for the appropriate analysis of longitudinal data. User-friendly PC programs for the estimation of average growth curves, computation of tracking indices, prediction of future values, diagnosis, classification, clustering, estimation of missing values, and testing hypotheses concerning individual and group differences are presented. Benefits of these methods over the usual techniques are illustrated with the example of maxillary growth in the rhesus monkey.

A PC program for computing confidence bands for average and individual growth curves

Dawson et al. ( Am. J. Med. Genet. 7, 529–536, 1980) developed a procedure for constructing confidence bands for both average and individual growth curves which may be of considerable value in the study of growth and development. This paper describes their method for constructing, and provides a menu-driven GAUSS386i program for computing these confidence bands. It is demonstrated how these bands are useful for both the diagnosis and prognostication of growth patterns with known levels of confidence. It is assumed that the study is planned so that individuals will be measured at the same times, but missing data are allowed.

Regression imputation of missing values in longitudinal data sets

A stand-alone, menu-driven PC program, written in GAUSS, which can be used to estimate missing observations in longitudinal data sets is described and made available to interested readers. The program is limited to the situation in which we have complete data on N cases at each of the planned times of measurement t 1, t 2,…, t T ; and we wish to use this information, together with the non-missing values for n additional cases, to estimate the missing values for those cases. The augmented data matrix may be saved in an ASCII file and subsequently imported into programs requiring complete data. The use of the program is illustrated. Ten percent of the observations in a data set consisting of mandibular ramus height measurements for N = 12 young male rhesus monkeys measured at T = 5 time points are randomly discarded. The augmented data matrix is used to determine the lowest degree polynomial adequate to fit the average growth curve (AGC); the regression coefficients are estimated and confidence intervals for them are determined; and confidence bands for the AGC are constructed. The results are compared with those obtained when the original complete data set is used.

Variation in the Life Span and Size of the Freshwater Pearl Mussel

Within the distribution area of the freshwater pearl mussel (Margaritifera margaritifera L.), the maximum observed life span attained in a population varies from 30 to 132 years and the maximum shell length from 80 to 145 mm. For both life-history traits, the growth constant k is a major determinant. The growth constant describes the shape of the average individual growth curve, the lower its value, the slower is the asymptote approached. Maximum size and life span increase as the growth constant declines and the maximum age almost equals the time necessary to complete the growth pattern

Growth patterns of two lines of Angus cattle selected using predicted growth parameters.

Linear functions of body weight and condition score at weaning and 18 mo of age were used to predict the mature weight (A) and maturing rate (k) parameters of an asymptotic growth model of Angus cows at the Subtropical Agricultural Research Station, Brooksville, FL. From 1981 through 1988 a heavy-mature-weight line (Line A) and a rapid-maturing line (Line K) were selected based on predicted A and k values. Linear contrasts (A-K) of least squares means for weight at fixed ages indicated that the weight difference between lines increased from birth to maturity during the period of the study. Animals from Line A were heavier (P less than .01) at all ages. A negative response in maternal ability, relative to increased growth potential of their calves, seems to have occurred in the cows of Line A. Mature weight was reached at approximately 4.5 yr of age in Line K and at approximately 5.5 yr in Line A. Brody's three-parameter and Richards' four-parameter functions were fitted to 2,855 quarterly weights of cows, from birth to 6.5 yr of age, to estimate the average growth curve for each line. Brody's model gave better estimates of weights from 18 mo to maturity, but the asymptotic residual mean squares were slightly higher because early weights were overestimated. Linear and nonlinear regression analyses of weight-age data and comparisons of degree of maturity at different premature ages showed differences in the growth patterns of the two lines selected for early predicted values of A and k.

A PC program for performing multigroup longitudinal comparisons using the Potthoff-Roy analysis and orthogonal polynomials

A PC-program performing the Potthoff-Roy (PR) multigroup ( G-sample) analysis of longitudinal data is described and illustrated. This program and the underlying statistical model are useful in the comparison of several longitudinal samples. Applications include the study of growth, development, adaptation, aging, and treatment effects (in short, any phenomenon in which the passage of time is important) for which serial data are available. Specifically, this method fits polynomials to the average growth curves in the samples, and tests hypotheses concerning the curves themselves and the individual coefficients of the polynomials. The program features the utilization of orthogonal polynomial regression coefficients (OPRCs) and is written in GAUSS, a relatively inexpensive yet comprehensive matrix programming language. It is documented that using OPRCs to comprise the within-individual or time design matrix has several advantages over the more usual choice of the successive-powers-of- t form of this matrix and an example of one important such advantage is provided. GAUSS was employed to make the program readily-accessible (i.e., executable code) to biomedical investigators. The GAUSS compiler is not required to run this program. Information regarding the availability of the program is provided in the Appendix.

Rao's polynomial growth curve model for unequal-time intervals: A menu-driven gauss program

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 hand, 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 have been made, facilitated by recent advances in microcomputer technology. This stand-alone GAUSS program (no compiler necessary) runs on PC-compatibles and is available at a nominal cost. In this report we provide an overview of the statistical model, the general structure of the program, and give an example in which a developmental variable (human upper incisor angulation) is analyzed. Ease of installation and use, speed of execution and color graphic displays of growth curves and confidence bands, and most importantly, suitability to longitudinal data, make this method/program a potentially valuable tool for those interested in growth, development, and treatment effects in humans and other species. Some areas in which this method will have immediate applications are orthodontics, maxillofacial surgery and pediatrics.

Ore lead isotopical composition of Lower Proterozoic volcanogenic sulfide ores at Garpenberg, south central Sweden

Abstract The isotopic composition of ore lead in galena from the volcanogenic sulfide ores at Garpenberg district is presented. Despite of textural, compositional, and mineralogical differences, as well as the variable extent of deformation of the various sulfide ore types, the ores are characterized by a narrow range in lead isotopic composition. Dolomite-hosted ores are commonly more radiogenic than those hosted by skarn or altered volcanic rocks. Compared with the average growth curve of Stacey & Kramers, the ore lead at Garpenberg is slightly enriched in radiogenic lead. The influence of metamorphism on the ore lead composition of galena samples is negligible. The observed trend in the standard diagrams may be explained in terms of a mixing line, where the ore lead was derived from two different crustal sources originally enriched in radiogenic lead (e.g. volcanic and sedimentary rocks). Alternatively, it could represent sulfide ores of slightly different ages derived from a common rock source. The composition of the ore lead in the Garpenberg district displays the typical signature of the volcanogenic sulfide ores in Bergslagen, which at a regional scale is relatively homogeneous and is interpreted as derived from an isotopically well mixed orogen-upper crust reservoir. The results are consistent with a common origin for all the sulfide ore types present in the Garpenberg and Garpenberg Norra deposits. However, at a local scale, minor variations in the ore lead composition can be detected within a particular district or single deposit. These differences may be interpreted as due to the influence of the local lithology on the ore lead or differences in mineralization age. Comparison of the ore lead composition at Garpenberg with that of other volcanogenic sulfide deposits in Bergslagen shows that the Garpenberg, Dammberg, Svärdsjö and Saxberget deposits have a very similar isotopic composition, whereas the Åmmeberg deposit is relatively more radiogenic, probably reflecting a large proportion of sediment-derived lead in the latter deposit. This difference reinforces the classical distinction of the volcanogenic sulfide deposits in Bergslagen into the Falun and Åmmeberg types.

A method for determining the dynamics and intensity of average growth

A new statistical method is presented for determining an average growth curve which is valid in the sense of representing both the average dynamic, or tempo, and the average intensity of the growth process studied. In this context, growth curve means either distance, velocity or acceleration curve. The principal idea is to shift individual curves continuously (and non-linearly) in age to an average developmental age scale. Since the resulting curves represent the typical shape rather than individual variations of it, they are of interest for comparisons of different variables of boys and girls and of subgroups. The method is illustrated with longitudinal growth data from the first Zurich longitudinal study.

Comparison of bite size, biting rate and grazing time of beef heifers from herds distinguished by mature size and rate of maturity.

Sixteen-month-old heifers from herds having known genetic growth patterns were compared for differences in grazing behavior in a 3-yr study. Treatments were heifers from four size-maturity groups defined by the mature size and maturing rate of cow herds in which they originated. Average growth curve parameters indicating mature BW and rate of maturing in these cow herds were 387 kg and .19%/d for treatment Group I; 413 kg and .18%/d for Group II; 468 kg and .15%/d for Group III; and 589 kg and .16%/d for treatment Group IV. Data were from three heifers per treatment group grazing Midland bermudagrass during June and July observation periods. With the exception of the Group II vs Group III comparison, bite size increased with current or mature BW. Biting rate values were similar for all treatment groups but lower than those previously reported on other grass swards. Grazing time increased (P less than .01) in treatment groups defined by larger mature BW. Differences in grazing time for Group IV vs the other treatments and Group I vs Group II and Group III were observed repeatedly; the Group II vs Group III comparison was significant in one period during each of the 3 yr. Diurnal variations in grazing patterns among the treatments were observed. Period of observation affected (P less than .001) bite size and grazing time. These effects were not associated with month but could best be explained by differences in forage height and total mass. Forage availability had a direct influence on bite size, and a compensating effect of longer grazing time with smaller bite size was demonstrated as a regulator of intake. Differences in ingestive behavior were associated with genetic growth patterns in cattle.

Longitudinal principal component analysis of somatic and motor characteristics.

Longitudinal principal component analysis was applied to the study of growth patterns of several somatic and motor characteristics. The data are from the "Leuven Growth Study of Belgian Boys," in which six annual observations were made. Peak growth velocity and age at peak growth velocity for each variable were estimated. The results for height show three components sufficient to provide an adequate representation of the original information. The first component can be interpreted as a growth distance component, which characterizes the general position of an individual growth curve relative to the average growth curve during the period analyzed. Components 2 and 3 reflect fluctuations in percentile level during the age period studied and can be conceived as indices of stability. Component 2 provides additional information about the age at peak height velocity; component 3 characterizes variation in peak height velocity. These interpretations can, in general, be assumed for the other characteristics analyzed.

Determination of growth and maturation in the common frog, Rana temporaria, by skeletochronology

Growth and maturation in a Swiss population of Rana temporaria were studied in 1983 and 1984 by means of skeletochronology. Resting line (growth ring) diameters were used to back‐calculate individual body sizes in previous years; these permitted establishment of an average growth curve and determination of individual ages and sizes at first reproduction. Growth was rapid up to maturation, but continued thereafter at a decreased rate. Males were larger than females at age two but females grew faster thereafter, causing sexual dimorphism in adult body sizes. Body size distributions for both years and for frogs recaptured and first captured in 1984 were established. Growth in immatures was positively, but in adults negatively correlated with body size, with considerable variation at all sizes. Individual adult sizes were positively correlated with body sizes at the end of the first year. Average individual age at first reproduction was 2.8 years in males and 3.1 years in females (range in both sexes two to four years). There is no evidence for a two‐year‐cycle of reproduction.

Lead-isotope compositions of galena in carbonate-hosted deposits of western Newfoundland: evidence for diverse lead sources

Carbonate-hosted zinc and lead deposits occur in two settings in the Humber Terrane of western Newfoundland: (i) associated with dolomitized units and breccias in Cambrian and Ordovician shelf-facies carbonate rocks; and (ii) as open-space, vein, and breccia fillings associated with calcite within or near the margins of Carboniferous basins. We report 11 new lead-isotope analyses from deposits of the former type on the Great Northern Peninsula (the GNP suite) and 8 new analyses from deposits of the latter type on the Port au Port Peninsula and the northern part of the Bay St. George subbasin (BSG suite).The isotopic composition of lead in galena from the GNP suite defines linear trends in which the lead-isotope ratios increase with stratigraphic height in the Cambro-Ordovician sequence. These trends are interpreted as mixing lines; samples at the non-radiogenic end have very low 207Pb/204Pb but high 208Pb/204Pb ratios relative to 206Pb/204Pb and are interpreted as representing substantial evolution in high-grade metamorphic rocks of the Grenville Structural Province that underlie the sedimentary succession. The more radiogenic source(s?) is probably located within the sedimentary pile and contributed metals to the fluids during their migration to the deposition sites.Lead isotopes in deposits in the Bay St. George area cluster near average crustal model growth curves. Metal sources for these deposits, considered by previous workers as diagenetic in origin, are interpreted as being clastic sediments within the sedimentary basin.