Non-parametric estimation of age-related centiles over wide age ranges

ISCEV standard pattern reversal VEP development: paediatric reference limits from 649 healthy subjects

PURPOSE

To establish the extent of agreement for ISCEV standard reference pattern reversal VEPs (prVEPs) acquired at three European centres, to determine any effect of sex, and to establish reference intervals from birth to adolescence.

METHODS

PrVEPs were recorded from healthy reference infants and children, aged 2 weeks to 16 years, from three centres using closely matched but non-identical protocols. Amplitudes and peak times were modelled with orthogonal quadratic and sigmoidal curves, respectively, and two-sided limits, 2.5th and 97.5th centiles, estimated using nonlinear quantile Bayesian regression. Data were compared by centre and by sex using median quantile confidence intervals. The 'critical age', i.e. age at which P100 peak time ceased to shorten, was calculated.

RESULTS

Data from the three centres were adequately comparable. Sex differences were not clinically meaningful. The pooled data showed rapid drops in P100 peak time which stabilised by 27 and by 34 weeks for large and small check widths, respectively. Post-critical-age reference limits were 87-115 ms and 96-131 ms for large and small check widths, respectively. Amplitudes varied markedly and reference limits for all ages were 5-57 μV and 3.5-56 μV for large and small check widths, respectively.

CONCLUSIONS

PrVEP reference data could be combined despite some methodology differences within the tolerances of the ISCEV VEP Standard, supporting the clinical benefit of ISCEV Standards. Comparison with historical data is hampered by lack of minimum reporting guidelines. The reference data presented here could be validated or transformed for use elsewhere.

Reference ranges for clinical electrophysiology of vision

INTRODUCTION

Establishing robust reference intervals for clinical procedures has received much attention from international clinical laboratories, with approved guidelines. Physiological measurement laboratories have given this topic less attention; however, most of the principles are transferable.

METHODS

Herein, we summarise those principles and expand them to cover bilateral measurements and one-tailed reference intervals, which are common issues for those interpreting clinical visual electrophysiology tests such as electroretinograms (ERGs), visual evoked potentials (VEPs) and electrooculograms (EOGs).

RESULTS

The gold standard process of establishing and defining reference intervals, which are adequately reliable, entails collecting data from a minimum of 120 suitable reference individuals for each partition (e.g. sex, age) and defining limits with nonparametric methods. Parametric techniques may be used under some conditions. A brief outline of methods for defining reference limits from patient data (indirect sampling) is given. Reference intervals established elsewhere, or with older protocols, can be transferred or verified with as few as 40 and 20 suitable reference individuals, respectively. Consideration is given to small numbers of reference subjects, interpretation of serial measurements using subject-based reference values, multidimensional reference regions and age-dependent reference values. Bilateral measurements, despite their correlation, can be used to improve reference intervals although additional care is required in computing the confidence in the reference interval or the reference interval itself when bilateral measurements are only available from some of subjects.

DISCUSSION

Good quality reference limits minimise false-positive and false-negative results, thereby maximising the clinical utility and patient benefit. Quality indicators include using appropriately sized reference datasets with appropriate numerical handling for reporting; using subject-based reference limits where appropriate; and limiting tests for each patient to only those which are clinically indicated, independent and highly discriminating.

Normal Percentiles for Respiratory Rate in Children-Reference Ranges Determined from an Optical Sensor

(1) Background: Increased respiratory rates (RRs) are described in several medical conditions, including pneumonia, bronchiolitis and asthma. There is variable methodology on how centiles for RR are derived in healthy children. Available age percentiles for RR have been generated using methods that have the potential themselves to alter the rate. (2) Methods: An optical respiratory sensor was used to measure RR. This technique enabled recording in awake children without the artefact of the observer's presence on the subject's RR. A cross-sectional sample of healthy children was obtained from maternity wards, childcare centres and schools in Brisbane, Queensland, Australia. (3) Results: RRs were observed in 560 awake and 103 sleeping children of which data from 320 awake and 94 sleeping children were used to develop centile charts for children from birth to 13 years of age. RR is higher when children are awake compared to asleep. There were significant differences between awake and sleeping RR in young children. The awake median RR was 59.3 at birth and 25.4 at 3 years of age. In comparison, the median sleeping RR was 41.4 at birth and 22.0 at 3 years. (4) Conclusions: The centile charts will assist in determining abnormal RRs in children and will contribute to further systematic reviews related to this important vital sign. This is particularly in relation to the data on children aged from 0 to 3 years, where data are presented on both the awake and sleeping state. Many studies in the literature fail to acknowledge the impact of sleep state in young children on RR.

A two-part model for reference curve estimation subject to a limit of detection

Reference curves are commonly used to identify individuals with extreme values of clinically relevant variables or stages of progression which depend naturally on age or maturation. Estimation of reference curves can be complicated by a technical limit of detection (LOD) that censors the measurement from the left, as is the case in our study of reproductive hormone levels in boys around the time of the onset of puberty. We discuss issues with common approaches to the LOD problem in the context of our pubertal hormone study, and propose a two-part model that addresses these issues. One part of the proposed model specifies the probability of a measurement exceeding the LOD as a function of age. The other part of the model specifies the conditional distribution of a measurement given that it exceeds the LOD, again as a function of age. Information from the two parts can be combined to estimate the identifiable portion (i.e. above the LOD) of a reference curve and to calculate the relative standing of a given measurement above the LOD. Unlike some common approaches to LOD problems, the two-part model is free of untestable assumptions involving unobservable quantities, flexible for modeling the observable data, and easy to implement with existing software. The method is illustrated with hormone data from the Third National Health and Nutrition Examination Survey.

Construction of the World Health Organization child growth standards: selection of methods for attained growth curves

The World Health Organization (WHO), in collaboration with a number of research institutions worldwide, is developing new child growth standards. As part of a broad consultative process for selecting the best statistical methods, WHO convened a group of statisticians and child growth experts to review available methods, develop a strategy for assessing their strengths and weaknesses, and discuss methodological issues likely to be faced in the process of constructing the new growth curves. To select the method(s) to be used, the group proposed a two-stage decision-making process. First, to select a few relevant methods based on a list of set criteria and, second, to compare the methods using available tests or other established procedures. The group reviewed 30 methods for attained growth curves. Using the pre-defined criteria, a few were selected combining five distributions and two smoothing techniques. Because the number of selected methods was considered too large to be fully tested, a preliminary study was recommended to evaluate goodness of fit of the five distributions. Methods based on distributions with poor performance will be eliminated and the remaining methods fully tested and compared.

Parametric methods for estimating covariate-dependent reference limits

Age-specific reference limits are required for many clinical laboratory measurements. Statistical assessment of calculated intervals must be performed to obtain reliable reference limits. When parametric, covariate-dependent limits are derived, normal distribution theory usually is applied due to its mathematical simplicity and relative ease of fitting. However, it is not always possible to transform data and achieve a normal distribution. Therefore, models other than those based on normal distribution theory are needed. Generalized linear model theory offers one such alternative. Regardless of the statistical model used, the assumptions behind the model should always be examined.

Infants' growth charts for southern Iran

Currently there are no growth charts based on local norms available for infants in Iran, and their growth is assessed by the National Centre for Health Statistics (NCHS) reference data, which is misleading. Growth charts for a cohort of 317 infants (164 girls and 153 boys) born in Shiraz (Southern Iran) in 1996 and followed for 2 years from birth are presented. All the centiles of length and weight charts are slightly above those of the NCHS charts under the age of 6 months and fall substantially below those over the age of 6 months. However, the spread is similar, so there is no suggestion that the difference is due to the prevalence of gross malnutrition. The difference shows that the use of locally based growth charts are essential for assessing the growth of children in Iran. The representativeness of our data leads us to conclude that the charts presented here are likely to be applied to the urban infant population of Iran.

Estimating age-related trends in cross-sectional studies using S-distributions

Growth trends in children are often based on cross-sectional studies, in which a sample of the population is investigated at one given point in time. Estimating age-related percentiles in such studies involves fitting data distributions, each of which is specific for one age group, and a subsequent smoothing of the percentile curves. The first requirement for this process is the selection of a distributional form that is expected to be consistent with the observed data. If a goodness-of-fit test reveals significant discrepancies between the data and the best-fitting member of this distributional form, an alternative distribution must be found. In practice, there is seldom an objective argument for selecting any particular distribution. Also, different distributions can yield very similar fits, so that any selection is somewhat arbitrary. Finally, the shapes of the observed distributions may change throughout the age range so drastically that no single traditional distribution can fit them all in a satisfactory manner. To overcome these difficulties in population studies, non-parametric smoothing techniques and normalizing transformations have been used to derive percentile curves. In this paper we present an alternative strategy in the form of a flexible parametric family of statistical distributions: the S-distribution. We suggest a method that guides the search for well-fitting S-distributions for groups of observed distributions. The method is first tested with simulated data sets and subsequently applied to actual weight distributions of girls of different ages. As far as the results can be tested, they are consistent with observations and with results from other methods.

Body mass index reference curves for Iran

Body Mass Index (BMI) charts for boys and girls aged 2-18 years in Iran are presented. The charts are based on a random cluster sample survey of 1702 boys and 1599 girls living in urban Tehran, whose height and weights were measured in the 1990-1992 National Health Survey of the whole country. Charts were constructed using Healy's method as modified by Pan, Goldstein and Yang (1990), and for boys at one point were smoothed manually. The resulting charts are shown to fit the data well and adequately describe raw BMI centiles of urban and rural children elsewhere in Iran. Comparison of these BMI charts with corresponding UK charts showed substantial differences at every age and emphasizes the necessity for the use of locally based BMI norms for assessing body mass of Iranian children.

Weight-for-height of children in Iran

Weight and height data were obtained from the 1990-1992 National Health Survey, a random cluster sample survey of 1 in 1000 families in Iran. Weight-for-height centiles of children and adolescents aged 2 to 18 in Tehran have been computed from relationships between weight for age and height for age Z-scores. The resulting centiles are compared to weight-for-height centiles based on BMI (weight/height2) charts. Investigation of the data points age by age revealed that there are very few observations between the two sets of 3rd and 97th centiles, so that the normal range of BMI for age is effectively equivalent to the normal range of weight-for-height by age. Further analysis shows that BMI charts based on the subset of children living in urban Tehran may be reliably used for all children in Iran to determine the normal range of weight-for-height except for short children aged 2 to 5 for whom a table of the upper centiles is given.

Calculating reference intervals for laboratory measurements

Reference intervals are used in laboratory medicine to detect measurements which are extreme, possibly abnormal. Methods of estimating reference intervals and age-specific reference intervals (where the measurement is dependent on a covariate, typically age) are reviewed. The issues of calculating confidence bands, determining appropriate sample sizes and assessing goodness-of-fit are discussed.

The growth and development of the Annals of Human Biology: a 25-year retrospective

The history of the founding in 1958 of the Society for the Study of Human Biology is outlined, and the circumstances in which the Annals of Human Biology began publication in 1974. The contents of the papers published 1974-1997 are reviewed; about 40% concern Population Biology, 40% Auxology and 20% Population Physiology. Some outstanding contributions in the first two of these fields are mentioned. Many consist of groups of papers from an ongoing study: 11 papers from the Otmoor villages study by Harrison and colleagues, and 11 concerning the growth of children in the Zurich Longitudinal Study, by Gasser and colleagues. Papers concerning the analysis of growth data and modelling of the growth curve, especially by Healy, are noted, and papers giving evidence of mini-spurts in growth and the saltation-stasis growth model are recalled. Wilson's papers on catch-up and growth regulation in twins are reviewed; also the contribution to growth-as-a-mirror of social conditions by workers at the Stockholm Institute of Education. The National Study of Health and Growth, led by Rona, contributed 13 papers over 14 years to the Annals, and there were outstanding one-off papers from the National Child Development Study, and the Cuban National Growth Study of 1972, and concerning the secular trend towards greater leg length in Japan, the upward social mobility of the taller of pairs of brothers, the growth of 18th century children in Vienna and Stuttgart and the measurements of 19th century slaves in the USA.

Growth charts for Iran

Growth charts for children aged 2-18 years old in Iran are presented. The charts are based on a random cluster sample survey of 3301 children living in urban Tehran, whose heights and weights were measured during the 1990-1992 National Health Survey of Iran. Because of differences between the data from the different provinces, these data were used as a representative subset of the total data. Charts were constructed using Healy's method, as modified by Pan, Goldstein and Yang, and are shown to fit the data well. Simulations show that the structure of the data does not affect the centile estimates. These charts may be used for all urban children in Iran and modifications are suggested to enable them to be used for rural children, who are generally smaller than urban children.

Growth of children in Iran

Weights and Heights of 22,349 children and adolescents aged 2 to 18 in Iran are reported. Data are from the 1990-1992 National Health Survey, a random cluster sample survey of 1 in 1000 families in all provinces of Iran. Multilevel models (Goldstein 1995) which take account of the survey design, reveal significant differences between provinces and between urban and rural children. Differences between urban and rural children, like differences between girls and boys, persist across all provinces and are certainly real. Differences between provinces may be partly due to differences in calibration. Charts based on the homogeneous subset of children living in urban Tehran may be used for all urban children, and in modified form, for all rural children. All the centiles of these charts are substantially below those of the NCHS charts, but the spread is similar so that there is no suggestion that the difference is due to the prevalence of gross malnutrition. The difference shows that the use of locally based growth charts are essential for assessing the growth of children in Iran.

Cross-sectional growth study of the child and adolescent population of Catalonia (Spain)

A cross-sectional growth study was undertaken on a sample of 5472 school-children aged between 4 and 17. The sample was representative of the Catalan population. Results on height, weight and age at menarche are presented. Cross-sectional centile curves on height and weight were constructed using non-parametric methods. The height of Catalan children was compared with that of children from the United Kingdom (1965 and 1990), France, Greece and the Basque country (Spain). Until puberty Catalan children were similar in height to English (1990) and Greek children, and taller than children in the other studies mentioned. Only differences in final height compared with the English (1990) population were detected. Parents' place of birth and father's profession are associated with height. 'Probit analysis' revealed that the average age of menarche (12.31 years) was similar to that of other Mediterranean countries and lower than in other parts of Spain and northern European countries. There were differences in age at menarche according to the father's occupation. The secular trend of height of the Catalan child population has increased during the twentieth century, rising more than 2 cm per decade.

Transvaginal Doppler ultrasound of the uteroplacental circulation in the early prediction of pre-eclampsia and intrauterine growth retardation

OBJECTIVE

To evaluate the predictive value of transvaginal Doppler ultrasound studies of the uterine and umbilical arteries in early pregnancy, in identifying pregnant women at risk of subsequently developing pre-eclampsia, or the delivery of a small for gestational age infant.

DESIGN

A multivariate logistic regression of Z scores of Doppler indices obtained from the uterine and umbilical arteries of 652 women with singleton pregnancies at 12 to 16 weeks of gestation. Measurements included the presence or absence of a notch, bilateral (right and left waveform) notching, vessel diameter, the resistance index, the pulsatility index, time averaged mean velocity (cm/s), maximum systolic velocity (cm/s), and volume flow (mL/min). Stepwise logistic regression and multivariate analysis of all the parameters measured was used to construct several scoring systems.

MAIN OUTCOME MEASURES

Pre-eclampsia, birthweight, preterm delivery.

RESULTS

In women that developed complications, there was a trend towards increased resistance and reduced velocity and volume flow. If bilateral notches were present there was an increased risk of pre-eclampsia (odds ratio [OR] 21.99, 95% CI 6.55-73.79), premature delivery (OR 2.38, 95% CI 1.19-4.75), and the delivery of a small for gestational age baby (OR 8.63, 95% CI 3.95-18.84). Using multivariate analysis, a seven parameter model was selected (after removal of vessel diameter, uterine and umbilical resistance index). This model produces a scoring system with a sensitivity of 92.9% and a specificity of 85.1% for the prediction of pre-eclampsia. A three parameter model (bilateral notches, uterine resistance index, umbilical pulsatility index) provides similar sensitivities, but lower specificities, when compared with the seven parameter model.

CONCLUSION

These data indicate that there are differences in uterine and umbilical artery Doppler blood flow indices at 12 to 16 weeks, in pregnancies with a normal or complicated outcome. Scoring systems derived from multivariate analysis of Doppler indices demonstrate the potential of being able to identify, in early pregnancy, a group of women at increased risk of the subsequent development of pre-eclampsia, premature delivery, or the birth of a small for gestational age baby.

Age-related standards for ordinal data: modelling the changes in visual acuity from 2 to 9 years of age

The visual acuities of 1140 children between the ages of 2 and 9 years were measured using the Sonksen-Silver Acuity System (SSAS) from a distance of 3 metres. Ordered logistic regression was used to construct smoothly changing age-related reference ranges for the proportions of children at different ages expected to have acuities in each of three ordinal categories. Exponential functions of age fitted the data better than polynomials. The resulting reference ranges can be used to derive the ages at which a given percentage of children achieve each of the acuity cut-offs. However, since it is unlikely that all children will be available for testing at the exact appropriate age, two possible alternatives are introduced and discussed. First, a new ordinal category that would result in a chosen outcome at a pre-selected age is calculated. Secondly, because it may be more feasible to use the current SSAS system whilst varying the distance of measurement, age-related standards showing the distances required to give constant pass-rates with the usual letter-sizes are also presented.

Age-related reference ranges: significance tests for models and confidence intervals for centiles

A method of fitting age-related reference ranges using maximized likelihood is presented. The method is illustrated using CD4 counts of uninfected children born to HIV-1 infected women. The likelihood incorporates exponential functions to describe the Box-Cox transformation parameter that induces Normality and the mean and standard deviation of the transformed data, at all ages in the range. This guarantees that the centiles are asymptotic to notional adult values and avoids edge effects. Likelihood ratio tests were used to assess the significance of the model parameters, and profile likelihood confidence intervals were constructed around the fitted centiles. The asymptotes of the resulting CD4 reference range for the childhood dataset were compared with CD4 counts available from a group of uninfected adults. The proposed approach limits the need for arbitrary decisions about grouping of the data, degree of smoothing or choice of model.

A two-level cross-sectional model using grafted polynomials

A new statistical model is proposed for the analysis of hierarchically structured cross-sectional growth data, especially for where measurements are made over long age ranges. The model combines a two-level model with grafted piecewise polynomials, to make efficient use of available data.

Smoothing reference centile curves: the LMS method and penalized likelihood

Refence centile curves show the distribution of a measurement as it changes according to some covariate, often age. The LMS method summarizes the changing distribution by three curves representing the median, coefficient of variation and skewness, the latter expressed as a Box-Cox power. Using penalized likelihood the three curves can be fitted as cubic splines by non-linear regression, and the extent of smoothing required can be expressed in terms of smoothing parameters or equivalent degrees of freedom. The method is illustrated with data on triceps skinfold in Gambian girls and women, and body weight in U.S.A. girls.