Model Selection in Continuous Test Norming With GAMLSS

Continuous Norming Approaches: A Systematic Review and Real Data Example

Norming of psychological tests is decisive for test score interpretation. However, conventional norming based on subgroups results either in biases or require very large samples to gather precise norms. Continuous norming methods, namely inferential, semi-parametric, and (simplified) parametric norming, propose to solve those issues. This article provides a systematic review of continuous norming. The review includes 121 publications with overall 189 studies. The main findings indicate that most studies used simplified parametric norming, not all studies considered essential distributional assumptions, and the evidence comparing different norming methods is inconclusive. In a real data example, using the standardization sample of the Need for Cognition-KIDS scale, we compared the precision of conventional, semi-parametric, and parametric norms. A hierarchy in terms of precision emerged with conventional norms being least precise, followed by semi-parametric norms, and parametric norms being most precise. We discuss these findings by comparing our findings and methods to previous studies.

Facilitating clinical use of the Amsterdam Instrumental Activities of Daily Living Questionnaire: Normative data and a diagnostic cutoff value

OBJECTIVE

The Amsterdam Instrumental Activities of Daily Living Questionnaire (A-IADL-Q) is well validated and commonly used to assess difficulties in everyday functioning regarding dementia. To facilitate interpretation and clinical implementation across different European countries, we aim to provide normative data and a diagnostic cutoff for dementia.

METHODS

Cross-sectional data from Dutch Brain Research Registry (N = 1,064; mean (M) age = 62 ± 11 year; 69.5% female), European Medial Information Framework-Alzheimer's Disease 90 + (N = 63; Mage = 92 ± 2 year; 52.4% female), and European Prevention of Alzheimer's Dementia Longitudinal Cohort Study (N = 247; Mage = 63 ± 7 year; 72.1% female) were used. The generalized additive models for location, scale, and shape framework were used to obtain normative values (Z-scores). The beta distribution was applied, and combinations of age, sex, and educational attainment were modeled. The optimal cutoff for dementia was calculated using area under receiver operating curves (AUC-ROC) and Youden Index, using data from Amsterdam Dementia Cohort (N = 2,511, Mage = 64 ± 8 year, 44.4% female).

RESULTS

The best normative model accounted for a cubic-like decrease of IADL performance with age that was more pronounced in low compared to medium/high educational attainment. The cutoff for dementia was 1.85 standard deviation below the population mean (AUC = 0.97; 95% CI [0.97-0.98]).

CONCLUSION

We provide regression-based norms for A-IADL-Q and a diagnostic cutoff for dementia, which help improve clinical assessment of IADL performance across European countries.

Normalization of Rowland Universal Dementia Assessment Scale (RUDAS) in Chilean older people

Rowland Universal Dementia Assessment Scale (RUDAS) is a cognitive screening that evaluates older people with low educational levels. In Chile, there are no normative data to assess this population.

Objective

To obtain normative data on RUDAS in older Chilean people with up to 12 years of schooling, and to determine whether age and schooling years influence a person's performance on RUDAS and on the items that constitute it.

Methods

A group of cognitively healthy people 60 years old or over, with up to 12 schooling years was evaluated (n=135). Multiple regression models were applied to obtain normative data on RUDAS, according to age and schooling years, and to measure the effects of schooling on different items.

Results

Regression analysis showed that none of the items had schooling as a significant predictor, except for the visuoconstruction item. The variables age and schooling explained 12.6% (R^2=0.126) of the RUDAS total score variance. The item visuoconstruction was the most associated with the educational level (OR=1,147).

Conclusion

This study showed that RUDAS is a recommended instrument for evaluating older people with low educational levels. However, more studies are needed to prove the validity of the RUDAS on Chilean older people.

Automated procedure for demographic adjustments on cognitive test scores

Performances of normal people on cognitive tests are known to vary by demographic characteristics, such as age, education, and sex. Thus, cognitive test scores should be corrected for demographic influences when they are used to detect below-expected results due to disease or injury involving the central nervous system (CNS). Normative corrections, if estimated from a large, diverse, and well-characterized cohort of controls, help to remove expected differences in cognitive performance associated with normal demographic characteristics and associated socio-economic disadvantages. In this paper, we (1) describe in detail the process of generating regression-based normative standards, and its advantages and limitations, (2) provide recommendations for applying these normative standards to data from individuals and populations at risk for CNS dysfunction, and (3) introduce an R package, test2norm, that contains functions for producing and applying normative formulas to generate demographically corrected scores for measuring deviations from expected, normal cognitive performances.

Reducing the Bias of Norm Scores in Non-Representative Samples: Weighting as an Adjunct to Continuous Norming Methods

We investigated whether the accuracy of normed test scores derived from non-demographically representative samples can be improved by combining continuous norming methods with compensatory weighting of test results. To this end, we introduce Raking, a method from social sciences, to psychometrics. In a simulated reference population, we modeled a latent cognitive ability with a typical developmental gradient, along with three demographic variables that were correlated to varying degrees with the latent ability. We simulated five additional populations representing patterns of non-representativeness that might be encountered in the real world. We subsequently drew smaller normative samples from each population and used an one-parameter logistic Item Response Theory (IRT) model to generate simulated test results for each individual. Using these simulated data, we applied norming techniques, both with and without compensatory weighting. Weighting reduced the bias of the norm scores when the degree of non-representativeness was moderate, with only a small risk of generating new biases.

Gestational weight gain charts for Latin American adolescents

Monitoring gestational weight gain (GWG) throughout pregnancy among adolescents is important for detecting individuals at risk and timely intervention. However, there are no specific tools or guidelines for GWG monitoring of this group. We aimed to construct GWG charts for pregnant adolescents (10-19 years old) according to pre-pregnancy body mass index (BMI) using a pooled dataset from nine Latin American countries. Datasets from Argentina, Brazil, Chile, Colombia, Mexico, Panama, Paraguay, Peru, and Uruguay collected between 2003 and 2021 were combined after data cleaning and harmonization. Adolescents free of diseases that could affect GWG and who gave birth to newborns weighing between 2,500-4,000 g and free of congenital malformations were included. Multiple imputation techniques were applied to increase the sample size available for underweight and obesity categories. Generalized Additive Models for Location, Scale, and Shape were used to construct the charts of GWG according to gestational age. Internal and external validation procedures were performed to ensure that models were not over-adjusted to the data. The cohort included 6,414 individuals and 29,414 measurements to construct the charts and 1,684 individuals and 8,879 measurements for external validation. The medians (and interquartile ranges) for GWG at 40 weeks according to pre-pregnancy BMI were: underweight, 14.9 (11.9-18.6); normal weight, 14.0 (10.6-17.7); overweight, 11.6 (7.7-15.6); obesity, 10.6 kg (6.7-14.3). Internal and external validation showed that the percentages above/below selected percentiles were close to those expected, except for underweight adolescents. These charts describe the GWG throughout pregnancy among Latin American adolescents and represent a significant contribution to the prenatal care of this group. GWG cut-offs based on values associated with lower risks of unfavorable outcomes for the mother-child binomial should be determined before implementing the charts in clinical practice.

Age-based centiles for diastolic blood pressure among children in the out-of-hospital emergency setting

Objective

To compare Pediatric Advanced Life Support (PALS) diastolic blood pressure (DBP) criteria to empirically derived DBP criteria for the prediction of out-of-hospital interventions in children.

Methods

We performed a retrospective study of pediatric (<18 years) encounters from the ESO Data Collaborative, which includes approximately 2000 Emergency Medical Services agencies in the United States. We developed age-based centile curves for DBP using generalized additive models for location, scale, and shape. We compared the proportion of encounters with a low DBP when using empirically derived and PALS criteria and calculated their associations with the delivery of out-of-hospital interventions (advanced airway management, cardiopulmonary resuscitation, cardiac epinephrine, any systemic epinephrine, defibrillation, and bolus intravenous fluids).

Results

We included 343,129 encounters. When using PALS criteria, 155,564 (45.3%) were classified as having  abnormal DBP, including 120,624 (35.2%) with high DBP and 34,940 (10.2%) with low DBP. When using empirically-derived criteria, 18.6% had an abnormal DBP (ie, a DBP <10th or >90th centile). The accuracy of low DBP for out-of-hospital interventions between the two criteria was similar.

Conclusion

PALS criteria for DBP classified a high proportion of children as having abnormal vital signs, particularly with diastolic hypertension. Empirically derived DBP thresholds more accurately predict the delivery of key out-of-hospital interventions. If externally validated, correlated to in-hospital outcomes, and combined with thresholds for other vital signs, these may better predict the need for out-of-hospital interventions.

Empirically Derived Age-Based Vital Signs for Children in the Out-of-Hospital Setting

STUDY OBJECTIVE

To compare Pediatric Advanced Life Support (PALS) vital signs criteria to empirically derived vital signs cut-points for predicting out-of-hospital interventions in children.

METHODS

We performed a cross-sectional study of pediatric encounters (<18 years) using the 2019 to 2020 datasets of the National Emergency Medical Services Information System, which we randomly divided into equal size derivation and validation samples. We developed age-based centile curves for initial heart rate, respiratory rate, and systolic blood pressure using generalized additive models for location, scale, and shape, which we evaluated in the validation sample. In addition, we compared the proportion of encounters with at least 1 abnormal vital sign when using empirically derived and PALS criteria and calculated their associations with the delivery of out-of-hospital medical interventions (eg, vascular access, medication delivery, or airway maneuvers).

RESULTS

We included 3,704,398 encounters. Among encounters with all 3 vital signs recorded (n=2,595,217), 45.9% had at least 1 abnormal vital sign using empirically derived criteria and 75.6% with PALS derived criteria. A higher proportion of encounters with a heart rate, respiratory rate, or systolic blood pressure less than 10th or more than 90th age-based empirically derived percentile had medical interventions than those with abnormal vital signs using PALS criteria.

CONCLUSION

PALS criteria classified a high proportion of children as having abnormal vital signs. Empirically derived vital signs developed from out-of-hospital encounters more accurately predict the delivery of the out-of-hospital medical interventions. If externally validated and correlated to inhospital outcomes, these cut-points may provide a useful assessment tool for children in the out-of-hospital setting.

Distributional regression modeling via generalized additive models for location, scale, and shape: An overview through a data set from learning analytics

The advent of technological developments is allowing to gather large amounts of data in several research fields. Learning analytics (LA)/educational data mining has access to big observational unstructured data captured from educational settings and relies mostly on unsupervised machine learning (ML) algorithms to make sense of such type of data. Generalized additive models for location, scale, and shape (GAMLSS) are a supervised statistical learning framework that allows modeling all the parameters of the distribution of the response variable with respect to the explanatory variables. This article overviews the power and flexibility of GAMLSS in relation to some ML techniques. Also, GAMLSS' capability to be tailored toward causality via causal regularization is briefly commented. This overview is illustrated via a data set from the field of LA. This article is categorized under:Application Areas > Education and LearningAlgorithmic Development > StatisticsTechnologies > Machine Learning.

Continuous norming in learning progress monitoring-An example for a test in spelling from grade 2-4

One of the main goals of the teacher and the school system as a whole is to close learning gaps and support children with difficulties in learning. The identification of those children as well as the monitoring of their progress in learning is crucial for this task. The derivation of comparative standards that can be applied well in practice is a relevant quality criterion in this context. Continuous normalization is particularly useful for progress monitoring tests that can be conducted at different points in time. Areas that were not available in the normalization sample are extrapolated, closing gaps in applicability due to discontinuity. In Germany, teachers participated in a state-funded research project to formatively measure their children's spelling performance in primary school. Data (N = 3000) from grade two to four were scaled, linked and translated into comparative values that can be used in classrooms independently from specific times. The tests meet the requirements of item response models and can be transferred well to continuous norms. However, we recommend using the 10th or 20th percentile as cut-off points for educational measures, as the 5th percentile is not discriminating enough.

Robust demographically-adjusted normative data for the Montreal Cognitive Assessment (MoCA): Results from the systolic blood pressure intervention trial

To generate robust, demographically-adjusted regression-based norms for the Montreal Cognitive Assessment (MoCA) using a large sample of diverse older US adults.

Baseline MoCA scores were examined for participants in the Systolic Blood Pressure Intervention Trial (SPRINT). A robust, cognitively-normal sample was drawn from individuals not subsequently adjudicated with cognitive impairment through 4 years of follow-up. Multivariable Beta-Binomial regression was used to model the association of demographic variables with MoCA performance and to create demographically-stratified normative tables.

Participants' (N = 5,338) mean age was 66.9 ± 8.8 years, with 35.7% female, 63.1% White, 27.4% Black, 9.5% Hispanic, and 44.5% with a college or graduate education. A large proportion scored below published MoCA cutoffs: 61.4% scored below 26 and 29.2% scored below 23. A disproportionate number falling below these cutoffs were Black, Hispanic, did not graduate from college, or were ≥75 years of age. Multivariable modeling identified education, race/ethnicity, age, and sex as significant predictors of MoCA scores (p<.001), with the best fitting model explaining 24.4% of the variance. Model-based predictions of median MoCA scores were generally 1 to 2 points lower for Black and Hispanic participants across combinations of age, sex, and education. Demographically-stratified norm-tables based on regression modeling are provided to facilitate clinical use, along with our raw data.

By using regression-based strategies that more fully account for demographic variables, we provide robust, demographically-adjusted metrics to improve cognitive screening with the MoCA in diverse older adults.

Ambient air pollution, temperature and hospital admissions due to respiratory diseases in a cold, industrial city

Background

The influences of air pollution exposure and temperature on respiratory diseases have become major global health concerns. This study investigated the relationship between ambient air pollutant concentrations and temperature in cold industrial cities that have the risk of hospitalization for respiratory diseases.

Methods

A time-series study was conducted in Changchun, China, from 2015 to 2019 to analyse the number of daily admissions for respiratory diseases, air pollutant concentrations, and meteorological factors. Time-series decomposition was applied to analyse the trend and characteristics of the number of admissions. Generalized additive models and distributed lag nonlinear models were constructed to explore the effects of air pollutant concentrations and temperature on the number of admissions.

Results

The number of daily admissions showed an increasing trend, and the seasonal fluctuation was obvious, with more daily admissions in winter and spring than in summer and autumn. There were positive and gradually decreasing lag effects of PM10, PM2.5, NO₂, and CO concentrations on the number of admissions, whereas O₃ showed a J-shaped trend. The results showed that within the 7-day lag period, 0.5°C was the temperature associated with the lowest relative risk of admission due to respiratory disease, and extremely low and high temperatures (<-18°C, >27°C, respectively) increased the risk of hospitalization for respiratory diseases by 8.3% and 12.1%, respectively.

Conclusions

From 2015 to 2019, respiratory diseases in Changchun showed an increasing trend with obvious seasonality. The increased concentrations of SO₂, NO₂, CO, PM2.5, O₃ and PM10 lead to an increased risk of hospitalization for respiratory diseases, with a significant lag effect. Both extreme heat and cold could lead to increases in the risk of admission due to respiratory disease.

SYmptom-Based STratification of DiabEtes Mellitus by Renal Function Decline (SYSTEM): A Retrospective Cohort Study and Modeling Assessment

Background: Previous UK Biobank studies showed that symptoms and physical measurements had excellent prediction on long-term clinical outcomes in general population. Symptoms and signs could intuitively and non-invasively predict and monitor disease progression, especially for telemedicine, but related research is limited in diabetes and renal medicine. Methods: This retrospective cohort study aimed to evaluate the predictive power of a symptom-based stratification framework and individual symptoms for diabetes. Three hundred two adult diabetic patients were consecutively sampled from outpatient clinics in Hong Kong for prospective symptom assessment. Demographics and longitudinal measures of biochemical parameters were retrospectively extracted from linked medical records. The association between estimated glomerular filtration rate (GFR) (independent variable) and biochemistry, epidemiological factors, and individual symptoms was assessed by mixed regression analyses. A symptom-based stratification framework of diabetes using symptom clusters was formulated by Delphi consensus method. Akaike information criterion (AIC) and Bayesian information criterion (BIC) were compared between statistical models with different combinations of biochemical, epidemiological, and symptom variables. Results: In the 4.2-year follow-up period, baseline presentation of edema (-1.8 ml/min/1.73m2, 95%CI: -2.5 to -1.2, p < 0.001), epigastric bloating (-0.8 ml/min/1.73m2, 95%CI: -1.4 to -0.2, p = 0.014) and alternating dry and loose stool (-1.1 ml/min/1.73m2, 95%CI: -1.9 to -0.4, p = 0.004) were independently associated with faster annual GFR decline. Eleven symptom clusters were identified from literature, stratifying diabetes predominantly by gastrointestinal phenotypes. Using symptom clusters synchronized by Delphi consensus as the independent variable in statistical models reduced complexity and improved explanatory power when compared to using individual symptoms. Symptom-biologic-epidemiologic combined model had the lowest AIC (4,478 vs. 5,824 vs. 4,966 vs. 7,926) and BIC (4,597 vs. 5,870 vs. 5,065 vs. 8,026) compared to the symptom, symptom-epidemiologic and biologic-epidemiologic models, respectively. Patients co-presenting with a constellation of fatigue, malaise, dry mouth, and dry throat were independently associated with faster annual GFR decline (-1.1 ml/min/1.73m2, 95%CI: -1.9 to -0.2, p = 0.011). Conclusions: Add-on symptom-based diagnosis improves the predictive power on renal function decline among diabetic patients based on key biochemical and epidemiological factors. Dynamic change of symptoms should be considered in clinical practice and research design.

In norming we trust

Zusammenfassung. Ziel der Untersuchung war ein systematischer Vergleich verschiedener Verfahren zur Normdatenmodellierung. Der auf Taylor-Polynomen basierende semi-parametrische Normierungsansatz (SPCN) mittels cNORM ( Lenhard, Lenhard & Gary, 2018 ) wurde parametrischen Anpassungen basierend auf Generalized Additive Models for Location, Scale and Shape (GAMLSS; Stasinopoulos et al., 2018 ) gegenübergestellt und die Normierungsgüte in Abhängigkeit der Faktoren Normstichprobengröße ( n = 525, 700, 1 050, 1 750), Itemanzahl (i = 10, 20, 40) sowie Itemschwierigkeit analysiert. Die Modellierung erfolgte kreuzvalidiert auf der Basis simulierter Rohdaten von Normierungs- und Validierungsstichproben: Mittels der verschiedenen Verfahren wurden auf der Basis der Normierungsstichprobe statistische Modelle berechnet und auf die Validierungsstichprobe übertragen, um die jeweils vorhergesagten mit den tatsächlichen Normwerten zu vergleichen. Der semi-parametrische Ansatz lieferte in den meisten Fällen den geringsten Normierungsfehler und damit das beste Normierungsergebnis. Die deutlichsten Unterschiede fanden sich bei leichten bzw. schweren Testskalen in Verbindung mit einer kleinen Itemanzahl. Der Einfluss der Normstichprobengröße war bei allen Methoden vergleichbar.

Improvement of Norm Score Quality via Regression-Based Continuous Norming

The interpretation of psychometric test results is usually based on norm scores. We compared semiparametric continuous norming (SPCN) with conventional norming methods by simulating results for test scales with different item numbers and difficulties via an item response theory approach. Subsequently, we modeled the norm scores based on random samples with varying sizes either with a conventional ranking procedure or SPCN. The norms were then cross-validated by using an entirely representative sample of N = 840,000 for which different measures of norming error were computed. This process was repeated 90,000 times. Both approaches benefitted from an increase in sample size, with SPCN reaching optimal results with much smaller samples. Conventional norming performed worse on data fit, age-related errors, and number of missings in the norm tables. The data fit in conventional norming of fixed subsample sizes varied with the granularity of the age brackets, calling into question general recommendations for sample sizes in test norming. We recommend that test norms should be based on statistical models of the raw score distributions instead of simply compiling norm tables via conventional ranking procedures.

Precision and Sample Size Requirements for Regression-Based Norming Methods for Change Scores

To interpret a person's change score, one typically transforms the change score into, for example, a percentile, so that one knows a person's location in a distribution of change scores. Transformed scores are referred to as norms and the construction of norms is referred to as norming. Two often-used norming methods for change scores are the regression-based change approach and the T Scores for Change method. In this article, we discuss the similarities and differences between these norming methods, and use a simulation study to systematically examine the precision of the two methods and to establish the minimum sample size requirements for satisfactory precision.

Bayesian Gaussian distributional regression models for more efficient norm estimation

A test score on a psychological test is usually expressed as a normed score, representing its position relative to test scores in a reference population. These typically depend on predictor(s) such as age. The test score distribution conditional on predictors is estimated using regression, which may need large normative samples to estimate the relationships between the predictor(s) and the distribution characteristics properly. In this study, we examine to what extent this burden can be alleviated by using prior information in the estimation of new norms with Bayesian Gaussian distributional regression. In a simulation study, we investigate to what extent this norm estimation is more efficient and how robust it is to prior model deviations. We varied the prior type, prior misspecification and sample size. In our simulated conditions, using a fixed effects prior resulted in more efficient norm estimation than a weakly informative prior as long as the prior misspecification was not age dependent. With the proposed method and reasonable prior information, the same norm precision can be achieved with a smaller normative sample, at least in empirical problems similar to our simulated conditions. This may help test developers to achieve cost-efficient high-quality norms. The method is illustrated using empirical normative data from the IDS-2 intelligence test.

Characterization of Plasma Protein Alterations in Pregnant and Postpartum Individuals Living With HIV to Support Physiologically-Based Pharmacokinetic Model Development

Background: Alterations in plasma protein concentrations in pregnant and postpartum individuals can influence antiretroviral (ARV) pharmacokinetics. Physiologically-based pharmacokinetic (PBPK) models can serve to inform drug dosing decisions in understudied populations. However, development of such models requires quantitative physiological information (e.g., changes in plasma protein concentration) from the population of interest. Objective: To quantitatively describe the time-course of albumin and α1-acid glycoprotein (AAG) concentrations in pregnant and postpartum women living with HIV. Methods: Serum and plasma protein concentrations procured from the International Maternal Pediatric Adolescent AIDS Clinical Trial Protocol 1026s (P1026s) were analyzed using a generalized additive modeling approach. Separate non-parametric smoothing splines were fit to albumin and AAG concentrations as functions of gestational age or postpartum duration. Results: The analysis included 871 and 757 serum albumin concentrations collected from 380 pregnant (~20 to 42 wks gestation) and 354 postpartum (0 to 46 wks postpartum) women, respectively. Thirty-six and 32 plasma AAG concentrations from 31 pregnant (~24 to 38 wks gestation) and 30 postpartum women (~2-13 wks postpartum), respectively, were available for analysis. Estimated mean albumin concentrations remained stable from 20 wks gestation to term (33.4 to 34.3 g/L); whereas, concentrations rapidly increased postpartum until stabilizing at ~42.3 g/L 15 wk after delivery. Estimated AAG concentrations slightly decreased from 24 wks gestation to term (53.6 and 44.9 mg/dL) while postpartum levels were elevated at two wks after delivery (126.1 mg/dL) and subsequently declined thereafter. Computational functions were developed to quantitatively communicate study results in a form that can be readily utilized for PBPK model development. Conclusion: By characterizing the trajectory of plasma protein concentrations in pregnant and postpartum women living with HIV, our analysis can increase confidence in PBPK model predictions for HIV antiretrovirals and better inform drug dosing decisions in this understudied population.

Particle Size Distributions for Cellulose Nanocrystals Measured by Transmission Electron Microscopy: An Interlaboratory Comparison

Particle size is a key parameter that must be measured to ensure reproducible production of cellulose nanocrystals (CNCs) and to achieve reliable performance metrics for specific CNC applications. Nevertheless, size measurements for CNCs are challenging due to their broad size distribution, irregular rod-shaped particles, and propensity to aggregate and agglomerate. We report an interlaboratory comparison (ILC) that tests transmission electron microscopy (TEM) protocols for image acquisition and analysis. Samples of CNCs were prepared on TEM grids in a single laboratory, and detailed data acquisition and analysis protocols were provided to participants. CNCs were imaged and the size of individual particles was analyzed in 10 participating laboratories that represent a cross section of academic, industrial, and government laboratories with varying levels of experience with imaging CNCs. The data for each laboratory were fit to a skew normal distribution that accommodates the variability in central location and distribution width and asymmetries for the various datasets. Consensus values were obtained by modeling the variation between laboratories using a skew normal distribution. This approach gave consensus distributions with values for mean, standard deviation, and shape factor of 95.8, 38.2, and 6.3 nm for length and 7.7, 2.2, and 2.9 nm for width, respectively. Comparison of the degree of overlap between distributions for individual laboratories indicates that differences in imaging resolution contribute to the variation in measured widths. We conclude that the selection of individual CNCs for analysis and the variability in CNC agglomeration and staining are the main factors that lead to variations in measured length and width between laboratories.

Age-dependent changes of total and differential white blood cell counts in children

BACKGROUND

Total and differential white blood cell counts are important for the diagnostic evaluation of suspected diseases. To facilitate the interpretation of total and differential white blood cell counts in pediatric patients, the present study investigated age-dependent changes in total and differential white blood cell counts in healthy reference children.

METHODS

Data were obtained from the Pediatric Reference Intervals in China study (PRINCE), which aims to establish and verify pediatric reference intervals for Chinese children based on a nationwide multicenter cross-sectional study from January 2017 to December 2018. Quantile curves were calculated using the generalized additive models for location, shape, and scale method. The 2.5th, 50th, and 97.5th quantile curves were calculated for both total and differential white blood counts. Percents of stacked area charts were used to demonstrate the proportions of differential white blood cells. All statistical analyses were performed using R software.

RESULTS

Both 50th and 97.5th quantiles of total white blood cell count and monocyte count were highest at birth, then rapidly decreased in the first 6 months of life; relatively slow reduction continued until 2 years of age. The lymphocyte count was low during infancy and increased to its highest level at 6 months of age; it then exhibited moderate and continuous reduction until approximately 9 years of age. The pattern of neutrophil count changed with age in a manner opposite to that of lymphocyte count. Besides, there were two inter-sections of lymphocyte count and neutrophil count during infancy and at approximately 5 years of age, based on locally weighted regression (LOESS) analysis. There were no apparent age-related changes in eosinophil or basophil counts.

CONCLUSION

These data regarding age-related changes in total and differential white blood cell counts can be used to assess the health of pediatric patients and guide clinical decisions.

Bias and Precision of Continuous Norms Obtained Using Quantile Regression

Continuous norming is an increasingly popular approach to establish norms when the performance on a test is dependent on age. However, current continuous norming methods rely on a number of assumptions that are quite restrictive and may introduce bias. In this study, quantile regression was introduced as more flexible alternative. Bias and precision of quantile regression-based norming were investigated with (age-)group as covariate, varying sample sizes and score distributions, and compared with bias and precision of two other norming methods: traditional norming and mean regression-based norming. Simulations showed the norms obtained using quantile regression to be most precise in almost all conditions. Norms were nevertheless biased when the score distributions reflected a ceiling effect. Quantile regression-based norming can thus be considered a promising alternative to traditional norming and mean regression-based norming, but only if the shape of the score distribution can be expected to be close to normal.

Improving confidence intervals for normed test scores: Include uncertainty due to sampling variability

Test publishers usually provide confidence intervals (CIs) for normed test scores that reflect the uncertainty due to the unreliability of the tests. The uncertainty due to sampling variability in the norming phase is ignored. To express uncertainty due to norming, we propose a flexible method that is applicable in continuous norming and allows for a variety of score distributions, using Generalized Additive Models for Location, Scale, and Shape (GAMLSS; Rigby & Stasinopoulos, 2005). We assessed the performance of this method in a simulation study, by examining the quality of the resulting CIs. We varied the population model, procedure of estimating the CI, confidence level, sample size, value of the predictor, extremity of the test score, and type of variance-covariance matrix. The results showed that good quality of the CIs could be achieved in most conditions. The method is illustrated using normative data of the SON-R 6-40 test. We recommend test developers to use this approach to arrive at CIs, and thus properly express the uncertainty due to norm sampling fluctuations, in the context of continuous norming. Adopting this approach will help (e.g., clinical) practitioners to obtain a fair picture of the person assessed.