Within-subject Variance Components Research Articles

Mitigation of the convergence issues associated with semi-replicated bioequivalence data.

Semi-replicated designs for investigation of bioequivalence constitute a challenge when mixed models are applied. With the commonly available packages and regardless of choice of covariance structure the software may force variance components into the covariance matrix that render it over-specified. This may give rise to arbitrary estimates of certain variance components, lack of convergence or warnings. Classically the covariance matrix is decomposed as V=ZGZt +R, with G containing the between-subject variance components, Z being the design matrix for the random effects and R containing the within-subject variance components. By abandoning the definitions of G and R, and instead working directly in V, it is possible to specify a correct model with only the variance components of interest. Proof-of-concept for this idea is delivered with a script in the statistical language R. The script is available as supplementary material(Data S1).

Characteristics and determinants of personal exposure to PM2.5 mass and components in adult subjects in the megacity of Guangzhou, China

Understanding the heterogeneity between ambient concentration and personal exposure is crucial in studies regarding the health risks of air pollution exposure. We performed a panel study with 4–19 (average = 10) repeated personal monitoring in 16 adult subjects (ages 18–30) for three consecutive weeks during the winter and summer of 2011–2012 in the Chinese megacity of Guangzhou. Also, we conducted simultaneous ambient measurements at eight districts (including five urban sites, two suburban locations, and one rural site) of Guangzhou. Significant seasonal variations were shown in personal PM2.5 exposure for most of the analyzed components (p < 0.05), with higher levels in winter than in summer. Average personal exposures exhibited a pattern of central urban > suburban > rural areas for PM2.5 mass and most of the constituents (e.g., carbonaceous aerosols, ions). We applied mixed-effects models to estimate within- and between-subject variance components and determinants of personal PM2.5 exposure after adjusting for potential confounders. The within-subject variance component dominated the total variability (63.7–95.6%) for most of the investigated PM2.5 components. Ambient PM2.5 mass and its components were the dominant predictors and contributors of the corresponding personal exposures (0.11 <Rc2 < 0.97; p < 0.05). The results indicate that season and district type affect personal PM2.5 exposure and its components, contributing to 4.9–51.6% and 8.0–77.8% of the variability. Time indoors and outdoors were also factors affecting personal exposure. The study findings revealed ambient concentrations at a fixed monitoring station underestimated residents’ true exposure levels. In conclusion, the current study emphasizes the need for incorporating spatio-temporal activity patterns complementing evenly-distributed air quality monitoring networks to increase the estimation power in epidemiological analysis linking true personal exposure to health effects.

A longitudinal model for functional connectivity networks using resting-state fMRI

Many neuroimaging studies collect functional magnetic resonance imaging (fMRI) data in a longitudinal manner. However, the current fMRI literature lacks a general framework for analyzing functional connectivity (FC) networks in fMRI data obtained from a longitudinal study. In this work, we build a novel longitudinal FC model using a variance components approach. First, for all subjects' visits, we account for the autocorrelation inherent in the fMRI time series data using a non-parametric technique. Second, we use a generalized least squares approach to estimate 1) the within-subject variance component shared across the population, 2) the baseline FC strength, and 3) the FC's longitudinal trend. Our novel method for longitudinal FC networks seeks to account for the within-subject dependence across multiple visits, the variability due to the subjects being sampled from a population, and the autocorrelation present in fMRI time series data, while restricting the number of parameters in order to make the method computationally feasible and stable. We develop a permutation testing procedure to draw valid inference on group differences in the baseline FC network and change in FC over longitudinal time between a set of patients and a comparable set of controls. To examine performance, we run a series of simulations and apply the model to longitudinal fMRI data collected from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database. Overall, we found no difference in the global FC network between Alzheimer's disease patients and healthy controls, but did find differing local aging patterns in the FC between the left hippocampus and the posterior cingulate cortex.

Nonlinear metrics assessing motor variability in a standardized pipetting task: Between- and within-subject variance components

The aim of this study was to estimate the between days test–retest reliability of nonlinear metrics used to quantify motor variability in a repetitive pipetting task. On three separate days, 14 healthy subjects performed pipetting as a general model of repetitive tasks. The task consisted of transferring liquid 20 times with a cycle time of 2.8s from a pickup tube to eight target tubes placed on a table in front of the subjects. The motion of hand, arm and the pipette tip was tracked in 3D and the shoulder elevation and elbow flexion angle were obtained. Motor variability was assessed using nonlinear metrics based on information theory and recurrence quantification analysis. Between- and within- (between-days) subject variance components were computed using a one-way random effect model, and intra-class correlation coefficients (ICC) were calculated from the variance components as standardized measures of reliability. Most of the metrics displayed a considerable between-days variance component and therefore the ICC showed a slight to moderate reliability. The reported data on between- and within-subject variability can be used to design future studies using nonlinear motor variability metrics on kinematics data.

Between- and within-subject variance of motor variability metrics in females performing repetitive upper-extremity precision work

Kinematic motor variability is extensively studied in occupational, clinical and sports biomechanics, but the consistency of most motor variability metrics have never been reported. In this study, fourteen subjects performed a repetitive pipetting task on three separate days. Movements of hand, arm and pipette tip were recorded in 3D and used to compute shoulder elevation, elbow flexion and shoulder-arm coordination angles, as well as pipette-tip endpoint precision. Cycle-to-cycle motor variability was quantified using linear dispersion measures of standard kinematics properties such as peak velocity, range of motion, and inter-segmental relative phase. Between- and within-subject consistencies of these variability metrics were quantified by variance components estimated using a nested random effects model. For most metrics, the variance between subjects was larger than that between days and cycles. Entering the variance components in statistical power equations showed that for most metrics, a total of 80–100 subjects will be required to detect a 20% difference between two groups with sufficient power, while this difference can typically be detected in repeated-measures (paired) designs using 25 subjects. The reported between and within-subject variance components can be used as a data base to facilitate efficient designs of future studies of kinematic motor variability.

Reliability of left ventricular noncompaction imaging criteria - the fractal facts

Background Left ventricular noncompaction (LVNC) is a cardiomyopathy with important prognostic implications. Identification of patients with LVNC using current criteria is challenging. Fractal analysis is a novel approach which summarises global LV trabecular complexity as a continuous variable, the fractal dimension, enabling the establishment of ethnically and disease-appropriate reference ranges for trabeculation. Methods We aimed to determine the reproducibility and accuracy of the fractal method compared to other LVNC criteria. We used these results to estimate sample size requirements for population studies of trabeculation. Two independent observers analyzed CMR data from 20 nonselected LVNC cases (mean age 47±13, 11 men) and 40 non-selected healthy volunteers (healthy whites, n=20; healthy blacks, n=20, mean age 45±14, 23 men). Datasets were evaluated using the fractal method (Figure 1) and two other CMR criteria (Petersen and Jacquier). Factorial repeated measures analysis of variance was performed to estimate within-subject variance components and total variability to be used in sample size calculations for the CMR criteria. Results The fractal approach was reproducible (for intra and inter-observer readings: repeatability coefficients, 0.059 and 0.067; intraclass correlation coefficients, 0.98 and 0.97; coefficients of variation, 5%, both). This reproducibility was greater than that calculated for the other LVNC analysis techniques (Figure 2a). Likelihood ratio graphs (Figure 2b) showed superior accuracy for the fractal method over the comparator techniques based on a composite of sensitivity, specificity and positive predictive values. These results translate into superior ability to detect difference and more powerful clinical trials - the minimum number of individuals needed to detect a clinically significant difference in trabeculation between diseased and healthy study populations would be 26 for the fractal method; 60 for the Petersen and 94 for the Jacquier technique (assuming power, 0.90; two-tailed a, 0.05). Conclusions Fractal analysis of LV trabeculae demonstrates good reproducibility and is more accurate in diagnosing LVNC than other techniques. The fractal dimension, if used in clinical trials would more than halve the number of patients required to detect clinically relevant differences in trabecular complexity.

Permutation Tests for Random Effects in Linear Mixed Models

Inference regarding the inclusion or exclusion of random effects in linear mixed models is challenging because the variance components are located on the boundary of their parameter space under the usual null hypothesis. As a result, the asymptotic null distribution of the Wald, score, and likelihood ratio tests will not have the typical χ(2) distribution. Although it has been proved that the correct asymptotic distribution is a mixture of χ(2) distributions, the appropriate mixture distribution is rather cumbersome and nonintuitive when the null and alternative hypotheses differ by more than one random effect. As alternatives, we present two permutation tests, one that is based on the best linear unbiased predictors and one that is based on the restricted likelihood ratio test statistic. Both methods involve weighted residuals, with the weights determined by the among- and within-subject variance components. The null permutation distributions of our statistics are computed by permuting the residuals both within and among subjects and are valid both asymptotically and in small samples. We examine the size and power of our tests via simulation under a variety of settings and apply our test to a published data set of chronic myelogenous leukemia patients.

Total Hemoglobin Mass-A New Parameter to Detect Blood Doping?

All kinds of blood manipulations aim to increase the total hemoglobin mass (tHb-mass). To establish tHb-mass as an effective screening parameter for detecting blood doping, the knowledge of its normal variation over time is necessary. The aim of the present study, therefore, was to determine the intraindividual variance of tHb-mass in elite athletes during a training year emphasizing off, training, and race seasons at sea level. tHb-mass and hemoglobin concentration ([Hb]) were determined in 24 endurance athletes five times during a year and were compared with a control group (n = 6). An analysis of covariance was used to test the effects of training phases, age, gender, competition level, body mass, and training volume. Three error models, based on 1) a total percentage error of measurement, 2) the combination of a typical percentage error (TE) of analytical origin with an absolute SD of biological origin, and 3) between-subject and within-subject variance components as obtained by an analysis of variance, were tested. In addition to the expected influence of performance status, the main results were that the effects of training volume (P = 0.20) and training phases (P = 0.81) on tHb-mass were not significant. We found that within-subject variations mainly have an analytical origin (TE approximately 1.4%) and a very small SD (7.5 g) of biological origin. tHb-mass shows very low individual oscillations during a training year (<6%), and these oscillations are below the expected changes in tHb-mass due to Herythropoetin (EPO) application or blood infusion (approximately 10%). The high stability of tHb-mass over a period of 1 year suggests that it should be included in an athlete's biological passport and analyzed by recently developed probabilistic inference techniques that define subject-based reference ranges.

The analysis of peak expiratory flow data using a three‐level hierarchical model

Peak expiratory flow (PEF) is a measure commonly used in clinical practice and research for respiratory diseases such as asthma. In research, PEF is usually recorded in a diary for a 2-week period with two or more measurements per day. Interest may lie in whether certain groups of individuals tend to have higher or lower PEF. In addition the variability of PEF may be of interest as, for example, asthmatics tend to have more variable airways. In this paper we develop a three-level hierarchical model that can simultaneously model the mean level and variability of PEF. The variability is broken down into three components, between-subject variability, between-day within-subject variability, and within-day within-subject variability. The latter two components are of specific clinical interest. We fit both classical and Bayesian models. The Bayesian models have the advantage of taking the uncertainty in the variance component estimates into account when estimating the standard errors of the fixed effects. In addition, the Bayesian models provide an intuitive and simple way to investigate the within-subject variance components.

Refinement of the association of serum C-reactive protein concentration and coronary heart disease risk by correction for within-subject variation over time: the MONICA Augsburg studies, 1984 and 1987.

The authors sought to assess the repeatability of measurements of C-reactive protein, an independent predictor of coronary heart disease, in a large cohort of apparently healthy men and to correct earlier estimates of the association of C-reactive protein and coronary heart disease for the measurement error in this protein. They measured C-reactive protein by a high-sensitivity assay in 936 men aged 45-64 years in the MONICA (Monitoring of Trends and Determinants in Cardiovascular Disease) Augsburg cohort in 1984-1985 and remeasured it 3 years later. All men were subjected to an 8-year follow-up of their cardiovascular status. The analytical variation of the assay was small, with the analytical variance component at 1 percent of the within-subject variance component, a repeatability coefficient of 25 percent, and a reliability coefficient of 1.00. In contrast, the within-subject variation of C-reactive protein corresponded to a repeatability coefficient of 740 percent and a reliability coefficient of 0.54, indicating considerable within-subject variation. Based on the authors' estimates, three serial determinations of C-reactive protein should be done to achieve a reliability of 0.75, the value they found for total cholesterol. Correcting the hazard ratios in their original analysis of the association of coronary heart disease and high-sensitivity-assay C-reactive protein for the measurement error in C-reactive protein and covariables leads to a considerably larger estimate. The results suggest that the true association between C-reactive protein and cardiovascular risk is underestimated by a single C-reactive protein determination, and that several serial C-reactive protein measurements should be taken.

Variance components in comparative bioavailability studies

Variance components in comparative bioavailability studies are examined. Assay measurement error is shown to be negligible relative to other variance components, and hence, repeat assay does not appreciably increase study precision and is unnecessary. More important is the finding that repeat administration of each formulation to each subject may substantially decrease the variance of the formulation difference and may allow the use of fewer subjects in a study. The benefit of repeat administration depends on the relative sizes of the within-subject variance component and the subject—formulation interaction component, In addition, repeat administration allows separate estimation of the within‐subject component and the subject—formulation component. The former component is important for assessing bioequivalence, and the latter component, for assessing interchangeability of formulations.

Variability in the Measurement of Human Ventricular Refractoriness

The degree of variability in ventricular refractoriness and factors potentially affecting this variability were evaluated in 80 patients undergoing an electrophysiological study. Each of seven variables (stimulation current, coupling interval of the basic drive train to spontaneous rhythm, pause between determinations, bipolar pacing configuration, bipolar vs unipolar pacing, atrioventricular synchrony, and autonomic tone) was evaluated in a group of ten patients to determine its effects on the reproducibility of refractoriness. Measurements were repeated ten times in every patient under each of two conditions. Five variables had significant effects on the reproducibility of measurements. Pacing at 10 mA was associated with less variability in the determination of ventricular refractoriness than pacing at twice threshold (within-subject variance component 4.5 vs 10.1 msec; P less than 0.001). The mean difference between the longest and shortest determinations of refractory periods (range) was 6.2 msec at 10 mA and 8.6 msec at twice threshold. The use of a conditioning period of pacing and continuous trains (eight beats with a 3-sec pause) rather than a variable pause between serial trials reduced the mean within-subject variance component from 16.5 to 3.3 (P less than 0.001) and the mean range of refractory period determinations from 10.8 to 4.8. The use of the distal rather than the proximal pole as the cathode decreased the mean within-subject variance component from 9.4 to 3.3 (P less than 0.001) and the range of determinations from 6.4 to 5.8 msec. Unipolar pacing was associated with less variability than bipolar pacing (mean within-subject variance component 4.6 vs 6.4; P less than 0.05, mean range 5.0 vs 7.6 msec).(ABSTRACT TRUNCATED AT 250 WORDS)

Clinical chemistry reference intervals for healthy elderly subjects

In 1979, 304 healthy elderly individuals in New Mexico were recruited for a longitudinal study of nutrition and aging. Repeat measurements on a yearly basis of commonly requested clinical chemistry analytes allowed the calculation of reference intervals, between and within-subject variance components, and percentiles for change in concentration between two yearly measurements. The latter was further divided into analytical and biological variance components. The upper 95th percentile for the difference between two yearly measurements, expressed as a percent of the population mean, ranged from 4% for Na+ to approximately 20% for total cholesterol and to greater than 90% for ferritin. Year-to-year differences attributable to the biological component ranged from a low of 2% of the population mean for Na+ to 70% for gamma-glutamyltransferase.

Clinical chemistry reference intervals for healthy elderly subjects

In 1979, 304 healthy elderly individuals in New Mexico were recruited for a longitudinal study of nutrition and aging. Repeat measurements on a yearly basis of commonly requested clinical chemistry analytes allowed the calculation of reference intervals, between and within-subject variance components, and percentiles for change in concentration between two yearly measurements. The latter was further divided into analytical and biological variance components. The upper 95th percentile for the difference between two yearly measurements, expressed as a percent of the population mean, ranged from 4% for Na+ to approximately 20% for total cholesterol and to greater than 90% for ferritin. Year-to-year differences attributable to the biological component ranged from a low of 2% of the population mean for Na+ to 70% for gamma-glutamyltransferase.