Identification and validity of accelerometer cut-points for toddlers

The purpose of this study was to derive ActiGraph cut-points for sedentary (SED), light-intensity physical activity (LPA), and moderate-to-vigorous physical activity (MVPA) in toddlers and evaluate their validity in an independent sample. The predictive validity of established preschool cut-points were also evaluated and compared. Twenty-two toddlers (mean age = 2.1 years ± 0.4 years) wore an ActiGraph accelerometer during a videotaped 20-min play period. Videos were subsequently coded for physical activity (PA) intensity using the modified Children's Activity Rating Scale (CARS). Receiver operating characteristic (ROC) curve analyses were conducted to determine cut-points. Predictive validity was assessed in an independent sample of 18 toddlers (mean age = 2.3 ± 0.4 years). From the ROC curve analyses, the 15-s count ranges corresponding to SED, LPA, and MVPA were 0-48, 49-418, and >418 counts/15 s, respectively. Classification accuracy was fair for the SED threshold (ROC-AUC = 0.74, 95% confidence interval = 0.71-0.76) and excellent for MVPA threshold (ROC-AUC = 0.90, 95% confidence interval = 0.88-0.92). In the cross-validation sample, the toddler cut-point and established preschool cut-points significantly overestimated time spent in SED and underestimated time in spent in LPA. For MVPA, mean differences between observed and predicted values for the toddler and Pate cut-points were not significantly different from zero. In summary, the ActiGraph accelerometer can provide useful group-level estimates of MVPA in toddlers. The results support the use of the Pate cut-point of 420 counts/15 s for MVPA.     

A strategy for full interrogation of prognostic gene expression patterns: exploring the biology of diffuse large B cell lymphoma

Background

Gene expression profiling yields quantitative data on gene expression used to create prognostic models that accurately predict patient outcome in diffuse large B cell lymphoma (DLBCL). Often, data are analyzed with genes classified by whether they fall above or below the median expression level. We sought to determine whether examining multiple cut-points might be a more powerful technique to investigate the association of gene expression with outcome.

Methodology/Principal Findings

We explored gene expression profiling data using variable cut-point analysis for 36 genes with reported prognostic value in DLBCL. We plotted two-group survival logrank test statistics against corresponding cut-points of the gene expression levels and smooth estimates of the hazard ratio of death versus gene expression levels. To facilitate comparisons we also standardized the expression of each of the genes by the fraction of patients that would be identified by any cut-point. A multiple comparison adjusted permutation p-value identified 3 different patterns of significance: 1) genes with significant cut-point points below the median, whose loss is associated with poor outcome (e.g. HLA-DR); 2) genes with significant cut-points above the median, whose over-expression is associated with poor outcome (e.g. CCND2); and 3) genes with significant cut-points on either side of the median, (e.g. extracellular molecules such as FN1).

Conclusions/Significance

Variable cut-point analysis with permutation p-value calculation can be used to identify significant genes that would not otherwise be identified with median cut-points and may suggest biological patterns of gene effects.     

Moderate Intense Physical Activity Depends on Selected Metabolic Equivalent of Task (MET) Cut-Off and Type of Data Analysis

Background

Accelerometry data are frequently analyzed without considering whether moderate-to-vigorous physical activities (MVPA) were performed in bouts of >10 minutes as defined in most physical activity guidelines. We aimed i) to quantify MVPA by using different commonly-applied physical activity guidelines, ii) to investigate the effect of bouts versus non-bouts analysis, and iii) to propose and validate a MVPA non-bouts cut-point to classify (in-) active subjects.

Methods

Healthy subjects (n=110;62±6yrs) and patients with Chronic Obstructive Pulmonary Disease (COPD) (n=113;62±5yrs) wore an activity monitor for 7 days. Three Metabolic Equivalent of Task (MET) cut-offs and one individual target (50% VO₂ reserve) were used to define MVPA. First, all minutes of MVPA were summed up (NON-BOUTS). Secondly, only minutes performed in bouts of >10 minutes continuous activity were counted (BOUTS). Receiver operating characteristic (ROC) curve analyses were used to propose and (cross-) validate new MVPA non-bout cut-points based on the criterion of 30 minutes MVPA per day (BOUTS). Likelihood ratios (sensitivity/[1-specificity]) were used to express the association between the proposed MVPA non-bout target and the MVPA bout target of 30 min*day^-1.

Results

MVPA was variable across physical activity guidelines with lowest values for age-specific cut-offs. Selecting a METs cut-point corresponding to 50% VO₂ reserve revealed no differences in MVPA between groups. MVPA’s analyzed in BOUTS in healthy subjects were 2 to 4 fold lower than NON-BOUTS analyses and this was even 3 to 12 fold lower in COPD. The MVPA non-bouts cut-point of 80 min*day^-1 using a 3 METs MVPA threshold delivered positive likelihood ratios of 5.1[1.5-19.6] (healthy subjects) and 2.3[1.6-3.3] (COPD).

Conclusion

MVPA varies upon the selected physical activity guideline/targets and bouts versus non-bouts analysis. Accelerometry measured MVPA non-bouts target of 80 min*day^-1, using a 3 METs MVPA threshold, is associated to the commonly-used MVPA bout target of 30 min*day^-1.     

Capture-Recapture Estimators in Epidemiology with Applications to Pertussis and Pneumococcal Invasive Disease Surveillance

IntroductionSurveillance networks are often not exhaustive nor completely complementary. In such situations, capture-recapture methods can be used for incidence estimation. The choice of estimator and their robustness with respect to the homogeneity and independence assumptions are however not well documented.MethodsWe investigated the performance of five different capture-recapture estimators in a simulation study. Eight different scenarios were used to detect and combine case-information. The scenarios increasingly violated assumptions of independence of samples and homogeneity of detection probabilities. Belgian datasets on invasive pneumococcal disease (IPD) and pertussis provided motivating examples.ResultsNo estimator was unbiased in all scenarios. Performance of the parametric estimators depended on how much of the dependency and heterogeneity were correctly modelled. Model building was limited by parameter estimability, availability of additional information (e.g. covariates) and the possibilities inherent to the method. In the most complex scenario, methods that allowed for detection probabilities conditional on previous detections estimated the total population size within a 20–30% error-range. Parametric estimators remained stable if individual data sources lost up to 50% of their data. The investigated non-parametric methods were more susceptible to data loss and their performance was linked to the dependence between samples; overestimating in scenarios with little dependence, underestimating in others. Issues with parameter estimability made it impossible to model all suggested relations between samples for the IPD and pertussis datasets. For IPD, the estimates for the Belgian incidence for cases aged 50 years and older ranged from 44 to58/100,000 in 2010. The estimates for pertussis (all ages, Belgium, 2014) ranged from 24.2 to30.8/100,000.ConclusionWe encourage the use of capture-recapture methods, but epidemiologists should preferably include datasets for which the underlying dependency structure is not too complex, a priori investigate this structure, compensate for it within the model and interpret the results with the remaining unmodelled heterogeneity in mind.     

A Note on the Theil-Sen Regression Estimator When the Regressor Is Random and the Error Term Is Heteroscedastic

In simple regression, two serious problems with the ordinary least squares (OLS) estimator are that its efficiency can be relatively poor when the error term is normal but heteroscedastic, and the usual confidence interval for the slope can have highly unsatisfactory probability coverage. When the error term is nonnormal, these problems become exacerbated. Two other concerns are that the OLS estimator has an unbounded influence function and a breakdown point of zero. Wilcox (1996) compared several estimators when there is heteroscedasticity and found two that have relatively good efficiency and simultaneously provide protection against outliers: an M-estimator with Schweppe weights and an estimator proposed by Cohen, Dalal and Tukey (1993). However, the M-estimator can handle only one outlier in the X-domain or among the Y values, and among the methods considered by Wilcox for computing confidence intervals for the slope, none performed well when working with the Cohen-Dalal-Tukey estimator. This note points out that the small-sample efficiency of theTheil-Sen estimator competes well with the estimators considered by Wilcox, and a method for computing a confidence interval was found that performs well in simulations. The Theil-Sen estimator has a reasonably high breakdown point, a bounded influence function, and in some cases its small-sample efficiency offers a substantial advantage over all of the estimators compared in Wilcox (1996).     

Review and comparison of ROC curve estimators for a time‐dependent outcome with marker‐dependent censoring

To quantify the ability of a marker to predict the onset of a clinical outcome in the future, time‐dependent estimators of sensitivity, specificity, and ROC curve have been proposed accounting for censoring of the outcome. In this paper, we review these estimators, recall their assumptions about the censoring mechanism and highlight their relationships and properties. A simulation study shows that marker‐dependent censoring can lead to important biases for the ROC estimators not adapted to this case. A slight modification of the inverse probability of censoring weighting estimators proposed by Uno et al. (2007) and Hung and Chiang (2010a) performs as well as the nearest neighbor estimator of Heagerty et al. (2000) in the simulation study and has interesting practical properties. Finally, the estimators were used to evaluate abilities of a marker combining age and a cognitive test to predict dementia in the elderly. Data were obtained from the French PAQUID cohort. The censoring appears clearly marker‐dependent leading to appreciable differences between ROC curves estimated with the different methods.     

Estimation of the coancestry coefficient: basis for a short-term genetic distance

A distance measure for populations diverging by drift only is based on the coancestry coefficient θ, and three estimators of the distance D = -ln(1 - θ) are constructed for multiallelic, multilocus data. Simulations of a monoecious population mating at random showed that a weighted ratio of single-locus estimators performed better than an unweighted average or a least squares estimator. Jackknifing over loci provided satisfactory variance estimates of distance values. In the drift situation, in which mutation is excluded, the weighted estimator of D appears to be a better measure of distance than others that have appeared in the literature.     

Comparison of density and basal area estimation of mountain natural forests based on distance-based sampling methods in Zhejiang,China

ObjectiveThe sustainable development of forest ecology and forest management practices is inseparable from the support of forest surveys. Different sampling methods have an unavoidable impact on the collection of natural community characteristic information. An appropriate method reduces the cost of the investigation to the maximum degree under the premise of ensuring accuracy. Distance-based sampling methods are widely used because of their excellent performance in estimating forest population characteristics. The purpose of this study is to compare and find an efficient sampling method of natural broad-leaved forests in mountainous areas of Zhejiang, China, which is of great significance to large-scale field survey practice in similar areas.MethodOur study used census survey data from fixed monitoring sample plots of natural broad-leaved forest in Wuyanling National Nature Reserve, Zhejiang, China as an example and simulated different distance-based sampling methods, including n-tree distance (NTD), point-centered quarter (PCQ), and T-square (Ts), combined with several estimators to estimate the stand density and basal area. The results were compared with the actual mean values of the 100% survey.ResultWe found that different sampling methods and estimators significantly influenced the results. NTD1 overestimated both the stand density and basal area, while NTD2 performed the best, with the lowest RMSE. Secondary performance was obtained with Ts3, Ts5, and Ts6, with small RMSEs of density and basal area. The RMSEs of the PCQ and Ts sampling methods based on a single distance were all large.ConclusionThe NTD sampling method with the NTD2 estimator is recommended to estimate the stand density and basal area for field investigation of natural forests in the Zhejiang mountainous area.     

Estimation of a common effect parameter from sparse follow-up data

Breslow (1981, Biometrika 68, 73-84) has shown that the Mantel-Haenszel odds ratio is a consistent estimator of a common odds ratio in sparse stratifications. For cohort studies, however, estimation of a common risk ratio or risk difference can be of greater interest. Under a binomial sparse-data model, the Mantel-Haenszel risk ratio and risk difference estimators are consistent in sparse stratifications, while the maximum likelihood and weighted least squares estimators are biased. Under Poisson sparse-data models, the Mantel-Haenszel and maximum likelihood rate ratio estimators have equal asymptotic variances under the null hypothesis and are consistent, while the weighted least squares estimators are again biased; similarly, of the common rate difference estimators the weighted least squares estimators are biased, while the estimator employing "Mantel-Haenszel" weights is consistent in sparse data. Variance estimators that are consistent in both sparse data and large strata can be derived for all the Mantel-Haenszel estimators.     

Relative Efficiency of Estimators of the Mean of a Normal Distribution when Coefficient of Variation is Known

A biased but simple and consistent estimator of the parameter ? has been obtained for the normal distribution N(?, a?₂), ?>0 where a is a known constant. It is shown that the estimator is more efficient than the sample mean or any suitably chosen constant multiple of the sample standard deviation. It is also proved to be more efficient than the mimumum variance unbiased estimator among a typical class of unbiased estimators derived by RASUL KHAN (1968).     

A Comparison of Accelerometer Cut-Points among Individuals with Coronary Artery Disease

Background

Accurate assessment of physical activity among coronary artery disease patients is important for assessing adherence to interventions. The study compared moderate-to-vigorous physical intensity activity and relationships with cardiometabolic health/fitness indicators using accelerometer cut-points developed for coronary artery disease patients versus those developed in younger and middle-aged adults.

Methods

A total of 231 adults with coronary artery disease wore an Actigraph GT3X accelerometer for ≥4 days (≥10 hours/day). Moderate-to-vigorous intensity physical activity between cut-points was compared using Bland-Altman analyses. Partial spearman correlations assessed relationships between moderate-to-vigorous intensity physical activity from each cut-point with markers of cardiometabolic health and fitness while controlling for age and sex.

Results

Average time spent in bouts of moderate-to-vigorous intensity physical activity using coronary artery disease cut-points was significantly higher than the young (mean difference: 13.0±12.8 minutes/day) or middle-aged (17.0±15.2 minutes/day) cut-points. Young and middle-aged cut-points were more strongly correlated with body mass index, waist circumference and systolic blood pressure, while coronary artery disease cut-points had stronger relationships with triglycerides, high-density and low-density lipoproteins. All were similarly correlated with measures of fitness.

Conclusion

Researchers need to exert caution when deciding on which cut-points to apply to their population. Further work is needed to validate which cut-points provide a true reflection of moderate-to-vigorous intensity physical activity and to examine relationships among patients with varying fitness.     

Sampling distributions, biases, variances, and confidence intervals for genetic correlations

Genetic correlations are frequently estimated from natural and experimental populations, yet many of the statistical properties of estimators of are not known, and accurate methods have not been described for estimating the precision of estimates of Our objective was to assess the statistical properties of multivariate analysis of variance (MANOVA), restricted maximum likelihood (REML), and maximum likelihood (ML) estimators of by simulating bivariate normal samples for the one-way balanced linear model. We estimated probabilities of non-positive definite MANOVA estimates of genetic variance-covariance matrices and biases and variances of MANOVA, REML, and ML estimators of and assessed the accuracy of parametric, jackknife, and bootstrap variance and confidence interval estimators for MANOVA estimates of were normally distributed. REML and ML estimates were normally distributed for but skewed for and 0.9. All of the estimators were biased. The MANOVA estimator was less biased than REML and ML estimators when heritability (H), the number of genotypes (n), and the number of replications (r) were low. The biases were otherwise nearly equal for different estimators and could not be reduced by jackknifing or bootstrapping. The variance of the MANOVA estimator was greater than the variance of the REML or ML estimator for most H, n, and r. Bootstrapping produced estimates of the variance of close to the known variance, especially for REML and ML. The observed coverages of the REML and ML bootstrap interval estimators were consistently close to stated coverages, whereas the observed coverage of the MANOVA bootstrap interval estimator was unsatisfactory for some H, n, and r. The other interval estimators produced unsatisfactory coverages. REML and ML bootstrap interval estimates were narrower than MANOVA bootstrap interval estimates for most H, and r. Received: 6 July 1995 / Accepted: 8 March 1996     

Effects of Varying Epoch Lengths,Wear Time Algorithms,and Activity Cut-Points on Estimates of Child Sedentary Behavior and Physical Activity from Accelerometer Data

Objective

To examine the effects of accelerometer epoch lengths, wear time (WT) algorithms, and activity cut-points on estimates of WT, sedentary behavior (SB), and physical activity (PA).

Methods

268 7–11 year-olds with BMI ≥ 85^th percentile for age and sex wore accelerometers on their right hips for 4–7 days. Data were processed and analyzed at epoch lengths of 1-, 5-, 10-, 15-, 30-, and 60-seconds. For each epoch length, WT minutes/day was determined using three common WT algorithms, and minutes/day and percent time spent in SB, light (LPA), moderate (MPA), and vigorous (VPA) PA were determined using five common activity cut-points. ANOVA tested differences in WT, SB, LPA, MPA, VPA, and MVPA when using the different epoch lengths, WT algorithms, and activity cut-points.

Results

WT minutes/day varied significantly by epoch length when using the NHANES WT algorithm (p < .0001), but did not vary significantly by epoch length when using the ≥ 20 minute consecutive zero or Choi WT algorithms. Minutes/day and percent time spent in SB, LPA, MPA, VPA, and MVPA varied significantly by epoch length for all sets of activity cut-points tested with all three WT algorithms (all p < .0001). Across all epoch lengths, minutes/day and percent time spent in SB, LPA, MPA, VPA, and MVPA also varied significantly across all sets of activity cut-points with all three WT algorithms (all p < .0001).

Conclusions

The common practice of converting WT algorithms and activity cut-point definitions to match different epoch lengths may introduce significant errors. Estimates of SB and PA from studies that process and analyze data using different epoch lengths, WT algorithms, and/or activity cut-points are not comparable, potentially leading to very different results, interpretations, and conclusions, misleading research and public policy.     

Examination of Different Accelerometer Cut-Points for Assessing Sedentary Behaviors in Children

Background

Public health research on sedentary behavior (SB) in youth has heavily relied on accelerometers. However, it has been limited by the lack of consensus on the most accurate accelerometer cut-points as well as by unknown effects caused by accelerometer position (wrist vs. hip) and output (single axis vs. multiple axes). The present study systematically evaluates classification accuracy of different Actigraph cut-points for classifying SB using hip and wrist-worn monitors and establishes new cut-points to enable use of the 3-dimensional vector magnitude data (for both hip and wrist placement).

Methods

A total of 125 children ages 7–13 yrs performed 12 randomly selected activities (from a set of 24 different activities) for 5 min each while wearing tri-axial Actigraph accelerometers on both the hip and wrist. The accelerometer data were categorized as either sedentary or non-sedentary minutes using six previously studied cut-points: 100counts-per-minute (CPM), 200CPM, 300CPM, 500CPM, 800CPM and 1100CPM. Classification accuracy was evaluated with Cohen''s Kappa (κ) and new cut-points were identified from Receiver Operating Characteristic (ROC).

Results

Of the six cut-points, the 100CPM value yielded the highest classification accuracy (κ = 0.81) for hip placement. For wrist placement, all of the cut-points produced low classification accuracy (ranges of κ from 0.44 to 0.67). Optimal sedentary cut-points derived from ROC were 554.3CPM (ROC-AUC of 0.99) for vector magnitude for hip, 1756CPM (ROC-AUC of 0.94) for vertical axis for wrist, and 3958.3CPM (ROC-AUC of 0.93) for vector magnitude for wrist placement.

Conclusions

The 100CPM was supported for use with vertical axis for hip placement, but not for wrist placement. The ROC-derived cut-points can be used to classify youth SB with the wrist and with vector magnitude data.     

Weighted regression analysis to correct for informative monitoring times and confounders in longitudinal studies

We address estimation of the marginal effect of a time‐varying binary treatment on a continuous longitudinal outcome in the context of observational studies using electronic health records, when the relationship of interest is confounded, mediated, and further distorted by an informative visit process. We allow the longitudinal outcome to be recorded only sporadically and assume that its monitoring timing is informed by patients' characteristics. We propose two novel estimators based on linear models for the mean outcome that incorporate an adjustment for confounding and informative monitoring process through generalized inverse probability of treatment weights and a proportional intensity model, respectively. We allow for a flexible modeling of the intercept function as a function of time. Our estimators have closed‐form solutions, and their asymptotic distributions can be derived. Extensive simulation studies show that both estimators outperform standard methods such as the ordinary least squares estimator or estimators that only account for informative monitoring or confounders. We illustrate our methods using data from the Add Health study, assessing the effect of depressive mood on weight in adolescents.     

Exact Results on the Inadmissibility of the Feasible Generalized Least Squares Estimator in Regression Models with Non‐Spherical Disturbances

In various guises, feasible generalized least squares (FGLS) estimation has occupied an important place in regression analysis for more than 35 years. Past studies on the characteristics of the FGLS estimators are largely based on large sample evaluations, and the important issue of admissibility remains unexplored in the case of the FGLS estimator. In this paper, an exact sufficient condition for the dominance of a Stein‐type shrinkage estimator over the FGLS estimator in finite samples based on squared error loss is given. In deriving the condition, we assume that the model's disturbance covariance matrix is unknown except for a scalar multiple. Further, for models with AR(1) disturbances, it is observed that the dominance condition reduces to one that involves no unknown parameter. In other words, in the case of AR(1) disturbances and where the condition for risk dominance is met, the FGLS estimator is rendered inadmissible under squared error loss.     

Youden Index and optimal cut-point estimated from observations affected by a lower limit of detection

The receiver operating characteristic (ROC) curve is used to evaluate a biomarker's ability for classifying disease status. The Youden Index (J), the maximum potential effectiveness of a biomarker, is a common summary measure of the ROC curve. In biomarker development, levels may be unquantifiable below a limit of detection (LOD) and missing from the overall dataset. Disregarding these observations may negatively bias the ROC curve and thus J. Several correction methods have been suggested for mean estimation and testing; however, little has been written about the ROC curve or its summary measures. We adapt non-parametric (empirical) and semi-parametric (ROC-GLM [generalized linear model]) methods and propose parametric methods (maximum likelihood (ML)) to estimate J and the optimal cut-point (c *) for a biomarker affected by a LOD. We develop unbiased estimators of J and c * via ML for normally and gamma distributed biomarkers. Alpha level confidence intervals are proposed using delta and bootstrap methods for the ML, semi-parametric, and non-parametric approaches respectively. Simulation studies are conducted over a range of distributional scenarios and sample sizes evaluating estimators' bias, root-mean square error, and coverage probability; the average bias was less than one percent for ML and GLM methods across scenarios and decreases with increased sample size. An example using polychlorinated biphenyl levels to classify women with and without endometriosis illustrates the potential benefits of these methods. We address the limitations and usefulness of each method in order to give researchers guidance in constructing appropriate estimates of biomarkers' true discriminating capabilities.     

Closed Form Estimators of Latent Cell Frequencies

One-stage and two-stage closed form estimators of latent cell frequencies in multidimensional contingency tables are derived from the weighted least squares criterion. The first stage estimator is asymptotically equivalent to the conditional maximum likelihood estimator and does not necessarily have minimum asymptotic variance. The second stage estimator does have minimum asymptotic variance relative to any other existing estimator. The closed form estimators are defined for any number of latent cells in contingency tables of any order under exact general linear constraints on the logarithms of the nonlatent and latent cell frequencies.     

A comparison of single‐sample estimators of effective population sizes from genetic marker data

In molecular ecology and conservation genetics studies, the important parameter of effective population size (N_e) is increasingly estimated from a single sample of individuals taken at random from a population and genotyped at a number of marker loci. Several estimators are developed, based on the information of linkage disequilibrium (LD), heterozygote excess (HE), molecular coancestry (MC) and sibship frequency (SF) in marker data. The most popular is the LD estimator, because it is more accurate than HE and MC estimators and is simpler to calculate than SF estimator. However, little is known about the accuracy of LD estimator relative to that of SF and about the robustness of all single‐sample estimators when some simplifying assumptions (e.g. random mating, no linkage, no genotyping errors) are violated. This study fills the gaps and uses extensive simulations to compare the biases and accuracies of the four estimators for different population properties (e.g. bottlenecks, nonrandom mating, haplodiploid), marker properties (e.g. linkage, polymorphisms) and sample properties (e.g. numbers of individuals and markers) and to compare the robustness of the four estimators when marker data are imperfect (with allelic dropouts). Extensive simulations show that SF estimator is more accurate, has a much wider application scope (e.g. suitable to nonrandom mating such as selfing, haplodiploid species, dominant markers) and is more robust (e.g. to the presence of linkage and genotyping errors of markers) than the other estimators. An empirical data set from a Yellowstone grizzly bear population was analysed to demonstrate the use of the SF estimator in practice.     

Least Squares and Minimum MSE Estimators of Variance Components in Mixed Linear Models

The paper deals with the quadratic invariant estimators of the linear functions of variance components in mixed linear model. The estimator with locally minimal mean square error with respect to a parameter ? is derived. Under the condition of normality of the vector Y the theoretical values of MSE of several types of estimators are compared in two different mixed models; under a different types of distributions a simulation study is carried out for the behaviour of derived estimators.