Change-point Regression Model Research Articles

Protein intake affects erythrocyte glutathione synthesis in healthy adults aged ≥60 years in a repeated-measures trial

BackgroundProtein recommendations for older adults are based on nitrogen balance data from young adults. Physiological studies using the indicator amino acid oxidation method suggest they need 30% to 50% more protein than current recommendations. We herein present glutathione (GSH) as a physiological estimate of protein adequacy in older adults. ObjectivesThe objective was to measure GSH kinetics in response to varying protein intakes in a repeated-measures design in healthy adults aged ≥60 y using the precursor-product method. MethodsSixteen healthy older adults (n = 8 male and n = 8 female; body mass index ≤30 kg/m2) were studied. Each received 4 of 6 protein intakes in random order (0.66, 0.8, 0.9, 1.1, 1.3 and 1.5 g⋅kg−1⋅d−1). At each intake level, participants underwent isotope infusion studies of 7 h duration following a 3-d adaptation to the test level of protein. On the fourth day, GSH fractional (FSR) and absolute synthesis (ASR) rates were quantified by measuring the incorporation of U-[13C2-15N]glycine into GSH at isotopic steady state. A mixed-effect change-point regression model was used to determine a breakpoint in FSR and ASR. Secondary outcomes included plasma concentrations of oxidative stress markers, homocysteine, 5-L-oxoproline (5-OP), and urinary sulfate. The effect of secondary outcomes on GSH kinetics was analyzed using a joint linear mixed-effect model and Tukey’s post hoc test. ResultsA protein intake of 1.08 g⋅kg−1⋅d−1 (95% confidence interval [CI]: 0.83, 1.32; Rm2 = 0.207; Rc2 = 0.671; P < 0.001) maximized GSH FSR. There was no effect of protein intake on concentrations of erythrocyte GSH, plasma homocysteine, oxidative stress markers, or 5-OP (P > 0.05). Protein intake had a positive effect on urinary sulfate excretion (P < 0.0001). ConclusionA protein intake of 1.08 g⋅kg−1⋅d−1 from a high-quality protein maximized GSH synthesis in adults ≥60 y. This lends support to data suggesting a requirement higher than the current recommendation.This study was registered at clinicaltrials.gov as NCT02971046.

Safety assessment of L-Arg oral intake in healthy subjects: a systematic review of randomized control trials

L-Arg is a nonessential amino acid but has many physiological roles. Accordingly, L-Arg has been used in various fields, but there is only limited information available about its safety upon overdose. Generally, the no-observed adverse effect level (NOAEL) is used when setting the upper amount for chemical substances. Recently, systematic reviews have been used to assess the safety as well as the effectiveness and usefulness of them. Therefore, we conducted an assessment of the safety of the oral intake of L-Arg in healthy subjects using gastrointestinal symptoms as an index. We limited the study design to only double-blind randomized controlled trials and searched PubMed, Cochrane Library, EBSCOhost, and Ichushi-Web from inception until May 2021. Assessment of the quality of studies was conducted using the Cochrane Collaboration tool and Jadad score, and the random effects model was used for data analysis. Ultimately, 34 studies were selected for inclusion in this work. The dosage of L-Arg used in the studies ranged from 2000 to 30,000 mg/day (or/one-time dose), and the treatment duration was 1–84 days. The increased risk of gastrointestinal symptoms associated with L-Arg intake from 23 studies (647 participants in total) in which such symptoms were reported was 0.01 (95% confidence interval: – 0.02–0.04), which was not significant difference. NOAEL was estimated as 7531 mg/ one-time dose using a weighted change-point regression model (UMIN000046133).Registration and protocol: Umin.ac.jp as UMIN000046133.

A change-point regression approach for estimating no observed adverse effect level from systematic review.

Systematic reviews can be used not only to evaluate the efficacy and usefulness of a drug or food ingredient, but also as a safety assessment method. One of the aims of safety assessment is to estimate the no observed adverse effect level and the lowest observed adverse effect level. However, no methodology to statistically estimate the no observed adverse effect level from systematic review results has yet been reported. Estimation of the no observed adverse effect level involves a search for the dose above which adverse events occur is even exploration of the thresholds in dose response. To search for the dose above which adverse events occur, we examined an estimation method using the weighted change-point regression model, which includes the weights of each study used for systematic reviews in the model. This model could be applied to safety data of an omega-3 study in the form of a systematic review. We demonstrated that the dose response to omega-3 intake regarding adverse events had a threshold value and that the no observed adverse effect level could be estimated using the developed model.

An Evaluation of the Protein Requirements of Japanese Young Men by Consuming Two Types of Dairy Proteins Using the Indicator Amino Acid Oxidation Method.

The indicator amino acid oxidation method is a relatively new method for determining protein requirements. Our hypothesis was that the protein requirement of the casein-whey protein mixture (70% casein and 30% whey protein) was lower than the protein requirement of plain casein, because casein and whey proteins compensate for the lack of the first-limiting amino acids. The optimal mixing ratio was determined based on the amino acid scoring pattern which is used to calculate the digestible indispensable amino acid score. In this study, digestibility was not considered to determine the optimal mixing ratio because dairy protein is a good source of digestible protein. This study aimed to evaluate the protein requirements of Japanese young men by consuming casein and casein-whey protein mixture. Ten healthy young men (22±0.2 y old) participated in 12 experiments according to a graded protein intake (0.5, 0.7, 0.9, 1.0, 1.2, 1.4 g/kg/d) of casein and casein-whey protein mixture. The mean protein requirement was calculated as the breakpoint of breath 13CO2 enrichment using change-point regression models. The mean protein requirements of Japanese young men by consuming casein and casein-whey protein mixture were estimated to be 1.00 g/kg/d and 0.90 g/kg/d, respectively. These estimated requirements were consistent with the protein quality expected from the amount of the first-limiting amino acids. The indicator amino acid oxidation method may be useful to evaluate protein quality.

Large Scale Energy Signature Analysis: Tools for Utility Managers and Planners

Building energy signature analysis is a well-established tool for understanding the temperature sensitivity of building energy consumption and measuring energy savings. This tool has been used to measure energy savings of residential, commercial, and even industrial buildings. The public availability of electricity loads (i.e., hourly electricity demand (MW)) from entire Balancing Authorities (BAs) provide an interesting opportunity to apply this approach to a large aggregate load. In this paper, we explore that opportunity for BAs and show that the correlations for large geographical areas are surprisingly coherent when the change-point linear regression analysis is used with the daily interval data of electricity demand and outside air temperature. The change-point linear regression models of all the BAs, except WAUW and OVEC, show R2 of 0.70 or more and CV-RMSE of 10.0% or less. We also suggest an analysis method that allows for meaningful comparisons between BAs and to assess changes in time for a given BA which could be used to interpret changes in load patterns year-to-year, accounting for changes in weather. This approach can be used to verify the impact of energy efficiency programs on a building component/system-wide basis. This study shows the annual electricity demand reductions for SCL and IPCO are 136,655 MWh (1.5%) and 182,053 MWh (1.1%), respectively.

The multifaceted history of the Walker Circulation during the Plio-Pleistocene

The Walker Circulation (WC) is an east-west trending band of atmospheric circulation cells along the equator and the predominant controller of heat and moisture transport in the tropics. Its variability is closely linked to the sea-surface temperature (SST) changes across the Pacific, the Indian and the Atlantic Oceans and can have pronounced effects on the humidity regimes of the adjacent continents. In recent years, the evolution of the WC during the Plio- and Pleistocene epochs has been intensely studied in the context of the effectiveness of the tropics in modulating global climate change (e.g., the intensification of Northern Hemisphere glaciation).However, the onset of the modern WC pattern as well as its global impact during the Plio- and Pleistocene is controversially assessed in the literature. For its onset, previous studies have suggested dates ranging between 2.4 and 0.8 million years ago (Myr), while its argued impact ranges from – crucially influencing the increase of Northern Hemisphere ice sheet growth by channelling heat and moisture from the tropics into the high latitudes to – having no effect on global ice volume changes. In order to achieve a comprehensive understanding of the spatiotemporal evolution of the WC during this time frame, we statistically analysed 30 globally distributed SST records covering the low and high latitudes between 3.5 and 1.5 Myr, encompassing the Late Pliocene to Early Pleistocene. We utilized a statistical change-point regression model to determine significant change points in the SST evolution of the (sub)-tropics and high latitudes that potentially relate to changes in the WC. We find that the WC experienced a multifaceted evolution between the Late Pliocene and the Early Pleistocene with significant transitional steps at ∼2.7 and ∼2.1 - Ma. Our results suggest after the Late Pliocene, a pre-modern WC set in, which was characterized by a progressively strengthened Pacific Walker Cell alongside a weakened Indian Ocean Walker Cell. This change was potentially triggered by the constriction of the Indonesian seaway, an important transmitter between the Pacific and Indian Ocean. The ensuing mode of the WC intensified until ∼2.1 Myr, when SST values around the global scale signalled a progressive strengthening of the Indian Walker Cell in phase with the progressive strengthening of the Pacific and Atlantic Cells. Our findings indicate that a shift from a pre-modern to a modern-like WC potentially only occurred during the mid-Pleistocene.

Hierarchical change-point regression models including random effects to estimate empirical critical loads for nitrogen using Bayesian Regression Models (brms) and JAGS

The concept of critical loads is used in the framework of the Convention on Long-range Transboundary Air Pollution (UNECE) to define thresholds below which no damaging effects on habitats occur based on the latest scientific knowledge. Change-point regression models applied in a Bayesian framework are useful statistical tools to estimate critical empirical loads. While hierarchical study designs are common in ecological research, previous methods to estimate critical loads using change-point regression did not allow to analyse data collected under such a design. This method update provides an implementation of hierarchical data structure by including random effects such as study sites or as in this example tree species within the Bayesian approach of change-point regression models using two different approaches. The example data set is an European wide gradient study of the impact of climate change and air pollution on forest tree health assessed by foliar nutrient status of nitrogen (N) to phosphorus (P) from 10 different conifer tree species originated from 88 forest sites and 9 countries covering 22 years (1995-2017). Both modelling approaches using JAGS and Bayesian Regression Models using ‘Stan’ (brms) resulted in reasonable and similar estimations of the critical empirical load for nitrogen (CLempN) for temperate forests. These methodological examples of using different approaches of Bayesian change-point regression models dealing with random effects could prove useful to infer CLempN for other ecosystems and long-term data sets.•Hierarchical change-point regression models are suitable for estimating critical empirical loads.•The Bayesian framework of these models provides the inclusion of the current critical load and various confounding or modifying variables.•Here we present two ways of implementing hierarchical data sets in Bayesian change-point regression models using JAGS and brms.

Robust Algorithms for Change-Point Regressions Using the t-Distribution

Regression models with change-points have been widely applied in various fields. Most methodologies for change-point regressions assume Gaussian errors. For many real data having longer-than-normal tails or atypical observations, the use of normal errors may unduly affect the fit of change-point regression models. This paper proposes two robust algorithms called EMT and FCT for change-point regressions by incorporating the t-distribution with the expectation and maximization algorithm and the fuzzy classification procedure, respectively. For better resistance to high leverage outliers, we introduce a modified version of the proposed method, which fits the t change-point regression model to the data after moderately pruning high leverage points. The selection of the degrees of freedom is discussed. The robustness properties of the proposed methods are also analyzed and validated. Simulation studies show the effectiveness and resistance of the proposed methods against outliers and heavy-tailed distributions. Extensive experiments demonstrate the preference of the t-based approach over normal-based methods for better robustness and computational efficiency. EMT and FCT generally work well, and FCT always performs better for less biased estimates, especially in cases of data contamination. Real examples show the need and the practicability of the proposed method.

A Change Point Regression Model for Treatment Effects Estimation of Functional Foods in a Pre-Post Design

In an intervention study for functional foods, the study population is often a mixed group of healthy individuals and/or those who are not so healthy but are not definitely disease. For such heterogeneous populations, we propose an alternative approach for evaluating the efficacy of dietary supplements and functional foods based on a changepoint regression model (CPRM). The CPRM can be performed without stratified or subgroup analysis. By using profile likelihood methods based on the Akaike information criterion, inferences can made easily using standard statistical software. The proposed method was applied to skeletal muscle ratio study data, and the merit of the proposed method was demonstrated by comparing it with the conventional method. Keywords: Change point regression model Clinical trial; Dietary supplements; AIC

Estimating the asphaltene critical nanoaggregation concentration region using ultrasonic measurements and Bayesian inference

Bayesian inference and ultrasonic velocity have been used to estimate the self-association concentration of the asphaltenes in toluene using a changepoint regression model. The estimated values agree with the literature information and indicate that a lower abundance of the longer side-chains can cause an earlier onset of asphaltene self-association. Asphaltenes constitute the heaviest and most complicated fraction of crude petroleum and include a surface-active sub-fraction. When present above a critical concentration in pure solvent, asphaltene “monomers” self-associate and form nanoaggregates. Asphaltene nanoaggregates are thought to play a significant role during the remediation of petroleum spills and seeps. When mixed with water, petroleum becomes expensive to remove from the water column by conventional methods. The main reason of this difficulty is the presence of highly surface-active asphaltenes in petroleum. The nanoaggregates are thought to surround the water droplets, making the water-in-oil emulsions extremely stable. Due to their molecular complexity, modelling the self-association of the asphaltenes can be a very computationally-intensive task and has mostly been approached by molecular dynamic simulations. Our approach allows the use of literature and experimental data to estimate the nanoaggregation and its credible intervals. It has a low computational cost and can also be used for other analytical/experimental methods probing a changepoint in the molecular association behaviour.

Robust Fuzzy Clustering Algorithms for Change-Point Regression Models

This article presents a robust fuzzy procedure for estimating change-point regression models. We propose incorporating the fuzzy change-point algorithm with the M-estimation technique for robust estimations. The fuzzy c partitions concept is embedded into the change-point regression model so the fuzzy c-regressions and fuzzy c-means clustering can be employed to obtain the estimates of change-points and regression parameters. The M estimation with a robust criterion is used to make the estimators robust to the presence of outliers and heavy-tailed distributions. We create two robust algorithms named FCH and FCT by using Huber’s and Tukey’s functions as the robust criterion respectively. Extensive experiments with numerical and real examples are provided for demonstrating the effectiveness and the superiority of the proposed algorithms. The experimental results show the proposed algorithms are resistant to atypical observations and outperform the existing methods. The proposed FCH and FCT are generally comparable but FCT performs better in the presence of extremely high leverage outliers and heavy-tailed distributions. Real data applications show the practical usefulness of the proposed method.

변화점 회귀모델을 이용한 연료접촉 고무오링의 수명예측

Purpose: The objective of this study was to predict the lifetime of a rubber O-ring in contact with fuel in cases involving a heterogeneous degradation pattern.BRMethods: We introduced a change-point regression model to detect the point at which the degradation rate changed. The data after the change-point were processed using the exponential degradation model to predict the B_p lifetime.BRResults: The prediction results were used to evaluated the superiority of different fuel types, and the results were noted to be in agreement with those presented in literature. BRConclusion: The rubber O-ring in contact with JET A-1 fuel corresponded to a more stable compression set degradation pattern and exhibited a larger lifetime compared to those of BIOJET fuel.

Estimation of inter-individual variability of protein requirement by indicator amino acid oxidation method.

The indicator amino acid oxidation (IAAO) method is a recently developed method to determine the protein requirement and is particularly useful for analyzing human subjects because of its minimal invasiveness. IAAO study is performed using two-phase regression analysis, with the break-point between these phases being the estimated average requirement. However, this method requires that the break-point lie within a certain range in advance, which is in practice difficult. Recently, the change-point regression model (CPRM) has been proposed to be more effective for two-phase regression analysis. There is also a need to re-evaluate the value corresponding to the recommended dietary allowance. Calculation of the recommended dietary allowance requires data on the average requirement and the inter-individual variability of this requirement. However, no inter-individual variability values have been reported in the IAAO method. The aim of this study was thus to estimate the inter-individual variation in protein requirement using CPRM. From seven IAAO studies, the inter-individual variability was estimated as a coefficient of variation of about 20%. The coefficient of variation of the protein requirement determined by IAAO study was wider than the ordinary coefficient of variation obtained from the nitrogen balance test.

Association of Modifiable Lifestyle Factors With Cortical Amyloid Burden and Cerebral Glucose Metabolism in Older Adults With Mild Cognitive Impairment

Understanding the association of lifestyle factors with mild cognitive impairment enables the development of evidence-based interventions for delaying cognitive impairment. To explore whether objectively measured lifestyle factors, such as physical activity, conversation, and sleep, are associated with cortical amyloid burden and cerebral glucose metabolism in older adults with mild cognitive impairment. This cohort study included 855 community-dwelling adults in Usuki, Oita Prefecture, Japan, aged 65 years or older. Data were collected from August 2015 to December 2017. Participants were reviewed to examine risk and protective lifestyle factors for dementia. Data analysis was conducted in June 2019. Wearable sensors, carbon-11 labeled Pittsburgh compound B positron emission tomography images, and fluorine-18 fluorodeoxyglucose positron emission tomography images. Wearable sensor data, such as walking steps, conversation time, and sleep, were collected from August 2015 to October 2017, and positron emission tomography images were collected from October 2015 to December 2017. A multiple regression model and change-point regression model were used to examine the association of lifestyle factors with mean amyloid or fluorodeoxyglucose uptake, assessed on the basis of a standardized uptake value ratio of the frontal lobes, temporoparietal lobes, and posterior cingulate gyrus with the cerebellar cortex as the reference region. The bootstrap method was used to obtain nonparametric 95% CIs on the associations of lifestyle factors with cognitive decline. Of the 855 adults in the study, 118 (13.8%) were diagnosed with mild cognitive impairment, with a mean (SD) age of 75.7 (5.8) years and 66 (55.9%) women. Total sleep time was inversely associated with fluorodeoxyglucose uptake after adjusting for covariates (β = -0.287; 95% CI, -0.452 to -0.121, P < .001). Change-point regression showed an inverse association between total sleep time and mean amyloid uptake when sleep duration was longer than 325 minutes (B = -0.0018; 95% CI, -0.0031 to -0.0007). To our knowledge, this is the first study to demonstrate that total sleep time was associated with brain function in older adults with mild cognitive impairment. Sleep duration is a potentially modifiable risk factor for dementia at the mild cognitive impairment stage.

Alternative Algorithm for Automatically Driving Best-Fit Building Energy Baseline Models Using a Data—Driven Grid Search

Change-point regression models are often used to develop building energy baselines that can be used to predict energy use and determine energy savings during a given performance period. However, the reliability of building energy baselines can depend on how well the change-point model fits the data measured during the baseline period. This research proposes the use of segmented linear regression models with one or two change points for automatically driving best-fit building energy baseline models, along with an algorithm using a data-driven grid search to find the optimal change point(s) within a given data boundary for the proposed models. The algorithm was programmed and tested with actual measured data (e.g., daily gas and electricity use) for case-study buildings. Graphical and statistical analysis was also performed to validate its reliability within acceptable deviations of an overall coefficient of variation of the root mean squared error (i.e., CV(RMSE)) of 1%, as compared to the results derived from the ASHRAE Inverse Model Toolkit (IMT) that was developed as a public domain program to manually derive the change-point model with user specified parameters. Consequently, it is expected that the algorithm can be applied for automatically deriving best-fit building energy baseline models with optimal change point(s) from measured data.

A 100-m Sprint Time Is Associated With Deep Trunk Muscle Thickness in Collegiate Male Sprinters.

Introduction: One reason athletes train their trunk muscles is that the body's trunk stability has been shown to prevent injury. However, the relationship between body trunk muscle thickness, particularly that of deep muscles, and athletic performance remains to be clarified.Purpose: We aimed to explore the relationship between 100-m sprint performance and the sizes of the trunk stabilizing muscles, the psoas major muscle (PM), transversus abdominis (TA), and multifidus muscle (MM), in collegiate sprinters.Methods: Fourteen male sprinters belonging to a university athletics club participated in this study. The thicknesses of the TA and MM were measured using an ultrasonic diagnostic apparatus (ProSound C3; Aloka, Tokyo, Japan). The cross-sectional area of the PM was assessed by a magnetic resonance imaging apparatus (Vantage Elan; Toshiba Medical Systems, Tokyo, Japan). The relationship between these anthropometric parameters and the 100-m sprint time was analyzed by Spearman's correlation coefficient, multi- regression analysis, and the change-point regression model.Results: The sizes (mean ± SD) of the muscles were: PM, 43.074 ± 7.35 cm2; TA, 4.36 ± 0.72 mm; and MM, 3.99 ± 0.48 cm. The mean 100-m sprint time was 11.00 ± 0.48 s. Spearman's correlation analysis revealed that the 100-m sprint time had a significant moderate negative correlation with TA (ρ = −0.691, p < 0.01) and a low negative but not significant correlation with MM (ρ = −0.327, p = 0.28), whereas PM did not show a significant or in-negligible correlation. The change-point regression model found the change-points in the 100-m sprint time and the thickness of the TA and MM at 4.70 mm (95% CI: 4.00–5.43 mm) and 3.84 cm (95% CI: 3.28–4.31 cm), respectively. The sprint time decreased with an increase in the thickness of the muscles up to the change-points, whereas it did not change even if the muscles became thicker than the change-points. The change-points were consistently observed when the thickness of the muscles was normalized by body mass.Conclusion: Sprint performance for 100-m was found to be associated with TA and MM thickness in a biphasic manner. As muscle thickness increased, the sprint time decreased, followed by a plateau phase.

A Change-point Regression Approach for Efficacy Evaluation of Dietary Supplements (P13-017-19)

ObjectivesIn clinical trials for dietary supplements and functional foods, the study population tends to be a mixture of healthy subjects and those who are not so healthy but are not definitely diseased (called “borderline subjects”). For such heterogeneous populations, the t-test and ANCOVA method often fail to provide the desired treatment efficacy. We propose an alternative approach for the efficacy evaluation of dietary supplements and functional foods based on a change-point linear regression model. MethodsSuppose we are interested in analyzing data from a randomized controlled clinical trial of dietary supplements which was conducted under what is called pre-post design. We propose the change-point regression model (CPRM) as new analysis method. The model does not require the assumption of a constant treatment effect and provides clinically interpretable results. By employing the AIC-based profile likelihood method, inferences can be made easily using standard statistical software. ResultsCPRM method was applied to (-)-hydroxycitric acid (HCA) study data, and the merit of the method was demonstrated by comparing it with traditional methods those are ANCOVA or t-test. The AICs of CPRM, ANCOVA and t-test were 667.2, 685.9 and 685.0 respectively. Therefore, CPRM is well fit than traditional methods. Advantage of CPRM is that it can simultaneously provide information on effect appearance points and we succeeded estimation of the point in (-)-HCA study. ConclusionsWe propose an alternative approach for the efficacy evaluation of dietary supplements and functional foods based on a CPRM. By employing the AIC-based profile likelihood method, inferences can be made easily using standard statistical software. The proposed method was applied to the Garcinia study data, and the merit of the method was demonstrated by comparing it with the ANCOVA models. Funding SourcesThis research did not received any specific grant from funding agencies in the public. commercial, or not for-profit sectors.

Quantifying the ossification of the carpus in skeletal age estimation: Radiographic standards for Australian subadults

An evaluation of the development of a child’s skeleton and estimation of bone age provides an insight into a child’s overall maturation. This study aimed to introduce a contemporary method for assessing bone age of Australian children using formulae incorporating carpal areal measurements. The standards introduced in this study can be used to assess the developmental status of Australian children who may be affected by growth-related illnesses. Additionally, in situations where the living age of a subadult is unknown, methodologies to accurately estimate age are required, particularly in the Western world where knowledge of the age of an individual is necessary for legal reasons. The sample consisted of retrospective hand and wrist radiographs acquired from 541 children (females: 246, males: 295) aged from birth to 20 years. Using the DICOM viewer Weasis, the carpal area ratio (B.Ar/T.Ar) was calculated for each individual radiograph by measuring the carpal bone area (B.Ar) and total tissue area of the carpus (T.Ar). A changepoint regression model demonstrated that the model constructed in this study was the most accurate in the younger age groups and was able to accurately determine whether a child was under 12 years if female and 13 years if male. A rapid acceleration of growth was observed at approximately 12–13 years in our sample, which may represent the onset of the pubertal growth spurt; this resulted in a high data variance and low model prediction accuracy in female and male children older than 12 and 13 years, respectively.

Longitudinal Macular Structure-Function Relationships in Glaucoma and Their Sources of Variability

To review central structure-function (SF) relationships in glaucoma; to compare contributions of within-session and between-session variability to total variability of macular optical coherence tomography (OCT) thickness measurements; and to test the hypothesis that longitudinal within-eye variability of central SF relationships is smaller than between-individual variability. We reviewed the pertinent literature on central SF relationships in glaucoma. Thirty-eight eyes (20 normal or glaucoma subjects) had×3 macular images per session over 3 sessions, and superpixels thickness measurements for ganglion cell layer (GCL), ganglion cell/inner plexiform layer (GCIPL), ganglion cell complex (GCC), and full macular thickness (FMT) were exported. Linear mixed models were used for estimating contributions of between- and within-session variability to total thickness variability. One hundred twenty eyes with ≥3 10° visual fields (VFs)/OCT images were enrolled for the longitudinal study. We investigated within-eye longitudinal SF relationships (GCIPL thickness vs VF total deviations) with a change-point regression model and compared within-eye to between-individual variabilities with components-of-variance models. In the cross-sectional study, the between-session component contributed 8%, 11%, 11%, and 36% of total variability for GCL, GCIPL, GCC, and FMT, respectively. In the longitudinal study, between-individual variability explained 78%, 77%, and 67% of total SF variability at 3.4°, 5.6°, and 6.8° eccentricities, respectively (P < .05). SF relationships remained stable over time within individual eyes. Within-session variability accounts formost of macular thickness variability over time. Longitudinal within-eye SF variability is smaller than between-individual variability. Study of within-eye SF relationships could help clinicians better understand SF linking in glaucoma and help refine progression algorithms. NOTE: Publication of this article is sponsored bythe American Ophthalmological Society.

A model-based multithreshold method for subgroup identification.

Thresholding variable plays a crucial role in subgroup identification for personalized medicine. Most existing partitioning methods split the sample based on one predictor variable. In this paper, we consider setting the splitting rule from a combination of multivariate predictors, such as the latent factors, principle components, and weighted sum of predictors. Such a subgrouping method may lead to more meaningful partitioning of the population than using a single variable. In addition, our method is based on a change point regression model and thus yields straight forward model-based prediction results. After choosing a particular thresholding variable form, we apply a two-stage multiple change point detection method to determine the subgroups and estimate the regression parameters. We show that our approach can produce two or more subgroups from the multiple change points and identify the true grouping with high probability. In addition, our estimation results enjoy oracle properties. We design a simulation study to compare performances of our proposed and existing methods and apply them to analyze data sets from a Scleroderma trial and a breast cancer study.