Random Coefficient Regression Model Research Articles

BOUNDED SUPPORT IN LINEAR RANDOM COEFFICIENT MODELS: IDENTIFICATION AND VARIABLE SELECTION

We consider linear random coefficient regression models, where the regressors are allowed to have a finite support. First, we investigate identification, and show that the means and the variances and covariances of the random coefficients are identified from the first two conditional moments of the response given the covariates if the support of the covariates, excluding the intercept, contains a Cartesian product with at least three points in each coordinate. We also discuss identification of higher-order mixed moments, as well as partial identification in the presence of a binary regressor. Next, we show the variable selection consistency of the adaptive LASSO for the variances and covariances of the random coefficients in finite and moderately high dimensions. This implies that the estimated covariance matrix will actually be positive semidefinite and hence a valid covariance matrix, in contrast to the estimate arising from a simple least squares fit. We illustrate the proposed method in a simulation study.

Locally optimal tests against periodic linear regression in short panels

This paper aims to detect the periodic coefficients of a Linear Regression model with Panel Data. Nonparametric locally and asymptotically optimal tests are proposed for testing the null hypothesis of a traditional linear regression model, against an alternative of a Periodic Coefficient Regression model. The Uniform Local Asymptotic Normality (ULAN) property is established for Periodic Linear Regression (PLR) model, to construct Locally asymptotically optimal tests. The rank-based version of the optimal parametric test is provided in particular cases. The performance of the proposed tests is valid with numerical simulations using the Monte Carlo study. Real data was studied for applying the periodic linear regression model which compared to both traditional regression and random coefficient regression models.

Statistical innovations in the API ADAD Colombia trial: a randomized, double‐blind, placebo‐controlled, parallel‐group study in cognitively unimpaired PSEN1 E280A mutation carriers evaluating efficacy and safety of crenezumab

AbstractBackgroundA number of extended families in Colombia with early‐onset ADAD have a PSEN1 mutation at codon 280 (E280A), comprise the largest ADAD kindred in the world. Trial participants have been treated with crenezumab (an experimental anti‐amyloid monoclonal antibody) or placebo. Topline results were presented in August, 2022 at AAIC. Although the trial did not demonstrate a statistically significant clinical benefit in either of its co‐primary endpoints, multiple statistical innovations were incorporated into this trial.MethodThe API ADAD Colombia trial is a randomized, double‐blind, placebo‐controlled, parallel‐group phase 2b study evaluating the efficacy, safety, and tolerability of crenezumab in cognitively unimpaired ADAD PSEN1 E280A mutation carriers in Colombia (NCT01998841). Due to under enrollment and concerns with the sensitivity of the primary endpoint, the protocol was amended mid‐trial to change from 260 weeks of treatment to a common‐close design whereby treatment continued in the double‐blind portion until the last enrolled participant received 260 weeks of treatment. Because of the change in trial design and power considerations, the primary analysis was adapted from a traditional mixed model with repeated measures (MMRM) based analysis to a random coefficient regression model (RCRM) based analysis. To quantitatively examine the adequacy of the RCRM assumptions, a robust variance estimator (Huber 1967; White 1982) was prespecified as a sensitivity analysis to calculate the standard errors and p‐values of the co‐primary endpoints. This study used a type‐I‐error‐controlled statistical procedure to identify and elevate the Free and Cued Selective Reminding Test (FCSRT) cueing index to a co‐primary endpoint. To comprehensively assess the crenezumab effect across primary and secondary endpoints, the prespecified relative reduction point estimates along with the bootstrapped 95% confidence intervals were generated.ResultInnovative statistical methods in this trial will be presented.ConclusionAlthough the API Colombia study did not meet its co‐primary endpoints, statistical learnings from this trial can benefit development of future AD trials. To further maximize the value of this unique trial dataset, participant‐level data will be made publicly available, including clinical, imaging, and biomarker data.Funding: NIA grants RF1‐AG041705, R01‐AG055444, Genentech, Roche, philanthropic contributions to Banner Alzheimer’s Foundation. FlorbetapirPET was partly supported by Avid and Lilly.

Remaining useful life prediction of aero-engines based on random-coefficient regression model considering random failure threshold

Remaining useful life (RUL) prediction is one of the most crucial components in prognostics and health management (PHM) of aero-engines. This paper proposes an RUL prediction method of aero-engines considering the randomness of failure threshold. Firstly, a random-coefficient regression (RCR) model is used to model the degradation process of aeroengines. Then, the RUL distribution based on fixed failure threshold is derived. The prior parameters of the degradation model are calculated by a two-step maximum likelihood estimation (MLE) method and the random coefficient is updated in real time under the Bayesian framework. The failure threshold in this paper is defined by the actual degradation process of aeroengines. After that, a expectation maximization (EM) algorithm is proposed to estimate the underlying failure threshold of aeroengines. In addition, the conditional probability is used to satisfy the limitation of failure threshold. Then, based on above results, an analytical expression of RUL distribution of aero-engines based on the RCR model considering random failure threshold (RFT) is derived in a closed-form. Finally, a case study of turbofan engine is used to demonstrate the effectiveness and superiority of the RUL prediction method and the parameters estimation method of failure threshold proposed.

Optimal designs for prediction in random coefficient regression with one observation per individual

The subject of this work is random coefficient regression models with only one observation per observational unit (individual). An analytical solution in form of optimality conditions is proposed for optimal designs for the prediction of individual random effect for a group of selected individuals. The behavior of optimal designs is illustrated by the example of linear regression models.

Remaining useful life prediction based on nonlinear random coefficient regression model with fusing failure time data

Remaining useful life (RUL) prediction is one of the most crucial elements in prognostics and health management (PHM). Aiming at the imperfect prior information, this paper proposes an RUL prediction method based on a nonlinear random coefficient regression (RCR) model with fusing failure time data. Firstly, some interesting natures of parameters estimation based on the nonlinear RCR model are given. Based on these natures, the failure time data can be fused as the prior information reasonably. Specifically, the fixed parameters are calculated by the field degradation data of the evaluated equipment and the prior information of random coefficient is estimated with fusing the failure time data of congeneric equipment. Then, the prior information of the random coefficient is updated online under the Bayesian framework, the probability density function (PDF) of the RUL with considering the limitation of the failure threshold is performed. Finally, two case studies are used for experimental verification. Compared with the traditional Bayesian method, the proposed method can effectively reduce the influence of imperfect prior information and improve the accuracy of RUL prediction.

Early caregiving adversity differentially shapes behavioral sensitivity to reward and risk during decision-making.

Cognitive systems that track, update, and utilize information about reward (consequences) and risk (uncertainty) are critical for adaptive decision-making as well as everyday functioning and well-being. However, it remains unclear how individual differences in reward and risk sensitivity are independently shaped by environmental influences and give rise to decision-making. Here, we investigated the impact of early life experience-a potent sculptor of development-on behavioral sensitivity to reward and risk. We administered a widely used decision-making paradigm to 55 adolescents and young adults who were exposed to early deprivation in the form of early institutional (orphanage) care (a type of early life adversity) and 81 comparison individuals who were reared by their biological parents and did not experience institutional care. Leveraging random coefficient regression and computational models, we observed that previously institutionalized individuals displayed general reward hyposensitivity, contributing to a decreased propensity to make decisions that stood to earn relatively large rewards relative to comparison individuals. By contrast, group differences in risk sensitivity were selectively observed on loss, but not gain, trials. These results are the first to independently and explicitly link early experiences to reward and risk sensitivity during decision-making. As such, they lay the groundwork for therapeutic efforts to identify and treat adversity-exposed individuals at risk for psychiatric disorders characterized by aberrant decision-making processes. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Joint Optimization Strategy of Condition-Based Maintenance and Spare Parts Ordering for Nonlinear Degraded Equipment under Imperfect Maintenance

When existing methods consider the impact of the imperfect maintenance activities on random degraded equipment, they usually assume that the degraded equipment is linear, and set the number of imperfect maintenance activities in advance. However, in engineering practice, most of the degraded equipment is nonlinear, and the number of imperfect maintenance activities has an impact on the development of maintenance strategies. Therefore, this paper proposes a new joint maintenance strategy considering the uncertainty of the number of imperfect maintenance activities for nonlinear degraded equipment. First, nonlinear degradation data are linearized based on Box-Cox transformation (BCT), and the degradation model under the influence of imperfect activities is constructed by the random coefficient regression model. Accordingly, the remaining useful life (RUL) probability distribution can be derived. Secondly, the number of maintenances is calculated by imperfect maintenance level and success probability. Then, the detection cycle, preventive maintenance threshold and maintenance times are taken as decision variables. The optimization objective is to minimize the expected average cost. However, this is restricted by availability and probability of success for imperfect maintenance activities. A multi-objective joint optimization model of condition-based maintenance and spare parts ordering is constructed. Finally, the analysis results based on numerical examples verify the feasibility of the proposed joint optimization strategy.

The Quantitative Analyses for the Effects of Two Wheat Varieties With Different Resistance Levels on the Fungicide Control Efficacies to Powdery Mildew.

Effective strategies to reduce the occurrence of wheat powdery mildew include the use of resistant varieties and application of fungicides. However, most studies rarely focus on the quantitative value of fungicide reduction using resistant varieties. To explore how the fungicides performed on different resistant wheat varieties to powdery mildew, field experiments were conducted during wheat growing seasons in 2018/19 and 2019/20 to investigate the control efficacies of enostroburin⋅epoxiconazole 18% SC and triadimefon 20% EC to wheat powdery mildew on a highly resistant wheat variety (“Baofeng104”) and a highly susceptible wheat variety (“Jingshuang16”). The analyses of variance on control efficacies showed that the control efficacies of enostroburin⋅epoxiconazole 18% SC to wheat powdery mildew were mostly significantly higher than triadimefon 20% EC under the same conditions (i.e., varieties, dosages). However, both fungicide and variety resistance made variabilities in the mildew disease index and played a significant role in mildew management. Particularly, the variety resistance made the greatest contribution in mildew-reducing, and the disease index could significantly be reduced on the highly resistant variety even in the absence of fungicide treatment. The control efficacies to mildew on the highly susceptible variety mainly depended on the high efficiency of fungicides whereas the highly resistant variety were mainly by virtue of variety resistance through the comparative analyses of linear regression models. Furthermore, the random-coefficient regression models and quantile models quantificationally expounded that the relationships between active ingredient dosage and disease index or control efficacy varied from the effects of variety, fungicide, and year, particular from variety. Thus, a dosage reference table of enostroburin⋅epoxiconazole 18% SC or triadimefon 20% EC for different resistant wheat varieties were provided; it would be helpful for users to formulate an appropriate dosage of fungicide on mildew management in the field and avoid overusing or superfluous application. Further study needs to consider the effects of fungicide reduction on wheat yields, only then the maximum-economic benefits on mildew management can be determined.

Interpreting Stochastic Frontier Model as Random Coefficient Model and Vice Versa

Abstract This note explores the relationship between the stochastic frontier model and the random coefficient regression model. It shows how to interpret the former as a special case of the latter and vice versa. JEL classification numbers: C13, C51, D24. Keywords: Stochastic production frontier, Random coefficient regression, Composite error, Technical inefficiency.

Equivalence theorems for multiple-design problems with application in mixed models

In the present paper we consider design criteria which depend on several designs simultaneously. We formulate equivalence theorems based on information matrices (if criteria depend on designs via information matrices) or with respect to the designs themselves (for finite design regions). We apply the obtained optimality conditions to multiple-group random coefficient regression models and illustrate the results by simple examples.

Dealing with elite sport competition demands: an exploration of the dynamic relationships between stress appraisal, coping, emotion, and performance during fencing matches

ABSTRACT The present research aimed to provide a more holistic analysis of stressful experiences in sport by examining how stress appraisal, coping and emotion are dynamically inter-related constructs and the extent to which their dynamic relationship is associated with objective performance. Based on process-oriented methods, two studies were conducted with elite athletes in order to investigate the dynamic relationship between these constructs and performance in highly demanding sport situations (Study 1: simulated competitive fencing matches during a training session; Study 2: real-life competitive fencing matches during an international competition). The results of the random coefficient regression models emphasise the dynamic nature of the relationship between stress appraisal, coping behaviour, emotion and objective performance over the course of fencing matches. They allowed identification of additional mediating effects of coping and emotion within dynamic relationships between stress appraisal and performance. These studies contribute to a deeper understanding of psychological adaptation in performance environments. The implications of the findings are discussed in relation to the design of effective coping interventions to support the learning of performance-related coping skills and the attainment of performance goals among individuals in highly demanding environments.

The pacifying effect of energy dependence on interstate conflict: A Large-N analysis

Energy remains essential to all forms of economic and military activity and constitutes one of the most valuable and strategic commodities in international trade. Using the newly released Global Energy Relations Dataset, we assess whether trade in energy resources systematically affect bilateral relations between an importer and its exporter. More specifically, we contrast the liberal expectation that dependence on trade in energy pacifies with the realist expectation that the vulnerabilities created via dependence on energy trade will lead to conflictual relations. Our random coefficient regression models indicate that the more dependent an importer is to an exporter for energy, the more pacific the importer will be towards that exporter. Different types of energy resources pacify importers to varying degrees; importers are less reluctant to initiate conflict against their exporters of more fungible energy resources. Accordingly, our findings show that this pacifying effect is minimal for coal and oil. Trade in electricity emerges as a stronger pacifier. We find natural gas to be the most potent pacifying energy resource. Our study also contributes to the debate on the geopolitical implications of global energy flows by pointing out to regional variations in how countries manage their relations vis-à-vis their energy suppliers.

Power and sample size for random coefficient regression models in randomized experiments with monotone missing data.

Random coefficient regression (also known as random effects, mixed effects, growth curve, variance component, multilevel, or hierarchical linear modeling) can be a natural and useful approach for characterizing and testing hypotheses in data that are correlated within experimental units. Existing power and sample size software for such data are based on two variance component models or those using a two-stage formulation. These approaches may be markedly inaccurate in settings where more variance components (i.e., intercept, rate of change, and residual error) are warranted. We present variance, power, sample size formulae, and software (R Shiny app) for use with random coefficient regression models with possible missing data and variable follow-up. We illustrate sample size and study design planning using data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database. We additionally examine the drivers of variability to better inform studydesign.

Efficacy and safety of nintedanib in patients with systemic sclerosis-associated interstitial lung disease treated with mycophenolate: a subgroup analysis of the SENSCIS trial

In the Safety and Efficacy of Nintedanib in Systemic Sclerosis (SENSCIS) trial, nintedanib reduced the rate of decline in forced vital capacity (FVC) in patients with systemic sclerosis-associated interstitial lung disease (SSc-ILD). Patients on stable treatment with mycophenolate for at least 6 months before randomisation could participate. The aim of this subgroup analysis was to examine the efficacy and safety of nintedanib by mycophenolate use at baseline. The SENSCIS trial was a randomised, double-blind, placebo-controlled trial, in which patients with SSc-ILD were randomly assigned (1:1) to receive 150 mg of oral nintedanib twice daily or placebo for at least 52 weeks. In a prespecified subgroup analysis, we analysed the primary endpoint of rate of decline in FVC over 52 weeks by mycophenolate use at baseline. In a post-hoc analysis, we analysed the proportion of patients with an absolute decrease in FVC of at least 3·3% predicted at week 52 (proposed minimal clinically important difference estimate for worsening of FVC in patients with SSc-ILD) in subgroups by mycophenolate use at baseline. Adverse events were reported in subgroups by mycophenolate use at baseline. Analyses were done in all participants who received at least one dose of study drug. We analysed the annual rate of decline in FVC using a random coefficient regression model (with random slopes and intercepts) including anti-topoisomerase I antibody status, age, height, sex, and baseline FVC as covariates and terms for baseline-by-time, treatment-by-subgroup, and treatment-by-subgroup-by-time interactions. SENSCIS is registered with ClinicalTrials.gov, NCT02597933, and is now complete. Between Nov 30, 2015, and Oct 31, 2017, 819 participants were screened and 576 were enrolled, randomly assigned to, and treated with nintedanib (n=288) or placebo (n=288). 139 (48%) of 288 in the nintedanib group and 140 (49%) of 288 in the placebo group were taking mycophenolate at baseline. In patients taking mycophenolate at baseline, the adjusted mean annual rate of decline in FVC was -40·2 mL per year (SE 19·8) with nintedanib and -66·5 mL per year (19·3) with placebo (difference: 26·3 mL per year [95% CI -27·9 to 80·6]). In patients not taking mycophenolate at baseline, the adjusted mean annual rate of decline in FVC was -63·9 mL per year (SE 19·3) with nintedanib and -119·3 mL per year (19·0) with placebo (difference: 55·4 mL per year [95% CI 2·3 to 108·5]). We found no heterogeneity in the effect of nintedanib versus placebo on the annual rate of decline in FVC between the subgroups by mycophenolate use (p value for interaction=0·45). In a post-hoc analysis, the proportion of patients with an absolute decrease in FVC of at least 3·3% predicted was lower with nintedanib than with placebo in both patients taking mycophenolate (40 [29%] of 138 vs 56 [40%] of 140; odds ratio 0·61 [0·37 to 1·01]) and those not taking mycophenolate (59 [40%] of 149 vs 70 [47%] of 148; 0·73 [0·46 to 1·16]) at baseline. The adverse event profile of nintedanib was similar between the subgroups. Diarrhoea, the most common adverse event, was reported in 106 (76%) of 139 patients in the nintedanib group and 48 (34%) of 140 in the placebo group among those taking mycophenolate at baseline, and in 112 (75%) of 149 in the nintedanib group and 43 (29%) of 148 in the placebo group among those not taking mycophenolate at baseline. Over the entire trial period, 19 patients died (ten in the nintedanib group and nine in the placebo group). One death in the nintedanib group was considered to be related to study drug. Nintedanib reduced the progression of interstitial lung disease both in patients with SSc-ILD who were and were not using mycophenolate at baseline, with no heterogeneity in its treatment effect detected between the subgroups. The adverse event profile of nintedanib was similar in the subgroups by mycophenolate use. Our findings suggest that the combination of mycophenolate and nintedanib offers a safe treatment option for patients with SSc-ILD. More data are needed on the benefits of initial combination therapy versus a sequential approach to treatment of SSc-ILD. Boehringer Ingelheim.

Influence of climatic conditions on tympanic temperature and milk production in grazing cows

The present study aimed to analyze large volumes of tympanic temperature (TT) data to identify its use as a physiological indicator of climatic conditions and its relationship with milk production in grazing cows under tropical lowland conditions. Three dairy farms and 21 multiparous early lactation cows were included in the study. Seven animals were equipped with tympanic temperature wireless sensors within each farm, and permanent information was collected hourly for 22 days on average. Ambient temperature (AT), relative humidity (RH), wind speed (WS), precipitation (PP), and THI information were obtained from meteorological stations located close to each farm. Statistical analyses included Spearman correlations and random coefficient regression models (P < 0.05). TT presented moderate and significant correlations with AT (0.35 to 0.49), SR (0.25 to 0.32), THI (0.35 to 0.49), and RH (-0.35 to -0.49). Climatic variables like AT, PP, SR, and WS were the most contributing factors to TT prediction (R2 =0.42 to 0.86). Grazing dairy cows in tropical scenarios accumulate heat during the day and dissipate it at nighttime, although higher producing animals deal with more problems to reach thermal homeostasis. Correlations between TT and daily milk production varied according to animal yield; however, higher TT values were related to the most productive cows. The effect of TT on milk production prediction was not conclusive among farms, possibly by animal management or others characteristics of the systems. TT determination through remote sensors allows a reliable diagnosis of the physiological temperature response to climatic conditions.

Estimating Residual Life Distributions of Complex Operational Systems Using a Remaining Maintenance Free Operating Period (RMFOP)-Based Methodology.

Recent developments in the area of condition monitoring research have been targeted towards predicting machinery health condition for the purpose of preventative maintenance. Typically, published research uses data collected from rotating components (bearings, cutting tools, etc.) working in an idealized lab environment as the case study for prognosis algorithm validations. However, the operational implementation in industry is still very sporadic, mainly owing to the lack of proper data allowing sufficiently mature development of comprehensive methodologies. The prognosis methodology presented herein bridges the gap between academic research and industrial implementations by employing a novel time period for prognosis and implementing random coefficients regression models. The definition of the remaining maintenance-free operating period (RMFOP) is proposed first, which helps to transform the usefulness of the degradation data that is readily available from data short of failure. Degradation patterns are subsequently extracted from the original degradation data, before fitting into either of two regression models (linear or exponential). The system residual life distributions are then computed and updated by estimating the parameter statistics within the model. This RMFOP-based methodology is validated using real-world degradation data collected from multiple operational railway switch systems across Great Britain. The results indicate that both the linear model and the exponential model can produce residual life distributions with a sufficient prediction accuracy for this specific application. The exponential model gives better predictions, the accuracy of which also improves as more of system life percentage has elapsed. By using the RMFOP methodology, switch system health condition affected by an incipient overdriving fault is recognized and predicted.

Rate-optimal nonparametric estimation for random coefficient regression models

Random coefficient regression models are a popular tool for analyzing unobserved heterogeneity, and have seen renewed interest in the recent econometric literature. In this paper, we obtain the optimal pointwise convergence rate for estimating the density in the linear random coefficient model over Hölder smoothness classes, and in particular show how the tail behavior of the design density impacts this rate. In contrast to previous suggestions, the estimator that we propose and that achieves the optimal convergence rate does not require dividing by a nonparametric density estimate. The optimal choice of the tuning parameters in the estimator depends on the tail parameter of the design density and on the smoothness level of the Hölder class, and we also study adaptive estimation with respect to both parameters.

1172-P: Impact of Telemedicine Clinics in the Management of Type 1 Diabetes

Background: Our institution began telemedicine clinics at rural hospitals in 2013, with standard office visits delivered synchronously via video conferencing. This project aims to assess the impact of telemedicine clinics in T1D care at our institution. Methods: IRB approval was obtained to access records of people with T1D with three or more telemedicine visits from Nov 2013 to Oct 2019. To assess change in A1c, we used a random coefficient regression model and estimated the effect of time on A1c, controlling for gender and age at start of treatment. Data were collected on change in treatment and prior provider (PCP, outside/academic endocrinologist). Results: The 139 patients evaluated (average age 45 y (range 16-94), 58% F) had an average of 8 A1c values (2-23) over an average duration of 32 mos (4-69). The scatterplot and fitted regression line show a temporal A1c decline. Similarly, random coefficient regression analysis provided overwhelming evidence for an A1c decline (P&amp;lt; 0.001). Each year in telemedicine care was associated with a decline of 0.13 in A1c (95% CI: -0.20, -0.06). Age and gender were not associated with A1c. A1c decline was noted irrespective of prior provider or treatment change (ie, starting CGM/pump therapy). Conclusions: Our data supports the concept that T1D can be effectively managed via telemedicine. Declines in A1c were seen in all groups, irrespective of age, prior provider and additions of diabetes technology. Disclosure L.A. Eiland: None. M. Siahpush: None. P. Akkireddy: None. L. Kuechenmeister: None.

Multi-stage nested classification credibility quantile regression model

In insurance (or in finance) practice, in a regression setting, there are cases where the error distribution is not normal and other cases where the set of data is contaminated due to outlier events. In such cases the classical credibility regression models lead to an unsatisfactory behavior of credibility estimators, and it is more appropriate to use quantile regression instead of the ordinary least squares estimation. However, these quantile credibility models cannot perform effectively when the set of data has nested (hierarchical) structure. This paper develops credibility models for regression quantiles with nested classification as an alternative to Norberg’s (1986) approach of random coefficient regression model with multi-stage nested classification. This paper illustrates two types of applications, one with insurance data and one with Fama/French financial data.