Designs For Linear Mixed Models Research Articles

Repeated-Measures Analysis in the Context of Heteroscedastic Error Terms with Factors Having Both Fixed and Random Levels

The design and analysis of experiments which involve factors each consisting of both fixed and random levels fit into linear mixed models. The assumed linear mixed-model design matrix takes either a full-rank or less-than-full-rank form. The complexity of the data structures of such experiments falls in the model-selection and parameter-estimation process. The fundamental consideration in the estimation process of linear models is the special case in which elements of the error vector are assumed equal and uncorrelated. However, different assumptions on the structure of the variance–covariance matrix of error vector in the estimation of parameters of a linear mixed model may be considered. We conceptualise a repeated-measures design with multiple between-subjects factors, in which each of these factors has both fixed and random levels. We focus on the construction of linear mixed-effects models, the estimation of variance components, and hypothesis testing in which the default covariance structure of homoscedastic error terms is not appropriate. We illustrate the proposed approach using longitudinal data fitted to a three-factor linear mixed-effects model. The novelty of this approach lies in the exploration of the fixed and random levels of the same factor and in the subsequent interaction effects of the fixed levels. In addition, we assess the differences between levels of the same factor and determine the proportion of the total variation accounted for by the random levels of the same factor.

Equivalence theorems for c and DA‐optimality for linear mixed effects models with applications to multitreatment group assignments in health care

AbstractWe construct and ‐optimal approximate designs for linear mixed models with group‐specific treatment for estimating parameters or contrasts in the population parameters. We establish equivalence theorems to confirm optimality of these designs under a linear mixed model and provide illustrative application to find , and ‐optimal designs for polynomial and fractional polynomial models with multitreatment group assignments. For more complex models, we briefly review metaheuristics and their potential applications to find various optimal designs, including optimal designs for problems considered here and their extensions.

D-optimal designs for linear mixed model with random effects of Dirichlet process

This paper considers D-optimal designs for linear mixed models involving random effects with unknown distributions. From Bayesian point of view, the Dirichlet process as a prior distribution on the space of all distributions is used. Based on the Dirichlet process as a prior, we give the Bayes estimate of the density function of the response variable, which result in a mixture of two normal distributions. An explicit form of the Fisher information matrix for the proposed model is derived by using the Fourier transform and then D-optimal design is obtained by numerical calculations.

G-optimal designs for hierarchical linear models: an equivalence theorem and a nature-inspired meta-heuristic algorithm

Hierarchical linear models are widely used in many research disciplines and estimation issues for such models are generally well addressed. Design issues are relatively much less discussed for hierarchical linear models but there is an increasing interest as these models grow in popularity. This paper discusses the G-optimality for predicting individual parameters in such models and establishes an equivalence theorem for confirming the G-optimality of an approximate design. Because the criterion is non-differentiable and requires solving multiple nested optimization problems, it is much harder to find and study G-optimal designs analytically. We propose a nature-inspired meta-heuristic algorithm called competitive swarm optimizer (CSO) to generate G-optimal designs for linear mixed models with different means and covariance structures. We further demonstrate that CSO is flexible and generally effective for finding the widely used locally D-optimal designs for nonlinear models with multiple interacting factors and some of the random effects are correlated. Our numerical results for a few examples suggest that G and D-optimal designs may be equivalent and we establish that D and G-optimal designs for hierarchical linear models are equivalent when the models have only a random intercept only. The challenging mathematical question of whether their equivalence applies more generally to other hierarchical models remains elusive.

Two-Year Longitudinal Monitoring of Amnestic Mild Cognitive Impairment Patients with Prodromal Alzheimer's Disease Using Topographical Biomarkers Derived from Functional Magnetic Resonance Imaging and Electroencephalographic Activity.

Auditory "oddball" event-related potentials (aoERPs), resting state functional magnetic resonance imaging (rsfMRI) connectivity, and electroencephalographic (rsEEG) rhythms were tested as longitudinal functional biomarkers of prodromal Alzheimer's disease (AD). Data were collected at baseline and four follow-ups at 6, 12, 18, and 24 months in amnesic mild cognitive impairment (aMCI) patients classified in two groups: "positive" (i.e., "prodromal AD"; n = 81) or "negative" (n = 63) based on a diagnostic marker of AD derived from cerebrospinal samples (Aβ42/P-tau ratio). A linear mixed model design was used to test functional biomarkers for Group, Time, and Group×Time effects adjusted by nuisance covariates (only data until conversion to dementia was used). Functional biomarkers that showed significant Group effects ("positive" versus "negative", p < 0.05) regardless of Time were 1) reduced rsfMRI connectivity in both the default mode network (DMN) and the posterior cingulate cortex (PCC), both also giving significant Time effects (connectivity decay regardless of Group); 2) increased rsEEG source activity at delta (<4 Hz) and theta (4-8 Hz) rhythms and decreased source activity at low-frequency alpha (8-10.5 Hz) rhythms; and 3) reduced parietal and posterior cingulate source activities of aoERPs. Time×Group effects showed differential functional biomarker progression between groups: 1) increased rsfMRI connectivity in the left parietal cortex of the DMN nodes, consistent with compensatory effects and 2) increased limbic source activity at theta rhythms. These findings represent the first longitudinal characterization of functional biomarkers of prodromal AD relative to "negative" aMCI patients based on 5 serial recording sessions over 2 years.

Longitudinal Assessment of Balance and Gait After Concussion and Return to Play in Collegiate Athletes.

In longitudinal studies tracking recovery after concussion, researchers often have not considered the timing of return to play (RTP) as a factor in their designs, which can limit the understanding of how RTP may affect the analysis and resulting conclusions. To evaluate the recovery of balance and gait in concussed athletes using a novel linear mixed-model design that allows an inflection point to account for changes in trend that may occur after RTP. Cohort study. University athletics departments, applied field setting. Twenty-three concussed (5 women, 18 men; age = 20.1 ± 1.3 years) and 25 healthy control (6 women, 19 men; age = 20.9 ± 1.4 years) participants were studied. Participants were referred by their team athletic trainers. Measures consisted of the Balance Error Scoring System (BESS) total score, sway (instrumented root mean square of mediolateral sway), single-task gait speed, gait speed while simultaneously reading a handheld article (dual-task gait speed), dual-task cost of reading on gait speed, and dual-task cost of walking on reading. We observed no significant effects or interactions for the BESS. Instrumented sway was worse in concussed participants, and a change in the recovery trend occurred after RTP. We observed group and time effects and group × time and group × RTP change interactions (P ≤ .046). No initial between-groups differences were found for single-task or dual-task gait. Both groups increased gait speed initially and then leveled off after the average RTP date. We noted time and RTP change effects and positive group × time interactions for both conditions (P ≤ .042) and a group × RTP change interaction for single-task gait speed (P = .005). No significant effects or interactions were present for the dual-task cost of reading on gait speed or the dual-task cost of walking on reading. Changes in the rate of recovery were coincident with the timing of RTP. Although we cannot suggest these changes were a result of the athletes returning to play, these findings demonstrate the need for further research to evaluate the effects of RTP on concussion recovery.

D-optimal designs for multiarm trials with dropouts.

Multiarm trials with follow‐up on participants are commonly implemented to assess treatment effects on a population over the course of the studies. Dropout is an unavoidable issue especially when the duration of the multiarm study is long. Its impact is often ignored at the design stage, which may lead to less accurate statistical conclusions. We develop an optimal design framework for trials with repeated measurements, which takes potential dropouts into account, and we provide designs for linear mixed models where the presence of dropouts is noninformative and dependent on design variables. Our framework is illustrated through redesigning a clinical trial on Alzheimer's disease, whereby the benefits of our designs compared with standard designs are demonstrated through simulations.

The importance of healthcare managers’ organizational preconditions and support resources for their appraisal of planned change and its outcomes

Background: Healthcare managers are expected to lead and manage planned organizational change intended to improve healthcare process quality. However, their complex working conditions offer limited decision control, and healthcare managers often feel ill prepared and inadequately supported to perform their duties. Healthcare managers have previously described their need for organizational support, but we lack knowledge of the preconditions and resources that help managers implement planned change.Methods: This prospective cohort study examined healthcare managers at three Swedish hospitals implementing lean production and two Swedish hospitals implementing their own improvement model. Questionnaire data from 2012, 2103, and 2014 were used in following up. We used t-tests and a linear mixed model design in analysing the data.Results: Healthcare managers who perceived strong support from managers, employees, colleagues, and the organization and managers with the longest managerial experience had the least negative appraisal of change. Managers who perceived strong support from employees, management, and the organizational structure perceived higher levels of healthcare process quality.Conclusions: Long managerial experience and strong support from managers, employees, and the organization are important formanagers’ appraisal of, work on, and successful implementation of planned change. Top management must therefore ensure that the healthcare managers have sufficient managerial experience and support before they delegate to them the responsibility to implement planned change.

S.P.42 Effects of a physical exercise programme in adults with myotonic dystrophy type 1 – A one-year follow-up study

Abstract Reduced physical activity can be a consequence of a progressive neuromuscular disease like myotonic dystrophy type 1 (DM1) and lead to an increased risk for secondary chronic conditions. Regular physical activity has a positive effect on health in able-bodied populations, but there is limited clinical research on people with DM1. The aim of this study was to evaluate functioning, in particular walking capacity, lower-extremity performance, and mobility and balance, one-year after the completion of a physical exercise programme. Thirty-five persons with DM1, stratified for functional level, were assigned to a control group (10 women and seven men, mean age 41 years) or a training group (10 women and eight men, mean age 44 years). The training group participated in an individually adapted group exercise programme incorporating aerobic activities, strength training and flexibility exercises, for 60 min twice a week during 14 weeks. Eleven persons completed the exercise programme with at least 75% adherence. No negative effects were reported. Primary outcome measure was the six-minute walk test (6MWT) and secondary were the timed-stands test and the timed up-and-go test. Assessments were made before, immediately after and 12 months after the intervention period by two independent physiotherapists, blinded to group allocation. A linear mixed-model design was used for evaluation. Intention-to-treat analyses did not reveal any significant differences between groups or interaction effects between time and group. There was, however, a significant time effect for the 6MWT ( p = 0.027). Pair-wise comparisons showed that the mean 6MWT distance decreased with 13.3 m (95% CI: 1.2–25.5), p = 0.032, from before to 12 months after the intervention, and with 15.7 m (95% CI: 3.5–28.0), p = 0.013, from immediately after to 12 months after the intervention. In conclusion, there were no long-term effects of the physical exercise programme and walking capacity decreased over time.

ODMixed: A tool to obtain optimal designs for heterogeneous longitudinal studies with dropout

ODMixed is a computer program to obtain optimal designs for linear mixed models of longitudinal studies. These designs account for heterogeneous correlated errors and for data with dropout. Designs are compared by using relative efficiencies, e.g., between a D-optimal design for homogeneous data and another for heterogeneous data or between a D-optimal design for complete data against another that optimizes designs when data is missing at random. Two examples are worked out to illustrate how researchers could use this computer program to profit of optimal design theory at the planning stage of longitudinal studies.

Pediatric Nurse Staffing and Quality of Care in the Hospital Setting

Indicators of quality and nurse staffing in pediatrics are distinct from adults. A retrospective, correlational, linear mixed model design was used to describe relationships between pediatric nurse staffing and 5 indicators of quality care from a convenience sample of 7 academic children's hospitals. Key findings supported a strong inverse relationship between the proportion of hours of pediatric nursing care delivered by registered nurses and the rate of occurrence of central line (P < .001) and bloodstream infections (P < .05). Supplemental nurse staffing hours also demonstrated relationships between bloodstream infections and parent/family complaints.

The effect of dropout on the efficiency of D‐optimal designs of linear mixed models

Dropout is often encountered in longitudinal data. Optimal designs will usually not remain optimal in the presence of dropout. In this paper, we study D-optimal designs for linear mixed models where dropout is encountered. Moreover, we estimate the efficiency loss in cases where a D-optimal design for complete data is chosen instead of that for data with dropout. Two types of monotonically decreasing response probability functions are investigated to describe dropout. Our results show that the location of D-optimal design points for the dropout case will shift with respect to that for the complete and uncorrelated data case. Owing to this shift, the information collected at the D-optimal design points for the complete data case does not correspond to the smallest variance. We show that the size of the displacement of the time points depends on the linear mixed model and that the efficiency loss is moderate.

Considerations on group-wise identical designs for linear mixed models

We consider a general class of mixed models, where the individual parameter vector is composed of a linear function of the population parameter vector plus an individual random effects vector. The linear function can vary for the different individuals. We show that the search for optimal designs for the estimation of the population parameter vector can be restricted to the class of group-wise identical designs, i.e., for each of the groups defined by the different linear functions only one individual elementary design has to be optimized. A way to apply the result to non-linear mixed models is described.