Relating the classical covariance adjustment techniques of multivariate growth curve models to modern univariate mixed effects models

Circadian variations in electric current responses at ryodoraku points across the waking stage: A prospective observational study

Human body undergoes the 24-hour daily rhythm in response primarily to light and darkness. The circadian rhythms of biomarkers reflect bodily conditions including the prognosis of some pathologies. As a sensitive index of sympathetic nervous response (SNR), electrodermal activity (EDA) is a recent research topic in healthcare industry as a noninvasive and easy-access biosignal. The EDA response at Ryodoraku points (RPs) is of potential clinical usage in relation to SNR and meridian theory, but still remains in its primitive development stage.In this study, the 24-hour variations of EDA for 14 hospitalized participants were monitored over 3 days using a Ryodoraku device, and a circadian model of EDA was constructed using a cosinor analysis based on the linear mixed effect model.As a result, EDA at every RP showed a circadian cycle with its value the lowest in the morning and increased gradually until the late afternoon, and monotonically decreased again until the next morning. Circadian variations were observed in EDAs of all 12 RPs. However, Ryodoraku-specific features were not detected. Midline estimating statistic of rhythm (MESOR) values in men and young group were higher than in women and old group, and cosinor analysis showed significant circadian rhythms, especially for men and young groups. Especially, circadian variation in EDA in the young group went above 35% of the MESOR value.It implies that the circadian rhythm should be considered for the Ryodoraku analysis to examine bodily conditions or the prognosis of some pathologies.

Morning surge in blood pressure using a random-effects multiple-component cosinor model

Blood pressure (BP) fluctuates throughout the day. The pattern it follows represents one of the most important circadian rhythms in the human body. For example, morning BP surge has been suggested as a potential risk factor for cardiovascular events occurring in the morning, but the accurate quantification of this phenomenon remains a challenge. Here, we outline a novel method to quantify morning surge. We demonstrate how the most commonly used method to model 24-hour BP, the single cosinor approach, can be extended to a multiple-component cosinor random-effects model. We outline how this model can be used to obtain a measure of morning BP surge by obtaining derivatives of the model fit. The model is compared with a functional principal component analysis that determines the main components of variability in the data. Data from the Mitchelstown Study, a population-based study of Irish adults (n = 2047), were used where a subsample (1207) underwent 24-hour ambulatory blood pressure monitoring. We demonstrate that our 2-component model provided a significant improvement in fit compared with a single model and a similar fit to a more complex model captured by b-splines using functional principal component analysis. The estimate of the average maximum slope was 2.857 mmHg/30 min (bootstrap estimates; 95% CI: 2.855-2.858 mmHg/30 min). Simulation results allowed us to quantify the between-individual SD in maximum slopes, which was 1.02 mmHg/30 min. By obtaining derivatives we have demonstrated a novel approach to quantify morning BP surge and its variation between individuals. This is the first demonstration of cosinor approach to obtain a measure of morning surge.

Adaptive Fitting of Linear Mixed-Effects Models with Correlated Random-effects

Linear mixed-effects model has been widely used in longitudinal data analyses. In practice, the fitting algorithm can fail to converge due to boundary issues of the estimated random-effects covariance matrix G, i.e., being near-singular, non-positive definite, or both. Current available algorithms are not computationally optimal because the condition number of matrix G is unnecessarily increased when the random-effects correlation estimate is not zero. We propose an adaptive fitting (AF) algorithm using an optimal linear transformation of the random-effects design matrix. It is a data-driven adaptive procedure, aiming at reducing subsequent random-effects correlation estimates down to zero in the optimal transformed estimation space. Simulations show that AF significantly improves the convergent properties, especially under small sample size, relative large noise and high correlation settings. One real data for Insulin-like Growth Factor (IGF) protein is used to illustrate the application of this algorithm implemented with software package R (nlme).

A linear mixed model approach to compare the evolution of multiple biological rhythms

The assessment and comparison of multiple biological rhythms represent an important challenge in chronobiology. They allow the investigation of whether a well-defined time-qualified relationship between biorhythms of the same frequency range is maintained in the presence of functional alterations, which may lead to chronodisruption or internal desynchronization. We propose a multivariate linear mixed model approach where functions of several biorhythms are jointly modeled in a multivariate longitudinal fashion, handling both the correlation between biorhythms of multiple outcomes and the correlation between measurements collected over time within the same biological entity. Furthermore, between-subject heterogeneity is also taken into account with the inclusion of random effects. Pairwise comparisons between biorhythms are performed by means of proper contrasts. As an example, we define contrasts which allow us testing whether or not two biorhythms are identical or opposing, providing additional support in clinical practice. Moreover, we illustrate the proposed method using both simulated and biological real data, concerning the comparison of three specific lymphocytes profiles which modulate the function of immune system between healthy subjects and non-small lung cancer patients. Finally, the corresponding SAS syntax is provided.

Metabolic characterization of nondiabetic severely obese patients undergoing Roux-en-Y gastric bypass: preoperative classification predicts the effects of gastric bypass on insulin-glucose homeostasis

INTRODUCTION

Obese individuals may have normal insulin-glucose homeostasis, insulin resistance, or diabetes mellitus. Whereas gastric bypass cures insulin resistance and diabetes mellitus, its effects on normal physiology have not been described. We studied insulin resistance and beta-cell function for patients undergoing gastric bypass.

METHODS

One hundred thirty-eight patients undergoing gastric bypass had fasting insulin and glucose levels drawn on days 0, 12, 40, 180, and 365. Thirty-one (22%) patients with diabetes mellitus were excluded from this analysis. Homeostatic model of assessment was used to estimate insulin resistance, insulin sensitivity, and beta-cell function. Based on this model, patients were categorized as high insulin resistance if their insulin resistance was >2.3.

RESULTS

Body mass index did not correlate with insulin resistance. Forty-seven (34%) patients were categorized as high insulin resistance. Correction of insulin resistance for this group occurred by 12 days postoperatively. Sixty (43%) patients were categorized as low insulin resistance. They demonstrated an increase of beta-cell function by 12 days postoperatively, which returned to baseline by 6 months. At 1 year postoperatively, the low insulin resistance group had significantly higher beta-cell function per degree of insulin sensitivity.

CONCLUSIONS

Adipose mass alone cannot explain insulin resistance. Severely obese individuals can be categorized by degree of insulin resistance, and the effect of gastric bypass depends upon this preoperative physiology.

Comparing linear and nonlinear mixed model approaches to cosinor analysis

The cosinor model, used for variables governed by circadian and other biological rhythms, is a nonlinear model in the amplitude and acrophase parameters that has a linear representation upon transformation. With linear cosinor analysis, amplitude and acrophase for each harmonic can be computed as nonlinear functions of the estimated linear regression coefficients. Here a flexible mixed model approach to cosinor analysis is considered, where the fixed effect parameters may enter nonlinearly as acrophase and amplitude for each harmonic or linearly after transformation to regression coefficients. In addition, the random effects may enter nonlinearly as subject-specific deviations from the acrophases and amplitudes or linearly as subject-specific deviations from the regression coefficients. It is also possible for the fixed effects to enter nonlinearly while the random effects enter linearly. Additionally, we evaluate whether including higher order linear harmonic terms as random effects, that is, Rao-Khatri 'covariance adjustment', improves precision. Applying the delta method to nonlinear functions of the parameters from linear mixed cosinor models to obtain approximate variances produces results that are often identical to results from nonlinear mixed models. Consequently, traditional linear cosinor analysis can often be used to estimate and compare the nonlinear parameters of interest, that is, amplitudes and acrophases, via the delta method. This is advantageous since the nonlinear mixed model may have convergence difficulties for more complex models. However, for some multiple-group analyses, the linear cosinor transformation should not be used and we clarify when the two methods are equivalent and when they differ.

Dynamic conditionally linear mixed models for longitudinal data

We develop a new class of models, dynamic conditionally linear mixed models, for longitudinal data by decomposing the within-subject covariance matrix using a special Cholesky decomposition. Here 'dynamic' means using past responses as covariates and 'conditional linearity' means that parameters entering the model linearly may be random, but nonlinear parameters are nonrandom. This setup offers several advantages and is surprisingly similar to models obtained from the first-order linearization method applied to nonlinear mixed models. First, it allows for flexible and computationally tractable models that include a wide array of covariance structures; these structures may depend on covariates and hence may differ across subjects. This class of models includes, e.g., all standard linear mixed models, antedependence models, and Vonesh-Carter models. Second, it guarantees the fitted marginal covariance matrix of the data is positive definite. We develop methods for Bayesian inference and motivate the usefulness of these models using a series of longitudinal depression studies for which the features of these new models are well suited.