Modeling Risk Factors for Intraindividual Variability: A Mixed-Effects Beta-Binomial Model Applied to Cognitive Function in Older People in the English Longitudinal Study of Ageing

Cognitive functioning in older age profoundly impacts quality of life and health. While most research on cognition in older age has focused on mean levels, intraindividual variability (IIV) around this may have risk factors and outcomes independent of the mean value. Investigating risk factors associated with IIV has typically involved deriving a summary statistic for each person from residual error around a fitted mean. However, this ignores uncertainty in the estimates, prohibits exploring associations with time-varying factors, and is biased by floor/ceiling effects. To address this, we propose a mixed-effects location scale beta-binomial model for estimating average probability and IIV in a word recall test in the English Longitudinal Study of Ageing. After adjusting for mean performance, an analysis of 9,873 individuals across 7 (mean = 3.4) waves (2002-2015) found IIV to be greater at older ages, with lower education, in females, with more difficulties in activities of daily living, in later birth cohorts, and when interviewers recorded issues potentially affecting test performance. Our study introduces a novel method for identifying groups with greater IIV in bounded discrete outcomes. Our findings have implications for daily functioning and care, and further work is needed to identify the impact for future health outcomes.

Changing trajectory of daily physical activity levels among at-risk adolescents: influences of motivational mechanisms

BACKGROUND

Guided by Self-Determination Theory (SDT), the purpose of this study was to determine changes in the 16-week moderate-to-vigorous physical activity (MVPA) trajectory of underserved adolescents who participated in the Connect through PLAY afterschool program intervention and the effects of changes in participating adolescents' intrinsic and autonomous extrinsic motivations on their MVPA trajectory over the 16-week intervention.

METHODS

A subsample of 113 adolescents (56.64% female; 61.06% African American; average age = 11.29) provided complete data throughout the 16-week intervention were examined. Adolescents' objective daily MVPA was measured using 7- day accelerometer data. Changes in adolescents' intrinsic motivation and autonomous extrinsic motivation were assessed using subscales from the Intrinsic Motivation Inventory [1] and the Treatment Self-Regulation Questionnaire [2] respectively. A hierarchical linear model was built and tested to address the research aims.

RESULTS

The results of hierarchical linear models showed that, on average, youth daily MVPA increased 6.36 minutes in each 8-week period. Intrinsic motivation change, but not autonomous extrinsic motivation, was a positive and significant level-2 predictor of daily MVPA changes.

CONCLUSION

The findings provide significant evidence suggesting a benefit of integrating SDT-based approaches and further suggest that nurturing intrinsic motivation can be an effective approach to supporting youth daily MVPA in under-resourced afterschool programs.

TRIAL REGISTRATION

Connect Through PLAY: A Staff-based Physical Activity Intervention for Middle School Youth (Connect). https://clinicaltrials.gov/ct2/show/NCT03732144 . Registered November 6th, 2018.

Effect of cumulative body mass index exposure and long-term related change on incident non-alcoholic fatty liver disease

BACKGROUND

To evaluate the association between cumulative body mass index (BMI) and long-term BMI change with non-alcoholic fatty liver disease (NAFLD).

METHODS

We included 19 477 adult participants (12 556 men and 6921 women) from the Kailuan study from January 2006 to December 2013. Cumulative BMI was assessed using a quadratic mixed-effects method by sex before the index year; then, the NAFLD outcome was followed till December 2019. The long-term BMI change was calculated as the percentage change in average cumulative BMI from the baseline BMI.

RESULTS

During a median follow-up of 5.63 years, 6229 individuals developed incident NAFLD. Independent of baseline BMI, the NAFLD risk escalated with the cumulative BMI with adjusted hazard ratios (HRs) (95% confidence interval [CI]) of 1.60 (1.48-1.73) and 2.28 (2.06-2.53) for the intermediate tertile and the highest tertile (P_trend  <0.001). The association is amplified in women and the young. Compared to a stable weight (BMI change: -3% to 3%), NAFLD risk increased in the baseline BMI < 24 kg/m² group with weight gain (BMI change: >3%) and decreased in BMI ≥24 kg/m² group with weight loss (BMI change: <-3%) for men and women. However, we only observed a decreased NAFLD risk in men (HR: 0.82, 95% CI: 0.69-0.97) with BMI < 24 kg/m² and weight loss.

CONCLUSIONS

Monitoring cumulative BMI may help to identify high-risk NAFLD populations. The association between weight gain or loss varies by sex and baseline BMI, suggesting the importance of individualized weight management for NAFLD prevention.

Comparing statistical methods in assessing the prognostic effect of biomarker variability on time-to-event clinical outcomes

Background

In recent years there is increasing interest in modeling the effect of early longitudinal biomarker data on future time-to-event or other outcomes. Sometimes investigators are also interested in knowing whether the variability of biomarkers is independently predictive of clinical outcomes. This question in most applications is addressed via a two-stage approach where summary statistics such as variance are calculated in the first stage and then used in models as covariates to predict clinical outcome in the second stage. The objective of this study is to compare the relative performance of various methods in estimating the effect of biomarker variability.

Methods

A joint model and 4 different two-stage approaches (naïve, landmark analysis, time-dependent Cox model, and regression calibration) were illustrated using data from a large multi-center randomized phase III trial, the Ocular Hypertension Treatment Study (OHTS), regarding the association between the variability of intraocular pressure (IOP) and the development of primary open-angle glaucoma (POAG). The model performance was also evaluated in terms of bias using simulated data from the joint model of longitudinal IOP and time to POAG. The parameters for simulation were chosen after OHTS data, and the association between longitudinal and survival data was introduced via underlying, unobserved, and error-free parameters including subject-specific variance.

Results

In the OHTS data, joint modeling and two-stage methods reached consistent conclusion that IOP variability showed no significant association with the risk of POAG. In the simulated data with no association between IOP variability and time-to-POAG, all the two-stage methods (except the naïve approach) provided a reliable estimation. When a moderate effect of IOP variability on POAG was imposed, all the two-stage methods underestimated the true association as compared with the joint modeling while the model-based two-stage method (regression calibration) resulted in the least bias.

Conclusion

Regression calibration and joint modelling are the preferred methods in assessing the effect of biomarker variability. Two-stage methods with sample-based measures should be used with caution unless there exists a relatively long series of longitudinal measurements and/or strong effect size (NCT00000125).

A Latent Variable Mixed-Effects Location Scale Model with an Application to Daily Diary Data

A mixed-effects location scale model allows researchers to study within- and between-person variation in repeated measures. Key components of the model include separate variance models to study predictors of the within-person variance, as well as predictors of the between-person variance of a random effect, such as a random intercept. In this paper, a latent variable mixed-effects location scale model is developed that combines a longitudinal common factor model and a mixed-effects location scale model to characterize within- and between-person variation in a common factor. The model is illustrated using daily reports of positive affect and daily stressors for a large sample of adult women.

WiSER: Robust and scalable estimation and inference of within-subject variances from intensive longitudinal data

The availability of vast amounts of longitudinal data from electronic health records (EHRs) and personal wearable devices opens the door to numerous new research questions. In many studies, individual variability of a longitudinal outcome is as important as the mean. Blood pressure fluctuations, glycemic variations, and mood swings are prime examples where it is critical to identify factors that affect the within-individual variability. We propose a scalable method, within-subject variance estimator by robust regression (WiSER), for the estimation and inference of the effects of both time-varying and time-invariant predictors on within-subject variance. It is robust against the misspecification of the conditional distribution of responses or the distribution of random effects. It shows similar performance as the correctly specified likelihood methods but is 103 ∼ 105 times faster. The estimation algorithm scales linearly in the total number of observations, making it applicable to massive longitudinal data sets. The effectiveness of WiSER is evaluated in extensive simulation studies. Its broad applicability is illustrated using the accelerometry data from the Women's Health Study and a clinical trial for longitudinal diabetes care.

Auxology of small samples: A method to describe child growth when restrictions prevent surveys

Background

Child growth in populations is commonly characterised by cross-sectional surveys. These require data collection from large samples of individuals across age ranges spanning 1–20 years. Such surveys are expensive and impossible in restrictive situations, such as, e.g. the COVID pandemic or limited size of isolated communities. A method allowing description of child growth based on small samples is needed.

Methods

Small samples of data (N~50) for boys and girls 6–20 years old from different socio-economic situations in Africa and Europe were randomly extracted from surveys of thousands of children. Data included arm circumference, hip width, grip strength, height and weight. Polynomial regressions of these measurements on age were explored.

Findings

Polynomial curves based on small samples correlated well (r = 0.97 to 1.00) with results of surveys of thousands of children from same communities and correctly reflected sexual dimorphism and socio-economic differences.

Conclusions

Fitting of curvilinear regressions to small data samples allows expeditious assessment of child growth in a number of characteristics when situations change rapidly, resources are limited and access to children is restricted.

Joint Modeling of Individual Trajectories, Within-Individual Variability, and a Later Outcome: Systolic Blood Pressure Through Childhood and Left Ventricular Mass in Early Adulthood

Within-individual variability of repeatedly measured exposures might predict later outcomes (e.g., blood pressure (BP) variability (BPV) is an independent cardiovascular risk factor above and beyond mean BP). Because 2-stage methods, known to introduce bias, are typically used to investigate such associations, we introduce a joint modeling approach, examining associations of mean BP and BPV across childhood with left ventricular mass (indexed to height; LVMI) in early adulthood with data (collected 1990-2011) from the UK Avon Longitudinal Study of Parents and Children cohort. Using multilevel models, we allowed BPV to vary between individuals (a "random effect") as well as to depend on covariates (allowing for heteroskedasticity). We further distinguished within-clinic variability ("measurement error") from visit-to-visit BPV. BPV was predicted to be greater at older ages, at higher body weights, and in female participants and was positively correlated with mean BP. BPV had a weak positive association with LVMI (10% increase in within-individual BP variance was predicted to increase LVMI by 0.21%, 95% credible interval: -0.23, 0.69), but this association became negative (-0.78%, 95% credible interval: -2.54, 0.22) once the effect of mean BP on LVMI was adjusted for. This joint modeling approach offers a flexible method of relating repeatedly measured exposures to later outcomes.

Improving convergence in growth mixture models without covariance structure constraints

Growth mixture models are a popular method to uncover heterogeneity in growth trajectories. Harnessing the power of growth mixture models in applications is difficult given the prevalence of nonconvergence when fitting growth mixture models to empirical data. Growth mixture models are rooted in the random effect tradition, and nonconvergence often leads researchers to modify their intended model with constraints in the random effect covariance structure to facilitate estimation. While practical, doing so has been shown to adversely affect parameter estimates, class assignment, and class enumeration. Instead, we advocate specifying the models with a marginal approach to prevent the widespread practice of sacrificing class-specific covariance structures to appease nonconvergence. A simulation is provided to show the importance of modeling class-specific covariance structures and builds off existing literature showing that applying constraints to the covariance leads to poor performance. These results suggest that retaining class-specific covariance structures should be a top priority and that marginal models like covariance pattern growth mixture models that model the covariance structure without random effects are well-suited for such a purpose, particularly with modest sample sizes and attrition commonly found in applications. An application to PTSD data with such characteristics is provided to demonstrate (a) convergence difficulties with random effect models, (b) how covariance structure constraints improve convergence but to the detriment of performance, and (c) how covariance pattern growth mixture models may provide a path forward that improves convergence without forfeiting class-specific covariance structures.

Extending the mixed‐effects model to consider within‐subject variance for Ecological Momentary Assessment data

Ecological Momentary Assessment data present some new modeling opportunities. Typically, there are sufficient data to explicitly model the within-subject (WS) variance, and in many applications, it is of interest to allow the WS variance to depend on covariates as well as random subject effects. We describe a model that allows multiple random effects per subject in the mean model (eg, random location intercept and slopes), as well as random scale in the error variance model. We present an example of the use of this model on a real dataset and a simulation study that shows the benefit of this model, relative to simpler approaches.

A Bayesian nonlinear mixed-effects location scale model for learning

We present a Bayesian nonlinear mixed-effects location scale model (NL-MELSM). The NL-MELSM allows for fitting nonlinear functions to the location, or individual means, and the scale, or within-person variance. Specifically, in the context of learning, this model allows the within-person variance to follow a nonlinear trajectory, where it can be determined whether variability reduces during learning. It incorporates a sub-model that can predict nonlinear parameters for both the location and scale. This specification estimates random effects for all nonlinear location and scale parameters that are drawn from a common multivariate distribution. This allows estimation of covariances among the random effects, within and across the location and the scale. These covariances offer new insights into the interplay between individual mean structures and intra-individual variability in nonlinear parameters. We take a fully Bayesian approach, not only for ease of estimation but also for inference because it provides the necessary and consistent information for use in psychological applications, such as model selection and hypothesis testing. To illustrate the model, we use data from 333 individuals, consisting of three age groups, who participated in five learning trials that assessed verbal memory. In an exploratory context, we demonstrate that fitting a nonlinear function to the within-person variance, and allowing for individual variation therein, improves predictive accuracy compared to customary modeling techniques (e.g., assuming constant variance). We conclude by discussing the usefulness, limitations, and future directions of the NL-MELSM.

Estimating the association between blood pressure variability and cardiovascular disease: An application using the ARIC Study

The association between visit-to-visit systolic blood pressure variability and cardiovascular events has recently received a lot of attention in the cardiovascular literature. But, blood pressure variability is usually estimated on a person-by-person basis and is therefore subject to considerable measurement error. We demonstrate that hazard ratios estimated using this approach are subject to bias due to regression dilution, and we propose alternative methods to reduce this bias: a two-stage method and a joint model. For the two-stage method, in stage one, repeated measurements are modelled using a mixed effects model with a random component on the residual standard deviation (SD). The mixed effects model is used to estimate the blood pressure SD for each individual, which, in stage two, is used as a covariate in a time-to-event model. For the joint model, the mixed effects submodel and time-to-event submodel are fitted simultaneously using shared random effects. We illustrate the methods using data from the Atherosclerosis Risk in Communities study.

A Mixed-Effects Location Scale Model for Dyadic Interactions

We present a mixed-effects location scale model (MELSM) for examining the daily dynamics of affect in dyads. The MELSM includes person and time-varying variables to predict the location, or individual means, and the scale, or within-person variances. It also incorporates a submodel to account for between-person variances. The dyadic specification can accommodate individual and partner effects in both the location and the scale components, and allows random effects for all location and scale parameters. All covariances among the random effects, within and across the location and the scale are also estimated. These covariances offer new insights into the interplay of individual mean structures, intra-individual variability, and the influence of partner effects on such factors. To illustrate the model, we use data from 274 couples who provided daily ratings on their positive and negative emotions toward their relationship - up to 90 consecutive days. The model is fit using Hamiltonian Monte Carlo methods, and includes subsets of predictors in order to demonstrate the flexibility of this approach. We conclude with a discussion on the usefulness and the limitations of the MELSM for dyadic research.

A 3-level Bayesian mixed effects location scale model with an application to ecological momentary assessment data

Ecological momentary assessment studies usually produce intensively measured longitudinal data with large numbers of observations per unit, and research interest is often centered around understanding the changes in variation of people's thoughts, emotions and behaviors. Hedeker et al developed a 2-level mixed effects location scale model that allows observed covariates as well as unobserved variables to influence both the mean and the within-subjects variance, for a 2-level data structure where observations are nested within subjects. In some ecological momentary assessment studies, subjects are measured at multiple waves, and within each wave, subjects are measured over time. Li and Hedeker extended the original 2-level model to a 3-level data structure where observations are nested within days and days are then nested within subjects, by including a random location and scale intercept at the intermediate wave level. However, the 3-level random intercept model assumes constant response change rate for both the mean and variance. To account for changes in variance across waves, as well as clustering attributable to waves, we propose a more comprehensive location scale model that allows subject heterogeneity at baseline as well as across different waves, for a 3-level data structure where observations are nested within waves and waves are then further nested within subjects. The model parameters are estimated using Markov chain Monte Carlo methods. We provide details on the Bayesian estimation approach and demonstrate how the Stan statistical software can be used to sample from the desired distributions and achieve consistent estimates. The proposed model is validated via a series of simulation studies. Data from an adolescent smoking study are analyzed to demonstrate this approach. The analyses clearly favor the proposed model and show significant subject heterogeneity at baseline as well as change over time, for both mood mean and variance. The proposed 3-level location scale model can be widely applied to areas of research where the interest lies in the consistency in addition to the mean level of the responses.