Multilevel growth curve models that incorporate a random coefficient model for the level 1 variance function

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.

\log σ_{i}

distribution,

μ_{σ, i} = ζ^{T} X_{i}^{σ}

. Similar models have previously been considered by Hedeker et al and Goldstein et al…”

Section: Discussionmentioning

confidence: 99%

σ_{i}^{2}

. )…”

Section: Methodsmentioning

confidence: 99%

Section: Mixed Effects Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Barrett

Huille

Parker

et al. 2018

“…Allowing for multiple random location effects (eg, random intercepts and slopes) is a natural extension of the MELS model, and several authors have developed such models using Bayesian estimation approaches . Here, we provide a similar extension of allowing multiple random location effects to the MELS model, however using a maximum marginal likelihood estimation approach.…”

Section: Introductionmentioning

confidence: 99%

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

Nordgren

Hedeker

Dunton

et al. 2019

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

Lin

Mermelstein

Hedeker

2018

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.