Multilevel Statistical Models

Goldstein, Harvey

doi:10.1002/9780470973394

Cited by 2,230 publications

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“…They are formed by the piecewise connection of polynomial curves between a series of 'knots' subject to certain penalties to encourage smoothness. Mixed models 15 may be fitted to data sets comprising repeated measures across multiple individuals to obtain subjectspecific growth curves 16 . As penalized splines can be handled BMI peak in infancy as a predictor for later BMI RJ Silverwood et al within the mixed model framework they can also be extended in a similar manner.…”

Section: Methodsmentioning

confidence: 99%

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BMI peak in infancy as a predictor for later BMI in the Uppsala Family Study

Silverwood

Stavola

Cole³

et al. 2009

Int J Obes

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Background: The development of obesity through childhood, often characterized by using body mass index (BMI), has received much recent interest because of the rapidly increasing levels of obesity worldwide. However, the extent to which the BMI trajectory in the first year of life (the BMI 'peak' in particular) is associated with BMI in later childhood has received little attention. Subjects: The Uppsala Family Study includes 602 families, comprising mother, father and two consecutive singleton offspring, both of whom were delivered at the Uppsala Academic Hospital, Sweden, between 1987 and 1995. The children's postnatal growth data, including serial measurements of height and weight (from which BMI was calculated), were obtained from health records. All children had a physical examination when they were aged between 5 and 13 years, at which height and weight were again recorded and used to calculate age-and sex-adjusted BMI z-scores. Methods: Subject-specific growth curves were fitted to the infant BMI data using penalized splines with random coefficients, and from these the location of the BMI peak for each participant was estimated. A multilevel modelling approach was used to assess the relationships between the BMI peak and BMI z-score in later childhood. Results: The BMI peak occurred, on average, slightly later in female children, with a higher BMI peak in male children. Considered separately, both age and BMI at BMI peak were positively associated with later BMI z-score. Considered jointly, both dimensions of BMI peak retained their positive associations. Conclusions: The growth trajectory associated with higher childhood BMI appears to include a later and/or higher BMI peak in infancy.

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Section: Methodsmentioning

confidence: 99%

“…To account for the dependencies caused by the inclusion of sibling pairs in the UFS, a mixed modelling approach 15 was used, with family-specific random intercepts. Sex, birth weight and age at physical examination were included, with interactions between BMI peak and each of these variables also considered.…”

Section: Methodsmentioning

confidence: 99%

BMI peak in infancy as a predictor for later BMI in the Uppsala Family Study

Silverwood

Stavola

Cole³

et al. 2009

Int J Obes

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“…Other nested designs-featuring three or more levels of nesting, experimental variables that do vary within levels (for example, when investigating whether the number of docked vesicles differs between observations from a dendrite or an axon), nested longitudinal data (data collected on multiple time points describing dynamical processes 22,23 ) or nested non normally dis tributed data (for example, binary or Poisson distributed data)-are, however, possible and can be analyzed using multilevel analysis. We refer to previous publications 12,13,24 for comprehensive introductions to multilevel modeling and to the Centre for Multilevel Modeling website (http://www.bristol.ac.uk/cmm/learning/mmsoftware/) for a recent overview of existing multilevel software.…”

Section: Box 3 Estimating the Power To Detect An Experimental Effectmentioning

confidence: 99%

A solution to dependency: using multilevel analysis to accommodate nested data

et al. 2014

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“…The separate parameters in ‰ and † i are assembled into the vector of variance components . Mixed models that assume † i D 2 I, where I is the (n i n i ) identity matrix, are sometimes termed random effect models [7] or multilevel models [8].…”

Section: The Linear Mixed Modelmentioning

confidence: 99%

“…We fitted models (8) and (9) to these data. Hence, no assumption was made about mean ADL over follow-up, whereas the treatment effect was assumed to be constant.…”

Section: Example: a Trial In Parkinson's Diseasementioning

confidence: 99%

Some consequences of assuming simple patterns for the treatment effect over time in a linear mixed model

Bamia

White

Kenward

2012

Statistics in Medicine

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Linear mixed models are often used for the analysis of data from clinical trials with repeated quantitative outcomes. This paper considers linear mixed models where a particular form is assumed for the treatment effect, in particular constant over time or proportional to time. For simplicity, we assume no baseline covariates and complete post-baseline measures, and we model arbitrary mean responses for the control group at each time. For the variance-covariance matrix, we consider an unstructured model, a random intercepts model and a random intercepts and slopes model. We show that the treatment effect estimator can be expressed as a weighted average of the observed time-specific treatment effects, with weights depending on the covariance structure and the magnitude of the estimated variance components. For an assumed constant treatment effect, under the random intercepts model, all weights are equal, but in the random intercepts and slopes and the unstructured models, we show that some weights can be negative: thus, the estimated treatment effect can be negative, even if all time-specific treatment effects are positive. Our results suggest that particular models for the treatment effect combined with particular covariance structures may result in estimated treatment effects of unexpected magnitude and/or direction. Methods are illustrated using a Parkinson's disease trial.

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Multilevel Statistical Models

Cited by 2,230 publications

References 0 publications

BMI peak in infancy as a predictor for later BMI in the Uppsala Family Study

BMI peak in infancy as a predictor for later BMI in the Uppsala Family Study

A solution to dependency: using multilevel analysis to accommodate nested data

Some consequences of assuming simple patterns for the treatment effect over time in a linear mixed model

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