Standard Multilevel Models Research Articles

Studying place effects on health by synthesising individual and area-level outcomes

It is well established that there exist substantial area-level socio-demographic variations in population health. However, area-level associations between deprivation and health cannot necessarily be interpreted as place effects on individual health. We demonstrate how recently developed statistical models for combining individual and aggregate data can help to separate the effects of place of residence and personal circumstances. We apply these to two health outcomes: risk of hospitalisation for cardiovascular disease (CVD) and risk of self-reported limiting long-term illness (LLTI). A combination of small-area data from UK hospital episode statistics and the UK census and individual data from the Health Survey for England are analysed, using a new multilevel modelling method termed hierarchical related regression (HRR). The standard multilevel model for place and health explains outcomes from individual data in terms of individual and area-level characteristics. HRR models increase precision by also explaining population aggregate outcomes, in terms of the same predictors. Aggregate outcomes are modelled by averaging the individual-level exposure–outcome relationship over the area, which can alleviate the ecological bias associated with interpreting the relationship between aggregate quantities as an individual-level relationship. We find that there are associations between area-level deprivation indicators and both area-level rates of hospital admission for CVD and area-level rates of LLTI. Multilevel models fitted to the individual data alone had insufficient power to determine whether these associations were due to compositional or contextual effects. Using HRR models which incorporate area-level outcomes in addition to individual outcomes, we found that for CVD, the area-level differences were mostly explained by individual-level effects, in particular the increased risk for individuals from non-white ethnic backgrounds. In contrast, there remained a significant association between LLTI and area-level deprivation even after adjusting for the significant increased risk associated with individual-level ethnicity and income. Our study illustrates that extending multilevel models to incorporate both individual and area-level outcomes increases power to distinguish between contextual and compositional effects.

Multilevel growth curve models with covariate effects: application to recovery after stroke

In measuring the progression of, or recovery from, a disease an individual's outcome may be assessed on a number of occasions. A model of the relationship between outcome and time since disease occurred which accounts for patient characteristics could be used to describe patterns of recovery, to predict outcome for a patient, or to evaluate health interventions. We use multilevel models to analyse such data, focusing on the choice of powers of time both for mean outcome and covariate effects. We give equations for predicted outcome and corresponding standard errors (i) based only on baseline characteristics, and (ii) by conditioning on previous outcomes for an individual. In a study of 331 stroke patients, outcome was measured approximately 0, 2,4,6 and 12 months after stroke. Patient characteristics included age, sex, and pre-stroke handicap, together with stroke-severity indicators (presence of limb deficit, dysphasia, dysarthria or incontinence). Of these, only the effects of age, dysphasia and presence of deficit varied with time. Conditioning on previous observations improved the accuracy of predictions. The outcome variable clearly had a skewed distribution, and the model residuals showed evidence of non-Normality. We discuss alternative models for non-Normal data, and show that, here, the standard (Normal errors) multilevel model gives equivalent parameter estimates and predictions to those obtained from alternative models.

Multilevel time series models with applications to repeated measures data.

The analysis of repeated measures data can be conducted efficiently using a two-level random coefficients model. A standard assumption is that the within-individual (level 1) residuals are uncorrelated. In some cases, especially where measurements are made close together in time, this may not be reasonable and this additional correlation structure should also be modelled. A time series model for such data is proposed which consists of a standard multilevel model for repeated measures data augmented by an autocorrelation model for the level 1 residuals. First- and second-order autoregressive models are considered in detail, together with a seasonal component. Both discrete and continuous time are considered and it is shown how the autocorrelation parameters can themselves be structured in terms of further explanatory variables. The models are fitted to a data set consisting of repeated height measurements on children.