Study objective: In social epidemiology, it is easy to compute and interpret measures of variation in multilevel linear regression, but technical difficulties exist in the case of logistic regression. The aim of this study was to present measures of variation appropriate for the logistic case in a didactic rather than a mathematical way. Design and participants: Data were used from the health survey conducted in 2000 in the county of Scania, Sweden, that comprised 10 723 persons aged 18–80 years living in 60 areas. Conducting multilevel logistic regression different techniques were applied to investigate whether the individual propensity to consult private physicians was statistically dependent on the area of residence (that is, intraclass correlation (ICC), median odds ratio (MOR)), the 80% interval odds ratio (IOR-80), and the sorting out index). Results: The MOR provided more interpretable information than the ICC on the relevance of the residential area for understanding the individual propensity of consulting private physicians. The MOR showed that the unexplained heterogeneity between areas was of greater relevance than the individual variables considered in the analysis (age, sex, and education) for understanding the individual propensity of visiting private physicians. Residing in a high education area increased the probability of visiting a private physician. However, the IOR showed that the unexplained variability between areas did not allow to clearly distinguishing low from high propensity areas with the area educational level. The sorting out index was equal to 82%. Conclusion: Measures of variation in logistic regression should be promoted in social epidemiological and public health research as efficient means of quantifying the importance of the context of residence for understanding disparities in health and health related behaviour.

The logistic regression model is frequently used in epidemiologic studies, yielding odds ratio or relative risk interpretations. Inspired by the theory of linear normal models, the logistic regression model has been extended to allow for correlated responses by introducing random effects. However, the model does not inherit the interpretational features of the normal model. In this paper, the authors argue that the existing measures are unsatisfactory (and some of them are even improper) when quantifying results from multilevel logistic regression analyses. The authors suggest a measure of heterogeneity, the median odds ratio, that quantifies cluster heterogeneity and facilitates a direct comparison between covariate effects and the magnitude of heterogeneity in terms of well-known odds ratios. Quantifying cluster-level covariates in a meaningful way is a challenge in multilevel logistic regression. For this purpose, the authors propose an odds ratio measure, the interval odds ratio, that takes these difficulties into account. The authors demonstrate the two measures by investigating heterogeneity between neighborhoods and effects of neighborhood-level covariates in two examples—public physician visits and ischemic heart disease hospitalizations—using 1999 data on 11,312 men aged 45–85 years in Malmö, Sweden.

Study objective: This didactical essay is directed to readers disposed to approach multilevel regression analysis (MLRA) in a more conceptual than mathematical way. However, it specifically develops an epidemiological vision on multilevel analysis with particular emphasis on measures of health variation (for example, intraclass correlation). Such measures have been underused in the literature as compared with more traditional measures of association (for example, regression coefficients) in the investigation of contextual determinants of health. A link is provided, which will be comprehensible to epidemiologists, between MLRA and social epidemiological concepts, particularly between the statistical idea of clustering and the concept of contextual phenomenon. Design and participants: The study uses an example based on hypothetical data on systolic blood pressure (SBP) from 25 000 people living in 39 neighbourhoods. As the focus is on the empty MLRA model, the study does not use any independent variable but focuses mainly on SBP variance between people and between neighbourhoods. Results: The intraclass correlation (ICC = 0.08) informed of an appreciable clustering of individual SBP within the neighbourhoods, showing that 8% of the total individual differences in SBP occurred at the neighbourhood level and might be attributable to contextual neighbourhood factors or to the different composition of neighbourhoods. Conclusions: The statistical idea of clustering emerges as appropriate for quantifying “contextual phenomena” that is of central relevance in social epidemiology. Both concepts convey that people from the same neighbourhood are more similar to each other than to people from different neighbourhoods with respect to the health outcome variable.

Multilevel data occur frequently in health services, population and public health, and epidemiologic research. In such research, binary outcomes are common. Multilevel logistic regression models allow one to account for the clustering of subjects within clusters of higher‐level units when estimating the effect of subject and cluster characteristics on subject outcomes. A search of the PubMed database demonstrated that the use of multilevel or hierarchical regression models is increasing rapidly. However, our impression is that many analysts simply use multilevel regression models to account for the nuisance of within‐cluster homogeneity that is induced by clustering. In this article, we describe a suite of analyses that can complement the fitting of multilevel logistic regression models. These ancillary analyses permit analysts to estimate the marginal or population‐average effect of covariates measured at the subject and cluster level, in contrast to the within‐cluster or cluster‐specific effects arising from the original multilevel logistic regression model. We describe the interval odds ratio and the proportion of opposed odds ratios, which are summary measures of effect for cluster‐level covariates. We describe the variance partition coefficient and the median odds ratio which are measures of components of variance and heterogeneity in outcomes. These measures allow one to quantify the magnitude of the general contextual effect. We describe an R² measure that allows analysts to quantify the proportion of variation explained by different multilevel logistic regression models. We illustrate the application and interpretation of these measures by analyzing mortality in patients hospitalized with a diagnosis of acute myocardial infarction. © 2017 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.

The aim of the paper is to critically review the notion of social capital and review empirical literature on the association between social capital and health across countries. The methodology used for the review includes a systematic search on electronic databases for peer-reviewed published literature. We categorize studies according to level of analysis (single and multilevel) and examine whether studies reveal a significant health impact of individual and area level social capital. We compare the study conclusions according to the country's degrees of economic egalitarianism. Regardless of study design, our findings indicate that a positive association (fixed effect) exists between social capital and better health irrespective of countries degree of egalitarianism. However, we find that the between-area variance (random effect) in health tends to be lower in more egalitarian countries than in less egalitarian countries. Our tentative conclusion is that an association between social capital and health at the individual level is robust with respect to the degree of egalitarianism within a country. Area level or contextual social capital may be less salient in egalitarian countries in explaining health differences across places.

Study objective: (1) To provide a didactic and conceptual (rather than mathematical) link between multilevel regression analysis (MLRA) and social epidemiological concepts. (2) To develop an epidemiological vision of MLRA focused on measures of health variation and clustering of individual health status within areas, which is useful to operationalise the notion of “contextual phenomenon”. The paper shows how to investigate (1) whether there is clustering within neighbourhoods, (2) to which extent neighbourhood level differences are explained by the individual composition of the neighbourhoods, (3) whether the contextual phenomenon differs in magnitude for different groups of people, and whether neighbourhood context modifies individual level associations, and (4) whether variations in health status are dependent on individual level characteristics. Design and participants: Simulated data are used on systolic blood pressure (SBP), age, body mass index (BMI), and antihypertensive medication (AHM) ascribed to 25 000 subjects in 39 neighbourhoods of an imaginary city. Rather than assessing neighbourhood variables, the paper concentrated on SBP variance between individuals and neighbourhoods as a function of individual BMI. Results: The variance partition coefficient (VPC) showed that clustering of SBP within neighbourhoods was greater for people with a higher BMI. The composition of the neighbourhoods with respect to age, AHM use, and BMI explained about one fourth of the neighbourhood differences in SBP. Neighbourhood context modified the individual level association between BMI and SBP. Individual level differences in SBP within neighbourhoods were larger for people with a higher BMI. Conclusions: Statistical measures of multilevel variations can effectively quantify contextual effects in different groups of people, which is a relevant issue for understanding health inequalities.