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A brief conceptual tutorial of multilevel analysis in social epidemiology: using measures of clustering in multilevel logistic regression to investigate contextual phenomena
  1. Juan Merlo1,
  2. Basile Chaix1,2,
  3. Henrik Ohlsson1,3,
  4. Anders Beckman1,
  5. Kristina Johnell1,4,
  6. Per Hjerpe1,5,
  7. L Råstam1,
  8. K Larsen6
  1. 1Department of Clinical Sciences (Community Medicine), Malmö University Hospital, Lund University, Malmö, Sweden
  2. 2Research Team on the Social Determinants of Health Care, National Institute of Health and Medical Research, Paris, France
  3. 3Skåne County Council, Regional Office for drug utilisation studies, Sweden
  4. 4Centre for Family Medicine, Karolinska Institutet, Huddinge, Sweden
  5. 5Skaraborg Institute, Skovde, Sweden
  6. 6Clinical Research Unit, Hvidovre University Hospital, University of Copenhagen, Hvidovre, Denmark
  1. Correspondence to:
 Professor J Merlo
 Department of Clinical Sciences (Community Medicine), Malmö University Hospital, Faculty of Medicine, Lund University, S-205 02 Malmö, Sweden; juan.merlo{at}


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.

  • logistic regession
  • mulilevel analysis
  • social epidemiology

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  • * This parameter represents the shrunken difference between the overall prevalence on the logistic scale and the prevalence in a given area on the logistic scale. In multilevel regression analysis, the area level residuals are “shrunken” towards their mean of 0, in an attempt to disentangle the part of the variations that may be attributable to true variations between areas from that part that might be better attributed to random variations. More detailed explanations are provided in a previous paper.3

  • When comparing two ORs fro two different variables one should use the same categorisation (for example, quartiles or median). In the present case the effect of individual education is a mean contrast between two groups (people with low compared with people with high educational achievement). Conversely, the MOR is the median in a distribution of contrast between pairwise neighbourhood comparisons. Therefore, the conclusion that the residual heterogeneity between areas was of greater relevance than the effect of individual education needs be interpreted with within this framework.

  • Funding: this study is supported by grants from the Swedish council for working life and social research (FAS) (PI Juan Merlo, Dnr: 2003 – 0580), the Swedish Research Council (VR) (PI Juan Merlo, Dnr 2004-6155), Region Skåne and the NEPI foundation.

  • Competing interests: none declared.

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