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Navigating non-positivity in neighbourhood studies: an analysis of collective efficacy and violence
  1. Jennifer Ahern1,
  2. Magdalena Cerdá2,
  3. Sheri A Lippman3,
  4. Kenneth J Tardiff4,
  5. David Vlahov5,
  6. Sandro Galea2
  1. 1Division of Epidemiology, Berkeley School of Public Health, University of California, Berkeley, California, USA
  2. 2Department of Epidemiology, Columbia University Mailman School of Public Health, New York, New York, USA
  3. 3Center for AIDS Prevention Studies, Department of Medicine, University of California, San Francisco, California, USA
  4. 4Cornell University Weill School of Medicine, New York, New York, USA
  5. 5School of Nursing, University of California, San Francisco, California, USA
  1. Correspondence to Dr Jennifer Ahern, School of Public Health, University of California, Berkeley, 101 Haviland Hall, Berkeley, CA 94720-7358, USA; jahern{at}


Background In multilevel studies, strong correlations of neighbourhood exposures with individual and neighbourhood confounders may generate problems with non-positivity (ie, inferences that are ‘off-support’). The authors used propensity restriction and matching to (1) assess the utility of propensity restriction to ensure analyses are ‘on-support’ and (2) examine the relation between collective efficacy and violence in a previously unstudied city.

Methods Associations between neighbourhood collective efficacy and violent victimisation were estimated in data from New York City in 2005 (n=4000) using marginal models and propensity matching.

Results In marginal models adjusted for individual confounders and limited to observations ‘on-support’, under conditions of high collective efficacy, the estimated prevalence of violent victimisation was 3.5/100, while under conditions of low collective efficacy, it was 7.5/100, resulting in a difference of 4.0/100 (95% CI 2.6 to 5.8). In propensity-matched analysis, the comparable difference was 4.0/100 (95% CI 2.1 to 5.9). In analyses adjusted for individual and neighbourhood confounders and limited to observations ’on-support’, the difference in violent victimisation associated with collective efficacy was 3.1/100 (95% CI 1.2 to 5.2) in marginal models and 2.4/100 (95% CI 0.2 to 4.5) in propensity-matched analysis. Analyses without support restrictions produced surprisingly similar results.

Conclusions Under conditions of high collective efficacy, there was about half the prevalence of violence compared with low collective efficacy. The results contribute to a growing body of evidence that suggests collective efficacy may shape violence, and illustrate how careful techniques can be used to disentangle exposures from highly correlated confounders without relying on model extrapolation.

  • Propensity score
  • violence
  • social environment
  • residence characteristics
  • multilevel analysis

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  • Funding Support for this work was provided in part by the National Institute on Drug Abuse at the National Institutes of Health (DA 017642 and DA 06534).

  • Competing interests None.

  • Ethics approval The study protocol was approved by the institutional review boards of the New York Academy of Medicine, the University of Michigan and the University of California, Berkeley.

  • Provenance and peer review Not commissioned; externally peer reviewed.