title: Within- and between-group regression for improving the robustness of causal claims in cross-sectional analysis.
abstract: BACKGROUND
  A major objective of environmental epidemiology is to elucidate exposure-health outcome associations. To increase the variance of observed exposure concentrations, researchers recruit individuals from different geographic areas. The common analytical approach uses multilevel analysis to estimate individual-level associations adjusted for individual and area covariates. However, in cross-sectional data this approach does not differentiate between residual confounding at the individual level and at the area level. An approach allowing researchers to distinguish between within-group effects and between-group effects would improve the robustness of causal claims.
  
  
  METHODS
  We applied an extended multilevel approach to a large cross-sectional study aimed to elucidate the hypothesized link between drinking water pollution from perfluoroctanoic acid (PFOA) and plasma levels of C-reactive protein (CRP) or lymphocyte counts. Using within- and between-group regression of the individual PFOA serum concentrations, we partitioned the total effect into a within- and between-group effect by including the aggregated group average of the individual exposure concentrations as an additional predictor variable.
  
  
  RESULTS
  For both biomarkers, we observed a strong overall association with PFOA blood levels. However, for lymphocyte counts the extended multilevel approach revealed the absence of a between-group effect, suggesting that most of the observed total effect was due to individual level confounding. In contrast, for CRP we found consistent between- and within-group effects, which corroborates the causal claim for the association between PFOA blood levels and CRP.
  
  
  CONCLUSIONS
  Between- and within-group regression modelling augments cross-sectional analysis of epidemiological data by supporting the unmasking of non-causal associations arising from hidden confounding at different levels. In the application example presented in this paper, the approach suggested individual confounding as a probable explanation for the first observed association and strengthened the robustness of the causal claim for the second one.
authors.affiliation: Mannheim Institute of Public Health, Social and Preventive Medicine, University of Heidelberg, Ludolf-Krehl-Strasse 7-11, Mannheim, 68167, Germany. bernd.genser@bgstats.com.|Instituto de Saúde Coletiva, Federal University of Bahia, Salvador, Brazil. bernd.genser@bgstats.com.
authors.forename: Bernd
authors.initials: B
authors.lastname: Genser
authors.affiliation: Instituto de Saúde Coletiva, Federal University of Bahia, Salvador, Brazil. carlosateles@yahoo.com.br.|Centro de Pesquisa Gonçalo Muniz, Fundação Oswaldo Cruz (FIOCRUZ), Salvador, Bahia, Brazil. carlosateles@yahoo.com.br.
authors.forename: Carlos A
authors.initials: CA
authors.lastname: Teles
authors.affiliation: Instituto de Saúde Coletiva, Federal University of Bahia, Salvador, Brazil. mauricio@ufba.br.|Centro de Pesquisa Gonçalo Muniz, Fundação Oswaldo Cruz (FIOCRUZ), Salvador, Bahia, Brazil. mauricio@ufba.br.
authors.forename: Mauricio L
authors.initials: ML
authors.lastname: Barreto
authors.affiliation: Mannheim Institute of Public Health, Social and Preventive Medicine, University of Heidelberg, Ludolf-Krehl-Strasse 7-11, Mannheim, 68167, Germany. jfischer@medma.uni-heidelberg.de.
authors.forename: Joachim E
authors.initials: JE
authors.lastname: Fischer
mesh_terms: D000328:Adult; D000368:Aged; D000369:Aged, 80 and over; D015415:Biomarkers / Q000097:blood; D002097:C-Reactive Protein / Q000032:analysis*; D002210:Caprylates / Q000097:blood*; D003430:Cross-Sectional Studies; D060766:Drinking Water / Q000032:analysis*; D004781:Environmental Exposure / Q000032:analysis*; D005466:Fluorocarbons / Q000097:blood*; D005843:Geography; D006801:Humans; D018655:Lymphocyte Count; D008875:Middle Aged; D012044:Regression Analysis; D014873:Water Pollutants / Q000032:analysis*; D055815:Young Adult
chemical_list: D015415:Biomarkers; D002210:Caprylates; D060766:Drinking Water; D005466:Fluorocarbons; D014873:Water Pollutants; D002097:C-Reactive Protein; C031492:octanoic acid