title: Bayesian factor analysis to calculate a deprivation index and its uncertainty.
abstract: BACKGROUND
  Procedures for calculating deprivation indices in epidemiologic studies often show some common problems because the spatial dependence between units of analysis and uncertainty of the estimates is not usually accounted for. This work highlights these problems and illustrates how spatial factor Bayesian modeling could alleviate them.
  
  
  METHODS
  This study applies a cross-sectional ecological design to analyze the census tracts of 3 Spanish cities. To calculate the deprivation index, we used 5 socioeconomic indicators that comprise the deprivation index calculated in the MEDEA project. The deprivation index was estimated by a Bayesian factor analysis using hierarchical models, which takes the spatial dependence of the study units into account. We studied the relationship between this index and the one obtained using principal component analysis. Various analyses were carried out to assess the uncertainty obtained in the index.
  
  
  RESULTS
  A high correlation was observed between the index obtained and the non-Bayesian index, but this relationship is not linear and there is disagreement between the methods when the areas are grouped according to quantiles. When the deprivation index is calculated using summary statistics based on the posterior distributions, the uncertainty of the index in each census tract is not taken into account. Failure to take this uncertainty into account may result in misclassification bias in the census tracts when these are grouped according to quantiles of the deprivation index.
  
  
  CONCLUSIONS
  Not taking uncertainty into account may result in misclassification bias in the census tracts. This bias could interfere in subsequent analyses that include the deprivation index. Our proposal provides another tool for identifying groups with greater deprivation and for improving decision-making for public policy planning.
authors.affiliation: CIBER Epidemiología y Salud Pública, Barcelona, Spain. mmari@aspb.cat
authors.forename: Marc
authors.initials: M
authors.lastname: Marí-Dell'Olmo
authors.forename: Miguel Angel
authors.initials: MA
authors.lastname: Martínez-Beneito
authors.forename: Carme
authors.initials: C
authors.lastname: Borrell
authors.forename: Oscar
authors.initials: O
authors.lastname: Zurriaga
authors.forename: Andreu
authors.initials: A
authors.lastname: Nolasco
authors.forename: M Felicitas
authors.initials: MF
authors.lastname: Domínguez-Berjón
mesh_terms: D001499:Bayes Theorem; D019352:Censuses; D003430:Cross-Sectional Studies; D003467:Cultural Deprivation; D004522:Educational Status; D004651:Employment / Q000706:statistics & numerical data; D005163:Factor Analysis, Statistical; D005260:Female; D005508:Food Deprivation; D006295:Health Resources / Q000191:economics; D006801:Humans; D008297:Male; D011203:Poverty; D012111:Residence Characteristics; D012959:Socioeconomic Factors; D013030:Spain; D035501:Uncertainty; D014505:Urban Population