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Bayesian Factor Analysis to Calculate a Deprivation Index and Its Uncertainty

Marí-Dell'Olmo, Marca,b,c; Martínez-Beneito, Miguel Ángeld; Borrell, Carmea,b,e; Zurriaga, Oscard,f; Nolasco, Andreug; Domínguez-Berjón, M. Felicitash

doi: 10.1097/EDE.0b013e3182117747
Methods: Original Article

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.

Author Information

From the aCIBER Epidemiología y Salud Pública (CIBERESP), Barcelona, Spain; bAgència de Salut Pública de Barcelona, Barcelona, Spain; cDoctorado en Biomedicina, UPF, Barcelona, Spain; dÁrea de desigualdades en salud, Centro Superior de Investigación en Salud Pública, Valencia, Spain; eUniversitat Pompeu Fabra, Barcelona, Spain; fÁrea de epidemiología, Dirección General de Salud Pública, Valencia, Spain; gUnidad de Investigación en Análisis de la Mortalidad y Estadísticas Sanitarias, Universidad de Alicante, San Vicente del Raspeig, Spain; and hServicio de Informes de Salud y Estudios, Dirección General de Atención Primaria, Consejería de Sanidad, Comunidad de Madrid, Madrid, Spain.

Submitted 23 March 2010; accepted 26 October 2010.

Supported by projects FIS (PI042013), (PI040170), and (PI081488), and by the CIBER for Epidemiology and Public Heath (CIBERESP) (C03/09).

This article will be included in the doctoral thesis of one of the authors (Marc Marí-Dell'Olmo), being carried out at Pompeu Fabra University.

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Editors' note: A commentary on this article appears on page 365.

Correspondence: Marc Marí-Dell'Olmo, Agència de Salut Pública de Barcelona, Pl Lesseps 1, 08023 Barcelona, Spain. E-mail:

© 2011 Lippincott Williams & Wilkins, Inc.