Using Bayesian Networks to Model Hierarchical Relationships in Epidemiological Studies
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OBJECTIVES: To propose an alternative procedure, based on a Bayesian network (BN), for estimation and prediction, and to discuss its usefulness for taking into account the hierarchical relationships among covariates. METHODS: The procedure is illustrated by modeling the risk of diarrhea infection for 2,740 children aged 0 to 59 months in Cameroon. We compare the procedure with a standard logistic regression and with a model based on multi-level logistic regression. RESULTS: The standard logistic regression approach is inadequate, or at least incomplete, in that it does not attempt to account for potentially causal relationships between risk factors. The multi-level logistic regression does model the hierarchical structure, but does so in a piecewise manner; the resulting estimates and interpretations differ from those of the BN approach proposed here. An advantage of the BN approach is that it enables one to determine the probability that a risk factor (and/or the outcome) is in any specific state, given the states of the others. The currently available approaches can only predict the outcome (disease), given the states of the covariates. CONCLUSION: A major advantage of BNs is that they can deal with more complex interrelationships between variables whereas competing approaches deal at best only with hierarchical ones. We propose that BN be considered as well as a worthwhile method for summarizing the data in epidemiological studies whose aim is understanding the determinants of diseases and quantifying their effects.
Abstract
OBJECTIVES: To propose an alternative procedure, based on a Bayesian network (BN), for estimation and prediction, and to discuss its usefulness for taking into account the hierarchical relationships among covariates. METHODS: The procedure is illustrated by modeling the risk of diarrhea infection for 2,740 children aged 0 to 59 months in Cameroon. We compare the procedure with a standard logistic regression and with a model based on multi-level logistic regression. RESULTS: The standard logistic regression approach is inadequate, or at least incomplete, in that it does not attempt to account for potentially causal relationships between risk factors. The multi-level logistic regression does model the hierarchical structure, but does so in a piecewise manner; the resulting estimates and interpretations differ from those of the BN approach proposed here. An advantage of the BN approach is that it enables one to determine the probability that a risk factor (and/or the outcome) is in any specific state, given the states of the others. The currently available approaches can only predict the outcome (disease), given the states of the covariates. CONCLUSION: A major advantage of BNs is that they can deal with more complex interrelationships between variables whereas competing approaches deal at best only with hierarchical ones. We propose that BN be considered as well as a worthwhile method for summarizing the data in epidemiological studies whose aim is understanding the determinants of diseases and quantifying their effects.
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