Modelling treatment effects in a clinical Bayesian network using Boolean threshold functions

Abstract

Appropriate antimicrobial treatment of infections in critically ill patients should be started as soon as possible, as delay in treatment may reduce a patient's prognostic outlook considerably. Ventilator-associated pneumonia (VAP) occurs in patients in intensive care units who are mechanically ventilated and is almost always preceded by colonisation of the respiratory tract by the causative microorganisms. It is very difficult to clinically diagnose VAP and, therefore, some form of computer-based decision support might be helpful for the clinician. As diagnosing and treating VAP involves reasoning with uncertainty, we have used a Bayesian network as the primary tool for building a decision-support system. The effects of usage of antibiotics on the colonisation of the respiratory tract by various pathogens and the subsequent antibiotic choices in case of VAP were modelled using the notion of causal independence. In particular, the conditional probability distribution of the random variable that represents the overall coverage of pathogens by antibiotics was modelled in terms of the conjunctive effect of the seven different pathogens, usually referred to as the noisy-AND model. In this paper, we investigate different coverage models, as well as generalisations of the noisy-AND, called noisy-threshold models, and test them on clinical data of intensive care unit (ICU) patients who are mechanically ventilated. Some of the constructed noisy-threshold models offered further improvement of the performance of the Bayesian network in covering present causative pathogens by advising appropriate antimicrobial treatment. By reconsidering the modelling of interactions between the random variables in a Bayesian network using the theory of causal independence, it is possible to refine its performance. This was clearly shown for our Bayesian network concerning VAP, indicating that only specific noisy-threshold models might be appropriate for the modelling of the interaction between pathogens and antimicrobial treatment with respect to susceptibility. The results obtained also provide evidence that the noisy-OR and noisy-AND might not always be the best functions to model interactions among random variables.