Arjen Hommersom

Checking the quality of clinical guidelines using automated reasoning tools

Requirements about the quality of clinical guidelines can be represented by schemata borrowed from the theory of abductive diagnosis, using temporal logic to model the time-oriented aspects expressed in a guideline. Previously, we have shown that these requirements can be verified using interactive theorem proving techniques. In this paper, we investigate how this approach can be mapped to the facilities of a resolution-based theorem prover, otter and a complementary program that searches for finite models of first-order statements, mace-2. It is shown that the reasoning required for checking the quality of a guideline can be mapped to such a fully automated theorem-proving facilities. The medical quality of an actual guideline concerning diabetes mellitus 2 is investigated in this way.

Meta-level Verification of the Quality of Medical Guidelines Using Interactive Theorem Proving

Requirements about the quality of medical guidelines can be represented using schemata borrowed from the theory of abductive diagnosis, using temporal logic to model the time-oriented aspects expressed in a guideline. In this paper, we investigate how this approach can be mapped to the facilities offered by a theorem proving system for program verification, KIV. It is shown that the reasoning that is required for checking the quality of a guideline can be mapped to such theorem-proving facilities. The medical quality of an actual guideline concerning diabetes mellitus 2 is investigated in this way, and some problems discovered are discussed.

Multilevel Bayesian networks for the analysis of hierarchical health care data

OBJECTIVE Large health care datasets normally have a hierarchical structure, in terms of levels, as the data have been obtained from different practices, hospitals, or regions. Multilevel regression is the technique commonly used to deal with such multilevel data. However, for the statistical analysis of interactions between entities from a domain, multilevel regression yields little to no insight. While Bayesian networks have proved to be useful for analysis of interactions, they do not have the capability to deal with hierarchical data. In this paper, we describe a new formalism, which we call multilevel Bayesian networks; its effectiveness for the analysis of hierarchically structured health care data is studied from the perspective of multimorbidity. METHODS Multilevel Bayesian networks are formally defined and applied to analyze clinical data from family practices in The Netherlands with the aim to predict interactions between heart failure and diabetes mellitus. We compare the results obtained with multilevel regression. RESULTS The results obtained by multilevel Bayesian networks closely resembled those obtained by multilevel regression. For both diseases, the area under the curve of the prediction model improved, and the net reclassification improvements were significantly positive. In addition, the models offered considerable more insight, through its internal structure, into the interactions between the diseases. CONCLUSIONS Multilevel Bayesian networks offer a suitable alternative to multilevel regression when analyzing hierarchical health care data. They provide more insight into the interactions between multiple diseases. Moreover, a multilevel Bayesian network model can be used for the prediction of the occurrence of multiple diseases, even when some of the predictors are unknown, which is typically the case in medicine.

Multilevel temporal Bayesian networks can model longitudinal change in multimorbidity

OBJECTIVES Although the course of single diseases can be studied using traditional epidemiologic techniques, these methods cannot capture the complex joint evolutionary course of multiple disorders. In this study, multilevel temporal Bayesian networks were adopted to study the course of multimorbidity in the expectation that this would yield new clinical insight. STUDY DESIGN AND SETTING Clinical data of patients were extracted from 90 general practice registries in the Netherlands. One and half million patient-years were used for analysis. The simultaneous progression of six chronic cardiovascular conditions was investigated, correcting for both patient and practice-related variables. RESULTS Cumulative incidence rates of one or more new morbidities rapidly increase with the number of morbidities present at baseline, ranging up to 47% and 76% for 3- and 5-year follow-ups, respectively. Hypertension and lipid disorders, as health risk factors, increase the cumulative incidence rates of both individual and multiple disorders. Moreover, in their presence, the observed cumulative incidence rates of combinations of cardiovascular disorders, that is, multimorbidity differs significantly from the expected rates. CONCLUSION There are clear synergies between health risks and chronic diseases when multimorbidity within a patient progresses over time. The method used here supports a more comprehensive analysis of such synergies compared with what can be obtained by traditional statistics.

Generalising the interaction rules in probabilistic logic

The last two decades has seen the emergence of many different probabilistic logics that use logical languages to specify, and sometimes reason, with probability distributions. Probabilistic logics that support reasoning with probability distributions, such as ProbLog, use an implicit definition of an interaction rule to combine probabilistic evidence about atoms. In this paper, we show that this interaction rule is an example of a more general class of interactions that can be described by nonmonotonic logics. We furthermore show that such local interactions about the probability of an atom can be described by convolution. The resulting extended probabilistic logic supports nonmonotonic reasoning with probabilistic information.

A new probabilistic constraint logic programming language based on a generalised distribution semantics

Probabilistic logics combine the expressive power of logic with the ability to reason with uncertainty. Several probabilistic logic languages have been proposed in the past, each of them with their own features. We focus on a class of probabilistic logic based on Satos distribution semantics, which extends logic programming with probability distributions on binary random variables and guarantees a unique probability distribution. For many applications binary random variables are, however, not sufficient and one requires random variables with arbitrary ranges, e.g. real numbers. We tackle this problem by developing a generalised distribution semantics for a new probabilistic constraint logic programming language. In order to perform exact inference, imprecise probabilities are taken as a starting point, i.e. we deal with sets of probability distributions rather than a single one. It is shown that given any continuous distribution, conditional probabilities of events can be approximated arbitrarily close to the true probability. Furthermore, for this setting an inference algorithm that is a generalisation of weighted model counting is developed, making use of SMT solvers. We show that inference has similar complexity properties as precise probabilistic inference, unlike most imprecise methods for which inference is more complex. We also experimentally confirm that our algorithm is able to exploit local structure, such as determinism, which further reduces the computational complexity.

Applying Bayesian networks for intelligent adaptable printing systems

Bayesian networks are around more than twenty years by now. During the past decade they became quite popular in the scientific community. Researchers from application areas like psychology, biomedicine and finance have applied these techniques successfully. In the area of control engineering however, little progress has been made in the application of Bayesian networks. We believe that these techniques are useful for systems that dynamically adapt themselves at runtime to a changing environment, which is usually uncertain. Moreover, there is uncertainty about the underlying physical model of the system, which poses a problem for modelling the system. In contrast, using a Bayesian network the needed model can be learned, or tuned, from data. In this paper we demonstrate the usefulness of Bayesian networks for control by case studies in the area of adaptable printing systems and compare the approach with a classic PID controller. We show that it is possible to design adaptive systems using Bayesian networks learned from data.

Understanding the Co-occurrence of Diseases Using Structure Learning

Multimorbidity, i.e., the presence of multiple diseases within one person, is a significant health-care problem for western societies: diagnosis, prognosis and treatment in the presence of of multiple diseases can be complex due to the various interactions between diseases. To better understand the co-occurrence of diseases, we propose Bayesian network structure learning methods for deriving the interactions between risk factors. In particular, we propose novel measures for structural relationships in the co-occurrence of diseases and identify the critical factors in this interaction. We illustrate these measures in the oncological area for better understanding co-occurrences of malignant tumours.

Integrating Logical Reasoning and Probabilistic Chain Graphs

Probabilistic logics have attracted a great deal of attention during the past few years. While logical languages have taken a central position in research on knowledge representation and automated reasoning, probabilistic graphical models with their probabilistic basis have taken up a similar position when it comes to reasoning with uncertainty. The formalism of chain graphs is increasingly seen as a natural probabilistic graphical formalism as it generalises both Bayesian networks and Markov networks, and has a semantics which allows any Bayesian network to have a unique graphical representation. At the same time, chain graphs do not support modelling and learning of relational aspects of a domain. In this paper, a new probabilistic logic, chain logic, is developed along the lines of probabilistic Horn logic. The chain logic leads to relational models of domains in which associational and causal knowledge are relevant and where probabilistic parameters can be learned from data.

Hybrid time Bayesian networks

Capturing heterogeneous dynamic systems in a probabilistic model is a challenging problem. A single time granularity, such as employed by dynamic Bayesian networks, provides insufficient flexibility to capture the dynamics of many real-world processes. The alternative is to assume that time is continuous, giving rise to continuous time Bayesian networks. Here the problem is that the level of temporal detail is too precise to match available probabilistic knowledge. In this paper, we present a novel class of models, called hybrid time Bayesian networks, which combine discrete-time and continuous-time Bayesian networks. The new formalism allows us to more naturally model dynamic systems with regular and irregularly changing variables. We also present a mechanism to construct discrete-time versions of hybrid models and an EM-based algorithm to learn the parameters of the resulting BNs. Its usefulness is illustrated by means of a real-world medical problem. Hybrid time Bayesian networks are defined.This new class of models allows reasoning with random variables that evolve regularly or irregularly.A discrete-time characterization of these new models is given.As an application of hybrid time Bayesian networks a medical example is modeled.