Towards Shared Hypothesis Testing in the Biomedical Domain

Abstract

Evidence-based hypothesis testing assumes the existence of a causal chain between the facts. By studying the propagation of evidenced facts in the causal chain (hypothesis) we gain new insights on the progression of a disease. In practice, a hypothesis cannot always be substantiated with a complete asserted knowledge (inability to collect the required evidence), yet it is possible to test a hypothesis with missing knowledge with a lower confidence. In this work we propose a method to perform evidence-based hypothesis testing in the biomedical domain, such that specialists can evaluate confidence of their hypothesis and communicate their findings. We assume that a hypothesis is formalized in an OWL 2 EL ontology and the KB contains incomplete asserted knowledge (ABox). We extract a causal chain from an ontology and represent it as a DAG (node - fact, arc - causal relationship). Users assign importance weights to the facts which they think are more important to support the hypothesis. Evaluation of the hypothesis confidence is then done by computing a weighted sum of fact confidences over the directed path in the DAG (corresponding to the causal chain).

Keywords

• biomedical ontology
• hypothesis testing
• incomplete knowledge

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Some pathologies, such as osteoarthritis (OA), may be evidenced across multiple biological scales (e.g., cellular, molecular, organic, behavioral). An evidence at each biological scale is obtained through the analysis of the results of a specific assay (e.g., cell viability, mechanical properties, MRI, gait analysis). Positive correlation between these evidenced facts is deduced from the statistical experiments or from the literature sources. The positive correlation may be represented as a causal chain of facts (e.g., f1 7! f2 7! : : : 7! fn). For such a causal chain to hold – and thus for a hypothesis to be satisfied – every node of this network must be evidenced by a corresponding analysis of an assay. To better convey the idea of hypothesis testing we will focus on the knee articular cartilage degradation due to OA to present our use-case scenario. However the analysis of the causal chain of the evidenced facts is applicable to other case studies. Use-case. A molecular biologist is studying the cartilage degradation due to OA. The death of chondrocytes (factor f1) is a common feature of an osteoarthritic cartilage, one way to evidence it is to run cell viability assays, which produce images. By analysing these images, a molecular biologist establishes that there was a decline of cell viability (evidence e1) [ 13 ] (i.e., f1 is evidenced by e1). From the literature it was hypothesized that there might be a connection between the death of chondrocytes and joint stiffness (f2), which affects the gait pattern (e2) [ 2 ]. To support this hypothesis, he collaborates with the Orthopaedics department and obtains an evidence of gait pattern alteration presumably due to cartilage degradation causing joint stiffness. Based on the results he establishes that causes(f1; f2) holds, which we denote f1 7! f2. Both may consider their work done, however there was a jump from cellular biological scale to behavior biological scale. Since cartilage degradation leads to Cartilage thinning (f3) (surface diminution) it must be seen on organ level via analysis of MRI (e3) [ 14 ]. It is therefore possible to refine the hypothesis by adding a new causal relationship, which would mean that instead of f1 7! f2, we actually need to prove f1 7! f3 7! f2. Hypothesis Testing with Incomplete Knowledge. In practice, the process of data collection and their analysis is very time-consuming and sometimes it is sufficient to have evidences for some nodes of the causal chain and not all of them. Alternatively, some of the nodes may be evidenced independently by different research groups and, if combined, they could support a pathology hypothesis. Lastly, some of the causal relationships between the facts may be unsatisfied by statistical results, however they could still be considered due to errors and low confidence in the statistical results. Therefore, it is a common case that a hypothesis is tested with incomplete knowledge.

In this work we propose a method to perform hypothesis testing, assuming that a hypothesis is formalized in an OWL 2 EL ontology with an open-world assumption. We extract a causal chain from an ontology and represent it as a DAG, where each node corresponds to a fact and an edge represents a causal relationship. Users assign importance weights to the facts which they think are more important to support the hypothesis. Evaluation of confidence of a hypothesis is then done by computing a weighted sum of the directed path in the DAG (corresponding to the causal chain). 2

Related Work

Application of Semantic Web technologies in the biomedical domain to infer missing information or new insights in the presence of incomplete knowledge are studied in [ 10, 12 ]. In [ 10 ] a method for rule-based reasoning with a multi-scale neuroanatomical ontology is presented. Authors conclude that OWL is an important technology for merging disparate data and performing multi-scale reasoning. They demonstrate how OWL-based ontologies and rule-based reasoning help infer novel facts about brain connectivity at large scale from the existence of synapses at a micro scale. Oberkampf et al. [ 12 ] propose a methodology for interpreting patient clinical data (medical images and reports), semantically annotated by concepts from large medical ontologies. They introduce an ontology containing lymphoma-related diseases and symptoms as well as their relations and use it to infer likely diseases of patients, based on annotations.

In [ 1, 11 ] the multi-scale biomedical factors causing cartilage degradation during the OA are considered in a framework for semantic biomedical data exploration. The causal chain is formalized in the MultiScaleHumanOntology [ 6 ].

Theoretical frameworks to marry formal methods (e.g., First-Order Logic) and probabilistic models (e.g., stochastic processes) are proposed in [ 15, 9 ]. In [ 5 ], the Stochastic Process Algebra language PEPA [ 7 ] was tuned to model biological pathways and complex biological networks, involving stochastic processes. Our work tries to bridge "uncertainty" and "formal methods", similarly to the above methods, but it stays in OWL with a specific application in the biomedical domain. 3

Methodology

Our methodology for hypothesis testing of a multi-scale pathology relies on the formalization of the causal chain, represented as an OWL ontology. Specifically, we consider OWL 2 EL profile, as its axioms are well suited for many of the biomedical formalizations [ 8 ]. We assume that the causal chain is modeled by using the existentially quantified restriction axiom to support the open-world assumption similar to anatomical relation modeling in FMA [ 16, 4 ] (i.e., Femur v 9constitutional_part_of:Thigh). For instance, the relation between f3 and f2 is formalized in MultiScaleHuman ontology [ 6 ] as:

Cartilage_thinning v rdfs:s|u{bzC}lassOf

blank node construction z9causes:Joi}n|t_stiffness{ (1) DAG Representation of Causal Chain. We build a DAG (Directed Acyclic Graph) representation of the causal chain starting from its formalization in an OWL 2 EL ontology. To build a causal chain we analyse EL [ 3 ] axioms corresponding to facts of the form A v 9R: B, where A and B are atomic DL concepts. That is, we assume that the ontology is built with atomic concepts only in the filler of the existential restrictions. The existential restriction is applied to a transitive relation R, which models causality (e.g., causes). In the case of nested existential restrictions := A v 9R1: (9R2: C) it must be the case that R1 = R2 and R1 is transitive. Then we can connect A 7! C with R1 in the DAG.

We analyse the RDF subgraph encoding such axioms and infer a causal relationship between Cartilage_thinning and Joint_stiffness, as depicted in Figure 1, to obtain a DAG of causal chains f1 7! f2 7! : : : 7! fn. We recursively apply the same strategy in the case of nested restrictions.

Importance of Facts and Identification of Missing Nodes. User asserts instances of evidences to the knowledge base, i.e., Cartilage_thinning(e1), if such an evidence is found. We also assume that the user provides importance measures for the evidences, which we store as an attribute of a node in the DAG. That is, for a node fi corresponding to some fact we add attribute importance: 0.45. To ease the notation we denote it if (fi). We check if the user asserted any instance for concepts representing evidences fi, and if so we add attribute satisfied: True, otherwise we add satisfied: False. We identify the missing nodes by filtering all nodes in the DAG for satisfied: False. Assessment of Hypothesis Confidence. To assess the confidence of the hypothesis, we compute the weighted path passing through the facts. For instance, if in our use-case the evidence f3 was missing, then we would give this node a negative weight (attribute weight: -1). By contrast, f1; f2 would be given positive weights since we have found an evidence for them. Thus, a weighted path (f1; f2) would give us the final confidence value of our hypothesis. For example, +1 if (f1) + ( 1) if (f3) + 1 if (f2). We use NetworkX Python library for network analysis tasks (weighted path computation) and basic graph querying (node and arc selection based on attribute values). 4

Discussion and Conclusion

Although the identification of the missing evidenced facts in the hypothesis could have been obtained by executing ad-hoc SPARQL queries, the DAG transformation metaphor allows us to naturally obtain confidence propagation. We consider a rather limited subset of OWL 2 EL axioms during the DAG construction, since the original causal chain formalization, which we built our arguments upon, used only those for causal chain modelling. However, in the future, other types of axioms would be taken into account.

We argue that reasoning on the formalized causal chain may identify the missing nodes which could be presented to the specialist to guide him in the conduction of his experiment, and notify him what is missing for the hypothesis to hold. Alternatively, the knowledge of the missing nodes, necessary to support a hypothesis, may help the specialist in finding a collaboration with other institutions. By using our methodology, depending on the richness of the knowledge model of a hypothesis and importance weights for the facts, researchers may evaluate the confidence of their hypotheses. Moreover, they can also identify what is missing for their hypothesis to be positive. It is also possible to publish the results by referring to a knowledge model of causality expressed in a standard ontology language (i.e., OWL). This work was partially funded by the EU Marie Curie ITN MultiScaleHuman (FP7PEOPLE-2011-ITN, Grant agreement no.: 289897), the EU project Optique (FP7-ICT318338), and the EPSRC projects MaSI3, Score!, and DBOnto.

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