Avian influenza: Temporal modeling of a human to human transmission case

Abstract

The aim of this paper is to demonstrate how temporal reasoning techniques can assist in the analysis of epidemiological data to determine the possibility of contagion among humans of the avian influenza virus (H5N1). To do so, we use a documented real case of a possible infection of H5N1 between humans, and formally substantiate the medical evidence. The need to represent and manage time is implicit in many reasoning processes. This is particularly evident in the field of medicine, in which the temporal distribution of symptoms is crucial for understanding the evolution of diseases. Many models have been proposed for time representation and management. In this paper we propose the use of a generic temporal reasoner, FuzzyTIME, which is able to represent both points and intervals, as well as relations, including quantitative and qualitative ones, through a specifically designed language. Moreover, being based on FTCN (fuzzy temporal constraint networks), the proposed model also allows us to capture both temporal imprecision and uncertainty present in complex domains as the medical one. Nevertheless, the reasoner has been design to have an easy integration with any knowledge based system that need this kind of representation and reasoning. To perform the analysis of the real case selected, we first clearly identified the temporal information in each of the timelines of the subjects under study. Subsequently, this information was formalized in the language provided by FuzzyTIME. After verifying the temporal consistency of such information in every subject, we proceeded to check the temporal consistency of such information with the generic clinical symptoms of evolution of avian influenza. Finally, the queries which were modeled allowed us to determine the temporal possibility of infection between human of the H5N1 virus. First, we demonstrate the usefulness of temporal reasoning in the modeling and analysis of epidemiological data, showing how the FTCN formalism and the proposed language is sufficiently expressive to represent qualitative and quantitative temporal relations as well as the temporal imprecision implicit in certain expressions extracted from the real case selected. Moreover, the temporal reasoner permits efficient determination of the temporal consistency of the medical evidence concerning the possibility of infection of H5N1 between humans.

Introduction

Time is a framework that allows the different observable states of a system to be located and sorted. Time is so common in our thinking and our daily activities that we sometimes obviate the vital importance that it has in our processes of perception. In physical models, time is the independent variable par excellence for describing the evolution and for supporting the concept of change. Time is inherent in the description of many problems, as in the medical domain, since, for example, diseases evolve over time, antecedents generate the patient’s medical record, and therapeutic actions cannot be described without the temporal component. For these domains, we need a computational model of time that allows formal representation of the temporal information and an efficient reasoning about this information.

The development of temporal reasoning models and their applications in medicine has led to the development of many decision support systems with the capability of managing temporal information. Some of these systems rely heavily on intermediate tasks, such as temporal data abstraction (Shahar and Musen, 1996, Stacey and McGregor, 2007), which are used for data summarization and validation (Bellazzi et al., 1998, Miksch et al., 1996), or the extraction of relevant features, such as states or trends (Haimowitz and Kohane, 1996, Salatian and Hunter, 1999). Moreover, some studies have been locked at including time in high-level tasks such as diagnosis. A number of diagnostic models that are based on temporal reasoning have been proposed (Brusoni et al., 1998, Gamper and Nejdl, 1997), including, in some cases, causal models along with temporal models (Palma, Juarez, Campos, & Marin, 2006), or case-based reasoning (Juarez, Guil, Palma, & Marin, 2009).

Within the field of medicine, epidemiology is an area where temporal reasoning seems to have special relevance. Epidemiology refers to studies of incidence, distribution, propagation and disease prevention, and studies, above all, the cause-effect relation between exposure and illness. In order to establish this causality relation, different models have been identified, that of Bradforf-Hill (1991) being one of the most complete and most widely accepted. Bradford-Hill established nine criteria to examine whether an association between two variables implies a causal relation. Among them are those that establish the plausibility of the relation, those that determine the correction, and others that establish the strength of the causal relation itself. One of these criteria refers to the temporal sequencing of the effects regarding the causes, namely a guarantee that exposure to the risk factor precedes the disease. In other words, a temporal evolution incompatible with this condition discards the existence of a causal network. Although the temporal relation may seem obvious sometimes, it is not always so, since there are scenarios where temporal relations are complex.

What is more, there is a high variability in the temporal evolution of different patients exposed to contagion. This variability gives rise to an important temporal imprecision in the description of generic cases. It is not infrequent to find that, in certain diseases, the incubation period takes from 2 to 17 days, as in the H5N1 virus. In such cases, it is convenient to make use of a modeling system that allows temporal inference and queries resolution while taking into account temporal imprecision and uncertainty. From a medical point of view, these temporal aspects are difficult to determine, especially in cases of prolonged or chronic diseases, or when a number of patients are involved.

In this article we propose the use of a temporal reasoner called FuzzyTIME (Fuzzy Temporal Information Management Engine) to assist in verifying the temporal criterion of causality in the epidemiology of avian influenza. This temporal reasoner is based on a formal model of temporal constraints networks to represent time. More specifically, our temporal reasoner uses the fuzzy temporary constraint network (Marín, Barro, Bosch, & Mira, 1994) formal model and is based on the language presented in Barro, Marín, Mira, and Patón (1994). Other authors have successfully used temporal constraints models for the resolution of a wide range of clinical problems (Badaloni and Falda, 2005, Dojat et al., 1998, Keravnou, 2002, Zhou et al., 2006), and found good expressiveness and representation capability.

We will show in this article some of the difficulties found when trying to model the temporal information of a real clinical case, which is very rich in temporal semantics. The information is initially provided in natural language, and, therefore, it presents a high degree of imprecision and ambiguity. The modeling of this type of information normally uses time intervals, time points, temporal qualitative relations that provide a partial order among events, and temporal imprecision. We will see that the temporal reasoner includes the tools to provide the expressivity necessary for the representation of qualitative and quantitative temporal relations, as well as for using time intervals and time points. To facilitate even more the translation from the linguistic representation into computational representation, we have defined a high level interface so that the user can easily introduce the temporal information.

The use of fuzzy temporal constraints is a powerful and expressive way of representing the imprecision and uncertainty that is quite often present in the medical domain, and assumes greater significance when we try to represent scenarios with data collected from the user (Steimann, 2001).

In addition, we will show that FuzzyTIME gives us enough reasoning capability and the efficiency necessary for the resolution of various types of queries made on scenarios of epidemiology. We will discuss also the limitations of this approach.

To analyze the capacity and expressive FuzzyTIME reasoning, we will use as an example a real case (Ungchusak et al., 2005) describing a possible contagion from person to person of avian influenza in a small set of subjects. FuzzyTIME allows us to check the temporal consistency of the scenarios that describe the evolution of the different subjects, and to determine the coherence of the cases with the generic scenarios of the disease.

The rest of the article is organized as follows. Section 2 presents the clinical case. Section 3 describes the temporal reasoning model on which our proposal is based. The architecture and language of the temporal reasoner FuzzyTIME are shown in Section 4. Sections 5 Query resolution, 6 Complexity give details about the queries allowed in FuzzyTIME and the computational complexity of the different processes of temporal reasoning. Section 7 contains the modeling of the problem and the discussion about the expressive power of the temporal reasoner presented. Finally, we include a comparison with some related works, the conclusions and the proposed future research.