Bayesian networks for pathological scarring due to burn injuries

Introduction: Burn injury is often a devastating event with long-term physical and psychosocial effects. Burn scars, meanly if hypertrophic or keloid, are cosmetically disfiguring and force the scarred person to deal with an alteration in body appearance, cosmetic deformities, discomfort, psychological stress (1). The exact mechanisms of normal and abnormal scar formation have long remained a mystery despite the extensive literature regarding wound healing. Recently researchers have begun to delineate the complex biochemical signalling pathways that regulate these processes (2). At same way it is important for clinicians to understand what are the clinical signs, the patient characteristics and the procedures that are mainly related with the occurrence of pathological scarring, to carry out a possible prognostic assessment of the scar. The aim of the present study, including a large sample of burns scars, is to evaluate the factors associated with an increased risk of the development of pathological burn scars, and to provide by means of Bayesian Network a model displaying all relations between demographic, clinical and treatment variables each others and with the final clinical outcome, the type of scar. Methods: From January 1994 at the Department of Plastic and Reconstructive Surgery – Burn Center of Traumatological Hospital in Turin a standard reporting form for collecting data referred to scar process has been used. The cohort consists of 703 patients and 2440 anatomical burn sites. Particularly in this study cohort the scar type was defined on the basis of the morphologic classification described in (6) and the scar evolution, calculated in days from the manifestation until its complete remission, was assessed according to the classification groups described in (7). A Bayesian Network (BN) is a graphical representation of the joint probability distributions over a set of random variables. Each node in a Bayesian network is associated with a set of probability tables. For those nodes without ingoing arcs, the probability distribution is a prior distribution which requires supplying a set of initial values. Following both the structure and the numerical parameters can be learned from data, since the structure of a BN is a representation of conditional independencies in the data, and the numerical parameters are a representation of the joint probability distributions. The second strategy based was chosen. There are a great number of algorithms for learning the structure of Bayesian networks from data. The well-known K2 algorithm (8) which is based on a scoring function and a search procedure was chosen. The algorithms based on a scoring function try to find a graph that best represents the data, according to a specific criterion. They use a scoring function in combination with a search method to measure the goodness of each explored structure from the space of feasible solutions. During the exploring process, the scoring function is applied to evaluate the fitness of each candidate structure to the data. With respect to parameter learning, continuous variables were discretized and the Expectation-Maximization (EM) algorithm was chosen to estimate the required conditional probabilities (9). A 10-fold cross validation was performed in order to evaluate the performance of the BN. A sensitivity analysis was carried out for hospitalization and complications nodes in order to identifying the most influential variables on injury severity. With categorical states, sensitivity is calculated as the degree of entropy reduction or mutual information, which measures how much uncertainty about a specific event is expected to decrease when a new finding is available (10), and the expected reduction of real variance.The Bayesian Network was implemented using GeNie to develop the structure (11) and Netica for the learning parameters and the validation phase. Results: Figure 1 depicted the Bayesian network along with the conditional probability tables learned by EM algorithm the Bayesian network which was built up using a subset of data without missing values. Discussion: Any expert that prospect to a patient a prognosis must take these factors into account. In medicine such Bayesian network systems are used for aiding in prognosis decisional process : inferring the most probable outcome of an observed problem given a set of symptoms, patient history, physical signs and applied treatment. They are especially useful in the medical domain because they allow the creation of a probabilistic network of causal dependencies in a given domain but can then be used for diagnostic inference (predicting probabilities in the reverse direction from effect to cause) .