# A Comparative Study of Two Rule-Based Explanation Methods for Diabetic Retinopathy Risk Assessment
## 1 Introduction  
Healthcare costs are continuously raising, due to the increase of life expectancy, the improvements in the management of chronic diseases and the development of new treatments. Diabetes Mellitus (DM), suffered by 382 million adults worldwide, is one of the most important chronic diseases. DM patients are estimated to increase up to 592 million adults by 2035 [1]. Moreover, specialists estimate that around 46% of diabetic patients have not been diagnosed [1]. DM has been growing steadily in the last few years. In Spain, the National Health Survey (NHS) detected that diabetes increased from 4.1% of the population in 1993 to 6.4% in 2009. Specialists predict an incidence of more than 3 million DM patients in Spain by 2030 [2]. Diabetic Retinopathy (DR) is an ocular disease related to DM. It is the main cause of blindness and visual impairment worldwide and the most common among working-aged adults [3]. Overall, DR affects 30% of diabetic patients, 11% show some degree of vision loss (sight-threatening diabetic retinopathy [4]), and 4% lose their sight completely. However, early detection through periodic screening can reduce this risk by as much as 95%. Artificial Intelligence (AI) techniques may improve the screening quality by identifying the patient's risk of developing DR using information from the Electronic Health Record. In the healthcare domain, it is common to build clinical decision support systems (CDSS) using Machine Learning (ML) tools and algorithms. These intelligent CDSS assist clinicians in diagnosing diseases and choosing treatment decisions. Recently, we observed significant and continuous success in the development of ML-based systems. Such success is attributed to many factors, including the presence of vast amounts of data, the advances in ML and the affordability of more advancedcomputer equipment. As a result, ML-based systems have become ubiquitous in our society and regular life, and a vital component of multiple applications in many domains, including healthcare. In line with this progress, our research group and the Ophthalmology Unit of the University Hospital Sant Joan (Reus, Tarragona) have developed a CDSS called RETIPORGRAM [5; 6], that helps clinicians to estimate the personalised risk of developing DR as early as possible. The AI core of RETIPROGRAM is a Fuzzy Random Forest (FRF) composed of 100 Fuzzy Decision Trees (FDTs). A FDT is a hierarchical structure that classifies patients based on the values of a set of attributes related to DR risk factors. Each node of the tree represents an attribute. A branch of a node is associated to a possible value of that attribute. Finally, the tree leaves assign patients to two categories: patients with/without risk of developing DR. Each branch is a rule, that provides a result if the attributes have certain values. Experimental results have shown that the system could be incorporated in DR screening programs and improve the quality of screening models [7]. However, it is known that, in domains such as healthcare, high precision is not enough to convince society to trust the decisions of ML-based systems. When a decision is made or suggested by an automated system, it is crucial for practical, social, and increasingly legal reasons to explain the rationale behind that decision to users, developers or regulators. In the case of RETIPROGRAM, a patient may want to know why she has a high risk of developing DR, so that she can try to change her lifestyle to reduce it. As a result, we started to develop methods to derive explanations for the predictions of the RETIPROGRAM system. In the literature, we can find a variety of techniques to achieve this goal. The simplest solution is to directly inspect the components of the models--e.g., the activated path in a fuzzy decision tree. However, such a naive solution is not feasible in the case of random forests with hundreds of trees. The internal structure of such models is complex, and it is not easy to be inspected. Alternatively, we can develop post-hoc explanation methods [8].