Fuzzy logic–based clinical decision support system for the evaluation of renal function in post‐Transplant Patients

Abstract Objectives In the context of the gradual development of artificial intelligence in health care, the clinical decision support systems (CDSS) play an increasing crucial role in improving the quality of the therapeutic and diagnostic efficiency in health care. The fuzzy logic (FL) provides an effective means for dealing with uncertainties in the health decision‐making process; therefore, FL‐based CDSS becomes a very powerful tool for data and knowledge management, being able to think like an expert clinician. This work proposes an FL‐based CDSS for the evaluation of renal function in posttransplant patients. Method Based on the data provided by the Department of Nephrology of the University Hospital Federico II of Naples, a statistical sample is selected according to appropriate inclusion criteria. Four fuzzy inference systems are implemented monitoring the renal function by the level of proteinuria and the glomerular filtration rate (GFR). Results The systems show an accuracy of more than 90% and the outputs are provided through easy to read graphics, so that physicians can intuitively monitor the patient's clinical status, with the objective to improve drugs dosage and reduce medication errors. Conclusions We propose that the CDSSs for the assessment and follow‐up of kidney‐transplanted patients built in this study are applicable to clinical practice.

The use of FL-based CDSS in health systems has spread success- In risk classification of renal diseases using FL-based CDSS, the works of Ahmed and Narasimhan are of interest. The work of Ahmed et al is interesting for diagnostic report of the healthiness of a patient's kidney used as a following input variables set: nephron functionality, blood sugar, blood pressure, age, weight, and alcohol intake. 28 The second for risk classification of diabetic nephropathy with following input parameters: plasma glucose concentration, diastolic blood pressure, body mass index, and age. 29 More recently, Santini et al 3  Cardarelli" Hospital in Naples. This work shows exemplary results on the online evaluation of iron overload during the health status assessment and care management of β-thalassemia patients. 3 CDSS can be used as an effective tool in order to reduce morbidity and mortality rates in patients with renal failures. Indeed, after renal transplantation, several complications may arise that result in a serious impaired renal function. 30 These dysfunctions may not only appear very early after transplantation (as early as in the operating room) but may also arise very late (months later). 31 Furthermore, some of the complications may also result in deterioration of renal function as a late permanent event and, hence, very careful monitoring of patients is required to detect complications before severe damage happen. 30 Among the risks resulting from a renal transplant, the most important is certainly rejection, evadable by using immunosuppressant drugs that have the purpose of controlling the activity of the immune system. However, these drugs have significant side effects that can seriously worsen the living conditions of the transplanted. Keeping a balance between the effective prevention of rejection and the side effects of immunosuppressant drugs is a key point for long-term renal transplantation success. 32 Moreover, maintaining this balance is made even more complex in diabetic patients because hyperglycaemia causes the excess of glucose that over time forms irreversible endproducts; the tissue accumulation of these products contributes to the associated renal and microvascular complications. 33 Another consequence of a transplant is hypertension that should be treated with ACE inhibitor drugs. In addition to blunting the hypotensive effects, these drugs increase the risk of acute renal failure especially when an NSAID (nonsteroidal anti-inflammatory drugs) is coadministered, leading to increased serum creatinine concentrations and GFR (glomerular filtration rate) decrease. Furthermore, these drugs can reduce proteinuria and slow the progression of renal proteinuric diseases towards chronic renal failure. 34 In addition, not only there is a variety of mechanisms that may determine the variation of proteinuria and GFR in posttransplant patients but some of them are difficult to be monitored, such as in cases of noncompliance, or instrumental clinical investigations, that cannot be translated into numerical input parameters.
The aim of this work is to implement a FL-based expert system in order to assess and to follow-up the transplanted patients due to renal pathology. To this aim, we evaluated how the blood glucose level and the use of immunosuppressive and ACE inhibitor drugs (considered among easily determinable clinical parameters, which change the renal function) can lead to changes in proteinuria and GFR. Different values of these two notable parameters are associated with the various stages of renal failure, and therefore, they allow the characterization of the severity of the renal pathology from which the patient is affected. For this purpose, it was necessary to implement two case studies by fuzzy inference systems (FIS).
The present study can be considered innovative because the CDSS's outputs represent two clinical parameters (level of proteinuria and GFR) of extreme importance for the evaluation of kidney health and easy to read for clinicians. Furthermore, all the rules of inference were carefully agreed with the physicians of the nephrology depart- In order to select the statistical sample of two case studies, these inclusion/exclusion criteria were followed: • The time elapsed since the transplant between 2 and 6 years, the upper limit of 6 years allows to include the largest number of cases, instead cases in the bottom to 2 years after transplantation were excluded for which it would have been premature to detect the side effects associated with immunosuppressive therapy.
• The age range of 30 to 60 years of both genders, the upper limit is determined by the fact that over 60 years the probability of alteration of the clinical parameters under examination for physiological ageing increases, while under 30 years, there are few cases that would have led to a statistical inhomogeneity.
• Exclusions: • Patients who lacked the clinical data of proteinuria in the 24 hours and of the sirolimus blood level were excluded.
• Similarly patients who did not take the cyclosporine and ACEinhibitor drugs were excluded.
• Patients were also excluded for medical considerations that showed his/her health strongly influenced by other factors different from those of interest. The overlap extent of the membership functions has been agreed with the physicians taking into account the narrow ranges of the different clinical parameters that are usually used for the evaluation of kidney health.

| Knowledge representation
The design of a fuzzy inferential system (FIS) requires, first of all, the definition of the domain knowledge in cooperation with clinical experts by means of interviews, questionnaires, and observation of their day-by-day clinical practice. 21 The domain of knowledge embedded into the decision mechanism of the system has been described in terms of linguistic variables, linguistic values, and membership functions. A linguistic variable is a variable whose values are words or sentences in a natural or artificial language that can be used to ease a gradual transition between states, so as to naturally. Definition 1. Linguistic variable. 45  is an expression that assigns linguistic values to the output variables. 21 Indeed, FL provides a tool that enables to approximate an inference process, ie, the mental process by which human reach a conclusion based on specific evidence.

| Knowledge reasoning
To create the inferential engine, for the evaluation of some clinical aspect related to the patients' status, all clinical variables have been linked in a Mamdani-style FIS according to different rules and membership functions. 47,48 The Mamdani scheme is a type of fuzzy relational model where each rule is represented by an "if antecedent then consequent" relationship. Mamdani method is widely accepted for capturing expert knowledge. It allows us to describe the expertise in more intuitive, more human-like manner. 49 In the following, the Mamdani method is described, and the basic knowledge is implemented into the system. At this stage of the implementation of the fuzzy inference engine, we refer to a multi-inputs single-output decision model.  Else if the antecedent clause is connected with OR, then μ i (u) = max(_A i ; 1(u 1 ); : : :; _A i ; n (u n )).
Each fuzzy rule yields a single number that represents the firing strength of that rule. The second step is "implication," or applying the result of the antecedent to the consequent. Indeed, the strength level is then used to shape the output fuzzy set that represents the consequent part of the rule.

Definition 5.
The operator of implication for the rule R i is defined as the shaping of the "consequent" (the output fuzzy set), based on the "antecedent." The input of the implication process is a single number given by the "antecedent" (ie, _i computed as in Definition 4), and the output is a fuzzy set: where y is the variable that represents the support value of output the membership function μ Bi (·). Now, in order to unify the outputs of all the rules, we need to aggregate the corresponding output fuzzy set into one single composite set. The inputs of the aggregation process are represented by the clipped fuzzy sets obtained by the implication process. The aggregation method we exploited in our application is the max(·) one. Finally, the defuzzification process has been performed starting from the output fuzzy set resulting from the aggregation process.

| Case study 1
As regards the first case study, the following two systems have been implemented:

| ProtFIS
The variation of proteinuria is evaluated by loading in input two parameters: glycaemia and the blood level of the m-Tor inhibitor.
Based on the above inclusion and exclusion criteria, 63 patients were evaluated, and they are characterized by  50 according to this agency, and with the medical support, this range is split in alarm down (0-5 ng/mL), sufficient (4-7 ng/mL), good The inference rules used in the system are shown in Table 1.

| GfrFIS
The variation of GFR is evaluated by loading two-parameter inputs, glycaemia, and the dosage of a calcineurin inhibitor.

| Case study 2
In this case: • For glycaemia input variable, for proteinuria and Gfr output variables, the same membership functions of case study 1 are used.
• For ACE-inhibitor (Ramipril), the reference drug is Triatec, (recom- The two implemented systems are the following:

| ProtACE
The variation of proteinuria is evaluated by loading in input two parameters: glycaemia and the decreasing of the dosage of the ACE-Inhibitor drug.
Based on the above inclusion and exclusion criteria, 70 patients were evaluated and characterized by: • mean proteinuria of 532.00 mg/24 h (physiological range of proteinuria: 100-4000 mg/24 h) with standard deviation of 516.00 mg/24 h; • average normalized sample: 0.15 mg/24 h with standard deviation 0.15 mg/24 h; • average age: 51 years; • number of patients with diabetes risk: 13.
The inference rules used in the ProtACE system are shown in Table 3.

| GfrACE
The variation of GFR is evaluated by loading two-parameter input, glycaemia, and the increase in the dose of the ACE-inhibitor drug.
By the same inclusion and exclusion criteria, 107 patients were evaluated and characterized by • mean GFR of 53.54 mL/min (physiological range of GFR: 0-130 mL/min) with standard deviation of 16.22 mL/min; • average normalized sample: 0.41 mL/min with standard deviation 0.13 mL/min; • average age: 48 years; • number of patients with diabetes risk:16.
The inference rules used in the GfrACE system are shown in Table 4:

| RESULTS
One of the major advantages of decision analysis models is their ability to rapidly test their assumptions and input data in order to validate the decision model. To evaluate the accuracy of the implemented systems, we have inserted in each of the four FISs the input data of all the selected patients and then the output of each system is subsequently compared with the clinical experimental data respectively of proteinuria and GFR. Following the results obtained for both case studies are reported.

| GfrFIS
Also for this system, we need to validate the model's answer, comparing it with the "true" answer provided by clinical data. For example, we report a clinical case related to the GfrFIS illustrated in Figure 3.

| GfrACE
The clinical case related to the GfrACE is illustrated in Figure 6 and has the following input values: 89 mg/dL of glycaemia and −2.50 difference of ACE-inhibitor dosage (Triatec). The GFR output is 43.10 mL/min, which is to be compared with the real value provided by the clinical examination of GFR equal to 53.60 mL/min. So then,    Table 5 shows the results of the performance analysis of the four implemented systems. For all the systems, an accuracy greater than 90% is obtained; this result is fundamental to trust a CDSS, and it is necessary that its reliability can be decidedly high. Nevertheless, the implemented systems in this work do not cover all the possible circumstances that can cause renal damage to posttransplant patients.
Indeed, the causes that lead to an increasing in proteinuria or a decreasing in the glomerular filtrate are many and may have more or less serious consequences. In this work, we analysed those factors that have the greatest impact on renal diseases of posttransplant patients; for this, the attention has been focused on the consequences of high blood glucose values and on the use of immunosuppressive and ACE-inhibitor drugs, these notoriously offer benefits, but can also worsen already critical situations.
However, the systems could offer greater efficiency if we consider into account additional input variables related to clinical parameters that could lead to an alteration of proteinuria and GFR. For example, an additional element that could be evaluated is the incidence of the sex of patients; in fact, it is known how it significantly affects the therapeutic response. Including more input and output variables, which no doubt is desirable, would lead to an increase in the number of rules and membership functions; all this, however, could involve a considerable increase in the complexity of the system.
Fuzzy-based CDSSs implemented for the assessment and followup of kidney-transplanted patients could improve complications control, using exclusively glucose values, easy to perform, reducing the costs of care and test's duplication, avoiding drugs excess. Moreover, viewing of the alert system, easy to read for both clinicians and patients could stimulate the clinicians to discuss treatment options with patients and consequently make the latter feel more involved in their medical treatment. The goal of the system is obviously to provide effective support, rather than to replace the physician, because, in any case, the physician must filter the information, review the suggestions, and decide how much to consider it before acting. With the gradual maturation of AI health care systems, the CDSSs should play a crucial role in reducing medical errors and in improving the quality of health care and the efficiency of the health care delivery system.

FUNDING INFORMATION
The are no funding available for this study. Sensitivity  91  96  90  89   Specificity  89  83  94  94