Fuzzy Logic-Based Formalisms for Gynecology Disease Diagnosis

1 Introduction

The diagnosis of a disease involves several levels of uncertainty and imprecision, and it is inherent to medicine. A single disease may manifest itself differently, depending on the patient, and with different intensities. A single symptom may correspond to different diseases. On the other hand, several diseases present in a patient may interact and interfere with the usual description of any of the diseases. Disease descriptions use linguistic expressions that are inherently imprecise/vague/fuzzy/ambiguous. The process of medical diagnosis is characterized by different stages of uncertainty in various forms like the symptoms (s) of the patient (p), symptoms (s)-diseases (d) association, and the indicated diagnosis (d) itself. Such uncertainty is crucial for the physician to determine a diagnostic label to entail the appropriate therapeutic regimen. The best and most precise description of disease entities uses linguistic terms that are also imprecise and vague [13]. However, diseases such as gynecological ones involve multiple concomitant causal factors, which are difficult to represent using conventional statistical methods. Medical documentation is in linguistic form. The physician uses his/her tactic knowledge, based on his/her experience, which is then represented as membership grades [24, 26], which is detailed in the paper.

Many times, the diagnostic process constitutes one type of imprecision and uncertainty, and the knowledge related to a patient’s state constitute another type. The physician generally gathers knowledge about the patient from the past history, physical examination, laboratory test results, and other investigative procedures such as ultrasonic diagnosis, X-ray, etc. The knowledge provided by each of these sources carries varying degrees of uncertainty. The past history furnished by the patient may be subjective, exaggerated, underestimated, or incomplete. Also, mistakes may be committed in the physical examination and symptoms may be sometimes overlooked. Nonetheless, measurements provided by laboratory tests are often of limited precision, and the exact borderline between normal and abnormal pathological results are often unclear. The diagnostic tests require a correct interpretation of the results [1, 30]. Thus, the state and symptoms of the patient can be known by the physician with only a limited degree of precision. The desire to better understand and teach this difficult and important technique of medical diagnosis has prompted attempts to model the process with the use of the fuzzy set theory [13].

Most of the medical decision support systems (MDSSs) are developed during 1970–1980 using Bayesian methods [7, 8, 12] and symbolic reasoning – PIP, MEDITEL [31], INTERNIST [15, 18], DXPLAIN [5, 17, 19], DiagnosisPro [10], Iliad, fuzzy diagnosis, and fuzzy sets in medical artificial intelligence [14, 28, 29]. In the mid-1970s, MYCIN [6, 11], a knowledge-based computer program, was designed to aid physicians in the diagnosis and treatment of meningitis and infectious diseases, and accommodates uncertainties and ambiguities in labeling the symptoms. It is a rule-based expert system with backward chaining that uses around 600 rules that are stored as LISP expressions. In the last two decades, systems based on other paradigms like information theory and fuzzy set theory have been developed; for example: Isabel is an information theory-based pediatric diagnostic system [21]. Early works in which the fuzzy set theory was effectively used for medical diagnosis were carried out by Sanchez [23], Esogbue [9], Adlassnig et al. [2–4, 16, 27], Kolarz et al. [3, 4, 16], and other researchers. CADIAG systems for the diagnosis of medical conditions such as rheumatic disorders and pancreatic diseases were developed by Adlassnig and his colleagues [16]. In 1970–1980s, some stand-alone systems like CADUCEUS, Iliad, and DxPlain, which use patient symptoms as input and give diagnosis, were developed [20]. Systems like DynaMed and UpToDate are based on the information from journals and expert experience [20]. This information along with the clinical guidelines and protocols are used to create value-added tools to support clinical care. Mobile devices and tools like InfoRetriever, ePocrates, and Micromedex help provide drug information, clinical guidelines, calculators, and emergency medicine resources at the point of care [20].

In medical science working with crisp values, concrete definitions are rather rare. As an example, the intensity of pain can be described verbally and depends on the subjective information of the patient. To model this subjective information, linguistic variables like Always, Often, Not Specific, Seldom, and Never are invariably used. Prof. Zadeh proposed the use of linguistic hedge. For example, “Very” to indicate “Very Often.” The concentration operator takes the form as A_very(x)=A²(x). In computer-assisted medical diagnosis, Adlassnig proposed that the medical knowledge should be stored as logical relationships between symptoms and diagnosis in terms of (i) presence of a symptom S_i in the case of diagnosis D_j ; (ii) conclusiveness of symptom S_i for diagnosis D_j. He defined fuzzy subsets presence and conclusiveness, and calculated membership functions and determined membership values for all the subsets [2]. In the paper, Zadeh’s exponents are used to calculate the linguistic hedges.

2 Mathematical Preliminaries

MDSS primarily depends on the perception of the domain experts due to the inherent uncertainty/imprecision at every stage in the diagnostic process. The fuzzy set theory, in our view, could be one of the possible soft computing formalisms that could be used effectively in medical diagnostic decision making. We therefore present an overview of the techniques used in the study reported in this sequel.

2.2 Type 1 FIS

The FIS defines a non-linear mapping of the input data vector into a scalar output, using fuzzy rules. A Mamdani-type FIS was used in this research, which uses center of gravity as a defuzzification method. The details of the method are available in standard literature [13, 22].

The fuzzy logic-based formalism to arrive at a correct diagnosis in gynecological diseases is presented in Figure 1.

Figure 1:

Fuzzy Logic-Based Formalism for the Diagnosis of Gynecological Diseases.

There is a relation between symptoms (s) and diseases (d). To model the descriptive information, two fuzzy relations can be formulated: (i) fuzzy occurrence relation (R_o) and (ii) fuzzy confirmability relation (R_c). The first one provides knowledge about the tendency or frequency of a symptom with respect to a specific disease. It corresponds to a question, “How often does a symptom ‘s’ occur with respect to a disease ‘d’?.” The second one describes the discriminating power of the symptom to confirm the disease and corresponds to a question, “How strongly does the symptom ‘s’ confirm the disease ‘d’?.” The distinction between occurrence and conformability is useful because a symptom may rather likely occur with respect to a given disease but may also commonly occur with several other diseases; therefore, limiting its power as a discriminating factor among them is necessary. Another symptom, on the other hand, may be relatively rare with respect to a given disease, but its presence may nevertheless constitute an almost certain confirmation of the presence of the disease. We then obtain a fuzzy relation R_s specifying the presence, absence, or otherwise status of symptom (s) for the patients [13].

2.4 Past History Parameter Screening: Stage 2

After taking a deeper look by the authors, it was inferred that the diagnostic efforts in gynecology heavily depend on some of the factors/history such as age of the patient, LMP, premenstrual cycle (PMC), irregular/regular nature of menses, married/unmarried status of the patient, and parity. These factors collectively decide some of the diseases. Thus, five fuzzy sets, namely, age, LMP, PMC_Flow, marital status, and parity, were defined (Figure 2A–E) and 72 fuzzy rules were formulated and using type 1 FIS [25].

Figure 2:

(A–E) Fuzzy Sets for History Parameter. (A) Fuzzy set for age. (B) Fuzzy set for PMC_Flow. (C) Fuzzy set for Marital_Status. (D) Fuzzy set for parity. (E) Fuzzy set for LMP.

3 Case Study

The study relates to the investigations carried out by a team of eight gynecologists, a fuzzy logic engineer, and a computer scientist in India, to finally arrive at a patient-disease matrix. The domain experts, based on their more than two decades of experience, confirmed that there are 31 commonly observed gynecological diseases and 123 related symptoms. The case study is divided into two parts.

The first part focuses on classifying the experts depending on their perceptions on the symptom-disease relationship. The second part of the case study initiates the process of initial screening to arrive at some diagnosis by one expert and also with eight experts.

The gynecologists recorded their perceptions linguistically with corresponding membership values (in bracket) as A – Always (1), Very Often – VO (0.5625), O – Often (0.75), NS – Not Specific (0.5), S – Seldom (0.25), VS – Very Seldom (0.0625), and N – Never (0) (Table 1) [Eq. (2)].

In order to explain the computational procedure, a sample set of 9/31 diseases and 17/123 related symptoms are considered (Table 1), and the names of diseases and symptoms are presented in the Appendix. We presuppose that if in a disease d_i, a symptom s_j is absent, the fuzzy occurrence and confirmation table entries for the [d_i, s_j ] will have membership value 0. Such entries in the tables are not further considered in the analysis for obvious reasons (Table 1).

4 Results and Discussion

In stage 1, fuzzy occurrence and fuzzy conformability indication relations are computed [Eqs. (1) and (3)]. Table 4 presents the final fuzzy conformability indication relation matrix using max-min composition.

Tables 4 and 5 infer that disease D₂ occurs “always” in patient P₂ and “always” confirms the disease. Thus, we can state that patient P₂ is suffering from disease D₂. Similarly, patient P₂ is also suffering from diseases D₂, D₆, D₈, and D₉.

Table 6 shows that max-min composition does not result only in one disease diagnosis but identifies more than one disease or multiple diagnoses in a patient. Physicians term it as initial screening of the disease in a patient, which is same as the model output. From the data set above, we can state that fuzzy model has diagnosed 4/31 diseases correctly in a patient P₁, 5/31 in patient P₂, and so on, as shown in Table 6. For patient P₉, the model diagnosed a single disease – pelvic inflammatory disease. In the cases of all other seven patients, the gynecologist suggested further investigative tests to arrive at the single disease diagnosis. In patient P₈, the diagnosis by model was “disease unspecific.” There are various reasons related to a “disease unspecific” output, such as that the symptoms narrated by the patient may not match with any of the currently selected 31 diseases, or the symptoms narrated may be very weak so it does not calculate both the fuzzy indication relations as the “always” linguistic value; this may require to cut down the result to the nearest α-cut level, or it is mostly observed in many patients that the patient with a psychological history cannot be diagnosed correctly.

In the study, 226 patients were studied and an overview of the diagnosis analysis for one expert is presented below.

1. Total number of patients diagnosed by the model: 226.

2. Number of patients with only one disease diagnosed by model and confirmed by the expert: 50.

3. Number of patients with multiple diseases diagnosed by model, all correct and confirmed by the expert: 40.

4. Number of patients with multiple diseases diagnosed by model, partial correct and confirmed by the expert: 107.

5. Diagnosis percentage with 100% accuracy by the model (only one disease was diagnosed by model and confirmed by the expert): 22.12%.

6. Diagnosis percentage of initial screening model diagnosis with one + multiple diseases confirmed by the expert: 87.17%.

7. Failure percentage of the initial screening model: 12.83%.

It was observed that the model gives 12.83% incorrect diagnosis. The possible reasons may be as follows:

1. The patient comes with a set of symptoms not covered in the study, as only 31 gynecology diseases are considered at present.

2. The patient may have history/symptoms other than gynecology-related symptoms, and so the model fails to diagnose the relevant diseases. In such a case, the patient is directed to another branch of medicine for the diagnosis.

3. It is noted in many psychological patients that the psychological imbalance causes changes in female hormones, namely estrogens and progesterone, and consequently causes disturbance in the functioning of the female reproductive system.

In this study, the perceptions of eight domain experts were considered, and the model was executed for each of the experts, keeping the patient’s data the same. Table 7 shows the detailed diagnosis analysis for 226 patients.

Table 1 rows 2 and 3 infer multiple disease diagnosis for some of the patients. Therefore, in the quest of arriving at a single disease, there was a need to look for an additional mathematical formalism.

In stage 2, out of 226 patients, 30 patients were identified using type 1 FIS, for whom the “history” criteria was applicable to arrive at a single disease. We can state in no uncertain terms that 29/30 patients were correctly diagnosed for a single disease. In stage 1, 50 patients were diagnosed correctly using type 1 fuzzy relational calculus, for a single disease diagnosis. In stage 2, only one patient (P₁₀₀) was incorrectly diagnosed. The reason for the failure is narrated below:

The history of the patient was as follows: Age – 25 years, fits in the fuzzy set Age-Fertile (F=1), Marital Status – Unmarried (M_Status=U), Amenorrhea for 4 years, which does not fit in any of the LMP fuzzy sets. In the fuzzy sets defined, Amenorrhea is termed when there are no menses for >1.5 months to 4–5 months. Then, till 9 months, the patient is Gravid, and after the birth of a child for next ~1.5 years, it is Lactational Amenorrhea. More than 4 years should fall into Menopause, but menopause is not possible at an early age like 25 years. Thus, none of the rules are fired and the model gives no output. The gynecologists invariably termed the diseases as Secondary Amenorrhea for the symptoms – “age 25 and no menses present.” As it is not good practice to redefine the fuzzy set for every extreme case, we consider this as exceptional case or it may be an outlier. The initial screening model also could diagnose this patient as “Disease Unspecific.” This patient P₁₀₀ can be considered as an outlier.

Table 8 shows the increased accuracy of performance in the overall diagnosis by each expert after the application of rules to all identified 30 patients out of 226 patients. It ranged from 22.12% to 30.53% for the single disease diagnosis as an output by eight experts.

In stage 3, hopefully, we will be able to identify most of the remaining 147 patients to confirm the single disease diagnosis. Though information on symptom and history of a patient can help in single disease diagnosis, the investigations carried out in sequel emphasize the need for further investigations to conduct tests such as blood tests, medical imaging tests (ultrasonic test, X-ray, magnetic resonance imaging, computed tomography scan, and so on), etc.

5 Concluding Remarks and Future Scope for Research

The limited study concludes that exponent 2, used as a concentration operator (fuzzy hedge) in the transformation from good to very good, initially proposed by Prof. Zadeh, works out well. The case study infers that the use of type 1 fuzzy relational calculus in the initial screening process (stage 1 of medical diagnosis) helps in arriving at a single disease diagnosis. Stage 1 also arrives at multiple diseases as an output, for which the FIS (stage 2) is used to refine the diagnosis for past history parameters. Stage 3 can be used to finally arrive at a single disease diagnosis.

The development of the software is an important activity and is aimed to simulate the process of differential diagnosis to achieve some level of machine intelligence in medical diagnosis.

In order to check the sensitivity and specificity of these results, the efficacy of the use of receiving operating curve is being studied. Implementation of these approaches will go a long way to achieving the ultimate objective of assisting a general physician/newcomer gynecologist. In the process, exhaustive user-friendly software will be developed.

A large proportion of routine clinical decision making depends on the availability of good quality clinical information and instant access to up-to-date medical knowledge. There is increasing evidence that the use of computer-aided clinical decision support to manage medical knowledge results in better health-care processes and patient outcomes. We believe that the three-stage approach detailed in the paper is a better proposition in the medical diagnosis system, especially in the field of gynecology. Though the use of type 1 fuzzy relational calculus and FIS is more appropriate, the possibility of additional bio-inspired computing methods could be explored. The software will help in arriving at a correct disease diagnosis in gynecology for general physicians/gynecologists.