The Prioritization of Clinical Risk Factors of Obstructive Sleep Apnea Severity Using Fuzzy Analytic Hierarchy Process

Recently, there has been a problem of shortage of sleep laboratories that can accommodate the patients in a timely manner. Delayed diagnosis and treatment may lead to worse outcomes particularly in patients with severe obstructive sleep apnea (OSA). For this reason, the prioritization in polysomnography (PSG) queueing should be endorsed based on disease severity. To date, there have been conflicting data whether clinical information can predict OSA severity. The 1,042 suspected OSA patients underwent diagnostic PSG study at Siriraj Sleep Center during 2010-2011. A total of 113 variables were obtained from sleep questionnaires and anthropometric measurements. The 19 groups of clinical risk factors consisting of 42 variables were categorized into each OSA severity. This study aimed to array these factors by employing Fuzzy Analytic Hierarchy Process approach based on normalized weight vector. The results revealed that the first rank of clinical risk factors in Severe, Moderate, Mild, and No OSA was nighttime symptoms. The overall sensitivity/specificity of the approach to these groups was 92.32%/91.76%, 89.52%/88.18%, 91.08%/84.58%, and 96.49%/81.23%, respectively. We propose that the urgent PSG appointment should include clinical risk factors of Severe OSA group. In addition, the screening for Mild from No OSA patients in sleep center setting using symptoms during sleep is also recommended (sensitivity = 87.12% and specificity = 72.22%).


Introduction
Obstructive sleep apnea (OSA) is a common medical disorder characterized by repetitive partial or complete collapse of the upper airway during sleep, resulting in sleep fragmentation and cyclic oxygen desaturation. The prevalence of OSA in adult population is approximately 3-7% for males and 2-5% for females [1][2][3][4]. This can be as high as 50-98% in the morbidly obese population [5]. OSA leads to neurocognitive consequences for example, unrefreshing sleep, excessive daytime sleepiness, motor vehicle accidents and work performance [6], impaired quality of life, and considerable morbidity for cardiovascular diseases [7,8] as well as a substantial economic impact [9]. OSA can progress to more severe if it is left untreated. Diagnosis and severity assessment required Respiratory Disturbance Index (RDI) obtained from polysomnography (PSG). The RDI is defined as the total numbers of apneas, hypopneas, and respiratory-effort related arousals (RERAs) per hour of sleep (events/hour).
Unfortunately, PSG is not widely available in Thailand because of the relative lack of sleep laboratories and results in a very long waiting list. Delayed diagnosis and treatment may lead to worse outcomes particularly in patients with Severe OSA. Therefore, the appointment for PSG should be based on OSA severity rather than the first-come-first-serve basis. Moreover, clinicians prefer a simple and nonexpensive tool to predict the severity of OSA. To date, no single clinical information can predict the severity of OSA. We believe that if symptoms and anthropometric data are categorized into groups, this may solve the problem. We previously studied 113 variables of 1,042 sleep questionnaires, anthropometric measurements, and PSGs data from suspected OSA patients of Siriraj Sleep Center. Using factor analysis, the 19 groups of clinical risk factors consisting of 42 variables were categorized into each OSA severity [10]. This research is the extended study aiming to prioritize these 19 groups of factors in each level of OSA severity by using Fuzzy Analytic Hierarchy Process (FAHP) approach. The study has been approved by 2 Computational and Mathematical Methods in Medicine  [10]. The abovementioned 42 variables which were categorized into No, Mild, Moderate, and Severe OSA group comprised 3, 5, 5, and 6 clinical risk factors, respectively. All these factors will be prioritized according to their importance to OSA ( Figure 1).

A Specialist
Team. The questionnaire of AHP was taken to 3 sleep specialists. They were individually face-to-face interviewed by author to determine which groups of factors they thought to be more important when compared to another. Then, the decision data were collected.

The Construction and Consistency Check of Pairwise
Comparison Matrix [17] Step 1 (establishing the hierarchical structure (Figure 1)). Then, the decision-makers are requested to make pairwise comparisons between decision alternatives and criteria using a nine-point scale from Table 2. Subsequently, all matrices are developed and all pairwise comparisons will be obtained from each decision-maker.
Step 2 (calculating the consistency). To ensure that the priority of elements is consistent, the maximum eigenvector or relative weights and max are calculated. Then, the consistency index (CI) for each matrix order using (1) is computed. Based on the CI and random index (RI), the consistency ratio (CR) is calculated by (2): where RI is the random consistency index obtained from a randomly generated pairwise comparison matrix. Table 3 shows the values of the RI for matrices of orders 1 to 15 [12]. If the value of CR is 0.1 or less, the pairwise comparisons will be considered as having an acceptable consistency.
Then, we construct a fuzzy pairwise comparison matrix in each criterion.

The Mathematics of Fuzzy Sets and Triangular Fuzzy
Number (TFN) [18]. The fuzzy set theory is an effective instrument for modeling in the lack of comprehensive and accurate information. A TFN is a particular fuzzy set̃, and its membership functioñ( ) is a continuous linear function. A TFN is defined by its basic particular equation which is [19] Computational and Mathematical Methods in Medicine 3 Table 2: 9-point intensity of relative weight (importance or well-being) scale (adapted from [11][12][13][14][15]  where and correspond to the lower and upper bounds of the fuzzy number̃, respectively, and is the midpoint. A TFN is indicated as̃= ( , , ). Arithmetic operations between fuzzy numbers or a fuzzy number and crisp number have been defined elsewhere in Bulut and Zadeh [18,19] by standard fuzzy arithmetic operations.

The Construction of Fuzzy Pairwise Comparison Matrix.
Consider the following: where VM 1 , PM 2 , and NM 3 are pairwise comparison matrix of each decision-maker and is the pairwise comparison score of each decision-maker . Integrating 3 decisionmakers' grades through (6) and yields TFN: By this procedure, decision-makers' pairwise comparison values are transformed into TFN. After forming fuzzy pairwise comparison matrix, weights of all factors are determined by FAHP method.
In this study, the extent FAHP which was originally introduced by Chang [20] is utilized. Let = { 1 , 2 , 3 , . . . , } be an object set and = { 1 , 2 , 3 , . . . , } a decision set. According to Chang's extent analysis, each decision is taken and extent analysis for each goal is performed, respectively. Therefore, extent analysis values for each decision can be obtained with the following: ] .
Step 4. Via normalization, the normalized weight vectors are where is a nonfuzzy number. Then, weights of main criteria and attributes ( ) can be calculated by 2.9. Diagnostic Test Evaluation of Sensitivity, Specificity, and 95% Confidence Interval (95% CI) [28,29]. Sensitivity and specificity are statistical measures of the performance of a binary classification test. Sensitivity is the proportion of people with the target disorder in whom the test result is positive. Specificity is the proportion of people without the target disorder in whom test result is negative. To use these concepts, we divide test results into normal and abnormal to create a 2 × 2 table (Table 4): The 95% CI of a proportion is estimated based on the binomial theorem: where is the observed proportion and is the number of people observed.

The Summarization of All Steps for the Prioritization of Clinical Risk
Factors. See (Figure 2).     (Table 5). From Table 5, the decision comparison matrices of the 3 sleep specialists in each severity group are then transformed into TFN by using (6) (Tables 6-9).

Procedure of Fuzzy Analytic Hierarchy Process (FAHP)
Step 1. We employ the calculation of fuzzy synthetic extents with respect to factors where the results of A1 -A19 are calculated in detail (Table 10).
From the calculation, the weights of significance of decision factors in terms of triangle fuzzy number with lower, mean, and upper bounds ( , , ) in each OSA severity are obtained.
Step 3. The minimum degree of possibilities values of clinical risk factors in No OSA to Severe OSA are calculated by (11) as in Table 15.
At this stage, factors affecting each level of OSA severity have been prioritized by using the FAHP methodology, which  is a scientific procedure of multicriteria decision-making method. It can reflect effectively the human thoughts with vagueness of real world decision-making. The results of this research have finally provided the optimal factors.

Final Ranking, Choosing the Optimal Factors Sensitivity/Specificity and 95% CI.
Next, we put them in an order from highest to lowest based on what the priority weight of each factor is and on their corresponding normalized weights vector. An optimal factor that has the highest score in a priority rating is selected. Finally, the overall sensitivity, specificity, and 95% CI of all OSA severities are calculated (Table 17). As can be seen in Table 17, in No OSA, first rank clinical risk factor is symptoms during sleep and the last one is underlying diseases and sleep posture. In Mild OSA, first rank clinical risk factor is choking and witnessed snoring and the last one is lung diseases and sleep-wake pattern. In Moderate OSA, first rank clinical risk factor is witnessed snoring and apnea plus awakening due to chest discomfort, whereas the last one is related personal variables. In Severe OSA, first rank clinical risk factor is witnessed snoring and apnea and the last one is underlying diseases and personal variables. It is observed that the sensibility and specificity of the approach to each group are high.

Discussion
Regarding the concept of factor analysis, each factor has its members (variable or symptom); whenever any variable is found, there is high tendency of the rest members to occur because they belong to the same factor. The FAHP methodology can provide the flexibility and robustness needed for the decision-maker to understand the decision problem as well as a standard control of consistency on the decision matrix for them. These merits of the approach lead to the developed FAHP questionnaire for detecting OSA patient in each level.
In Severe OSA group, the most related clinical risk factor is witnessed snoring and apnea that includes the witnessing of frequency of periodically stopped breathing and snoring as well as the intensity of the loudness of snoring. From Table 1 the Severe OSA patients have very high RDI (range 30.1-168.2 events/hour and mean ± S.D. = 60.6 ± 25.3 events/hour). Thus, in clinical practice, we propose that the appointment for the urgent sleep study and prompt management should include all clinical risk factors of Severe group (the sensitivity of 92.32% and specificity of 91.76%) ( Table 18).     Table 11: Degree of possibility of ( ≥ ) in No OSA.
In Moderate OSA, the overall sensitivity and specificity of the approach are 89.52% and 88.18%. Furthermore, the most at-risk factor is witnessed snoring and apnea plus chest discomfort as a cause of awakening during late night or getting up earlier than expectation. It should be noteworthy that apnea and snoring are observed in this Moderate group as well as in Severe group. Among 5 groups of factors in Moderate OSA, the first rank group carries extremely high normalized weight vector (0.481) compared to the remaining 4 groups (0-0.291). Therefore, in addition to the severe group the first rank clinical risk factors of Moderate OSA may be included in the urgent PSG appointment.
For the remaining clinical risk factors and variables in Moderate, Mild, and No OSA groups, they should be indicated for queueing up in the usual PSG waiting list.
In No OSA group, the details of symptoms during sleep included the troubles at night or during sleep within Table 12: Degree of possibility of ( ≥ ) in Mild OSA.  (Table 19).
To date, there have been no known previous studies concerning sleep questionnaire and anthropometrics data as the clinical risk factors for the prioritization of PSG appointment based on OSA severity.
Our future work will be planning to create the formula of clinical information for urgent sleep study appointment and screening of Mild OSA using fuzzy binary logistic regression equation approach.

Conclusion
Using FAHP based on normalized weight vectors to prioritize 19 clinical factors revealed that in each severity group based on RDI as No, Mild, Moderate, and Severe OSA, their first clinical risk factors are nighttime symptoms. Then, the prioritized factors are selected to propose the criteria for sleep study appointment. Therefore, the urgent sleep study appointments based on clinical risk factors of Severe OSA have been presented. In addition, the screening for Mild from No OSA patients in sleep center setting using symptoms during sleep is recommended. Finally, the questionnaires for these purposes can be constructed to cover the concerning factors.