Sagittal Abdominal Diameter as the Anthropometric Measure of Cardiovascular Risk

Obesity has a profound impact on the cardiovascular disease development, and is associated with a reduced overall survival. There is a strong correlation between the central (abdominal) type of obesity and the cardiovascular and metabolic diseases. Among a variety of anthropometric measurements of the abdominal fat size, sagittal abdominal diameter has been proposed as the valid measurement of the visceral fat mass and cardiometabolic risk level. Many studies have analyzed the relationship between sagittal abdominal diameter (SAD), visceral fat area, and different markers of cardiometabolic disturbances with respect to age, gender and ethnicity. Some of them have offered the cut-off values that could be useful in clinical practice, in identifying individuals who are at higher risk of comorbidities of the obesity. Using the principles of rough set theory, based on producing If-Then rules, we have developed a model that allows better applicability of SAD in identifying patients at higher cardiovascular risk. In this chapter, we describe the basic principles of the proposed model. Furthermore, we give a broad overview of the main concerns regarding the significance of SAD and its use in diagnosing the abdominal obesity and predicting the adverse cardiometabolic outcomes.


Introduction
Obesity has a profound impact on the cardiovascular disease development, and is associated with a reduced overall survival. There is a strong correlation between the central (abdominal) type of obesity and the cardiovascular and metabolic diseases. Among a variety of anthropometric measurements of the abdominal fat size, sagittal abdominal diameter has been proposed as the valid measurement of the visceral fat mass and cardiometabolic risk level. Many studies have analyzed the relationship between sagittal abdominal diameter (SAD), visceral fat area, and different markers of cardiometabolic disturbances with respect to age, gender and ethnicity. Some of them have offered the cut-off values that could be useful in clinical practice, in identifying individuals who are at higher risk of comorbidities of the obesity. Using the principles of rough set theory, based on producing If-Then rules, we have developed a model that allows better applicability of SAD in identifying patients at higher cardiovascular risk. In this chapter, we describe the basic principles of the proposed model. Furthermore, we give a broad overview of the main concerns regarding the significance of SAD and its use in diagnosing the abdominal obesity and predicting the adverse cardiometabolic outcomes.

Obesity as a cardiovascular risk factor
The prevalence of obesity has increased dramatically worldwide during the past few decades. Obesity is recognized as an independent factor for the development of the cardiovascular diseases. It also predisposes to the development of other cardiovascular risk factors.
Obesity implies increased body weight due to the enlargement of the adipose tissue to the extent that impairs health. Regional obesity appears to be an important indicator of the risk level. Thus, the diagnosis of obesity depends on three main aspects: relative weight (total body mass with relation to body height), total body fat, and fat distribution.
Body mass index (BMI) has been widely accepted as a simple and the most practical measure of fatness in clinical and epidemiological surveys, eventhough it doesn't distinguish fat from lean body mass. In fact, it is an indicator of the nutritional status, not a measure of body fat mass. It has been shown that BMI≥25 kg/m 2 is associated with increased morbidity, while BMI≥30 kg/m 2 carries increased risk for both morbidity and mortality, primarily from diabetes and cardiovascular diseases (Irribaren et al., 1995). However, recent studies showed that BMI can be a reliable predictor of cardiovascular mortality only in severe obesity (Romero-Corral et al., 2006). The category of overweight people (BMI: 25-29.9 kg/m 2 ) seems to be the most confusing, especially from the aspect of the therapeutic approach.
BMI doesn't provide sufficient information about fat mass. Therefore, body composition assessment is necessary for the diagnosis of obesity and prediction of its comorbidities. It discriminates individuals with true excess body fat from those with "normal weight obesity", as well as from overweight individuals with normal body fat mass. Using a cut-off value of 30% body fat, Marques-Vidal et al. (2008) reported prevalence of "normal weight obesity" of 10.1% in women, and 3.2% in men, with increasing prevalence with aging.
Specific fat distribution determines the risk level more accurately than the total body fatness per se. Excess adipose tissue in the abdominal region is more hazardous than the overall obesity, due to higher visceral fat deposition. Furthermore, it is associated with greater risk of cardiovascular diseases, metabolic disorders and type 2 diabetes mellitus (Després et al., 1990;Molarius & Seidell, 1998). Central or abdominal obesity (firstly assigned as android type of obesity) has been identified as a risk factor for the cardiovascular diseases, as well as a symptom of metabolic syndrome. Normal weight subjects with higher visceral fat mass are at a higher risk (metabolically obese normal weight subjects). In addition, obese subjects with normal visceral fat mass can present with normal metabolic profile (metabolically healthy obese subjects) (Ruderman et al., 1998;Sims, 2001).

Abdominal obesity
It is well known that the risk of cardiovascular and metabolic abnormalities is determined by specific distribution of the adipose tissue. Abdominal (central) obesity is associated with dyslipidemia, impaired fasting glucose, insulin resistance and hypertension, which result in increased risk of cardio-and cerebrovascular diseases, and consequently premature death (Guzzaloni, 2009).
Adverse effects of the abdominal obesity have been supported by many studies of the metabolism and endocrine activity of adipocytes from different regions of the abdominal adipose tissue. Abdominal fat includes two morphologically and functionally different depots: subcutaneous (superficial) and deep, visceral (intraabdominal). The latter is located in the abdominal cavity and includes intraperitoneal (omental and mesenterial) adipose tissue, which makes 80% of the intraabdominal fat mass, and retroperitoneal adipose tissue, which makes 20% of the intraabdominal fat mass (Misra&Vikram, 2003). Abdominal obesity can reflect expansion of either subcutaneous or visceral depot, or a combination of excess fat in both depots. However, visceral adipose tissue compartment has been considered more important in pathogenesis of the obesity complications. It is responsible for the development of insulin resistance, glucose intolerance and type 2 diabetes mellitus. According to Brochu et al. (2000), visceral fat depot explains 10% of variability of insulin resistance and 16% of blood glucose. Visceral adipose tissue enlargement is mainly associated with lower values of HDL-cholesterol, elevated tryglicerides, apolipoprotein B (Couillard et al., 1996), as well as with elevated atherogenic lipoprotein subfractions and reduced concentration of HDL particles (Nakata et al., 2010). It positivly correlates with glucose intolerance and hyperinsulinemia (Wajchenberg, 2000), as well as the markers of the proinflammatory and prothrombotic state.
Visceral adipose tissue function plays a crucial role in the development of metabolic abnormalities and insulin resistance, mainly due to the direct access of intraperitoneal adipose tissue to the liver through the portal circulation (Matsuzawa et al. 1995. In comparison to the subcutaneous adipose tissue, visceral adipose tissue contains higher number of adipocytes per unit mass, higher number of endothelial cells in the stromal vascular fraction, higher β 3 -adrenoreceptor and α 2 -adrenergic receptor sensitivity, and it is better vascularized (Misra & Vikram, 2003;van Harmelen et al., 2004). Visceral adipocytes are more metabolically active, have higher lipolytic activity when stimulated by catecholamines, and are poorly responsive to the antilipolythic action of insulin. In addition, they secrete more proinflammatory (interleukin-6, interleukin-8, interleukin-1 ) and prothrombotic (plasminogen-acivator inhibitor-1) adipokines. Obesity is characterized by an increased number of β 3 -and decreased number of α 2 -adrenergic receptors, decreased insulin activity, increased activity of lipoprotein-lipase and acylationstimulating protein, with higher upload of triglycerides and lower postprandial suppression of lipolysis (Wajchenberg, 2000;van Herpen & Schrauwen-Hinderling, 2008). All of the above mentioned changes in the visceral adipose tissue provide increased release of free fatty acids and their flux towards the liver, where they induce gluconeogenesis, synthesis of triglycerides and apolipoprotein-B rich lipoproteins, as well as impairment of insulin action (Lonnquist et al., 1995, Freedland, 2004. Free fatty acids also exhibit proarrhythmic properties which explains association between the visceral fat and sudden death (Empana et al. 2004). On the other hand, obese adipose tissue is characterized by impairment of blood flow, development of hypoxia and local inflammation, infiltration by macrophages, and by disturbances in secretion of adipokines, which all together result in insulin resistance and systemic inflammation (Berg & Scherer, 2005;Coppack, 2005;Goossens, 2008).
Computerized tomography (CT) and magnetic resonance imaging (MRI), performed at the L 4 -L 5 level, are the most reliable anatomical methods for abdominal fat assessment, since they discriminate between the subcutaneous and the visceral fat depots (van der Kooy et al., 1993). However, these methods are expensive, not feasible and unportable, which makes their use in clinical and epidemiological practice limited. Anthropometric parameters are more suitable as they are inexpensive, non-invasive and simple. Besides, most of them show a strong correlation with visceral abdominal fat size.

Anthropometric parameters of abdominal obesity
Several anthropometric indicators of abdominal obesity have been developed to measure abdominal adipose tissue mass. Some of them are presented in the form of ratios, especially the ones that incorporate body height, which gives more realistic picture of body proportions. On the other hand, it is difficult to interpret them biologically . Many studies have compared them in order to demonstrate advantages of a particular www.intechopen.com parameter in predicting the risk and visceral fat mass. As a rule, an ideal anthropometric measure of abdominal adiposity should predict individual cardiometabolic risk and clearly show effects of different preventative and therapeutic approaches.
Waist-to-hip and waist-to-thigh ratios (WHR and WTR, respectively) were originally proposed as the key determinants of android and gynoid obesity (Krotkiewski et al., 1983;Molarius & Seidell, 1998). WHR has been most commonly used in identifying abdominal fat distribution. Waist circumference alone has received more attention in management of obesity since it requires only one measurement. It showed to be a better predictor of visceral fat volume and related cardiovascular risk profile than WHR (Després et al., 1991;Pouilot et al., 1994;Vissher et al., 2001;Wajchenberg, 2000;Logfren et al., 2004). Moreover, changes in waist circumference better reflect changes in cardiovascular risk factors. It is widely accepted as a surrogat marker of abdominal fat. On the other hand, waist circumference has been criticized for measuring both visceral and subcutaneous adipose tissues (Molarius & Seidell, 1998). Other studies suggest waist-to-height ratio (WHTR) as the better marker because it correlates highly with cardiometabolic risk factors (Hsieh & Yoshinaga, 1995;Ashwell, 2005). Conicity index, which is based on cylindrical shape of the body, has also been introduced as a potentially useful measure of abdominal adiposity (Valdez, 1991). However, it is considered to be very complex because it requires calculations from several different anhropometric values (Molarius & Seidell, 1998).
Sagittal abdominal diameter (SAD), or abdominal height was first demonstrated by Kvist et al. (1988) to be a good correlate of visceral adipose tissue volume, observed by CT. Sjöstrom et al. (1994) proposed the use of sagittal abdominal diameter in the assessment of visceral fat mass. Soon after, Richelsen and Pedersen (1995) confirmed its value in assessing the abdominal fatness and prediction of the metabolic risk profile.

Sagittal abdominal diameter -Visceral fat measure and cardiovascular risk predictor
First measures of SAD were done on CT images and showed good predictive values in the assessment of visceral adipose tissue volume (Kvist et al., 1988). SAD, thus, may be a reliable represent of the visceral fat size. Moreover, two recent studies confirmed that SAD was a stronger predictor of metabolic syndrome than the whole visceral fat area (Valsamakis et al., 2008;Hoenig, 2010), which could pointed to functionally different adipose tissue in the midline.
External, anthropometric measurement of SAD is usually done using Holtain-Kahn abdominal caliper, at the level of the iliac crest, which approximates to the L 4 -L 5 interspace ( Figure 1). Since it has been proposed, SAD has been considered as more closely related to visceral fat mass than the other anthropometric measures beacuse it is measured in a supine position, when a subcutaneous fat is moved to the sides of the waist (van der Kooy et al., 1993;Mukunddem-Petersen, 2006;Sampaio et al., 2007). Measuring SAD in that position reflects the width of intraabdominal fat in the antero-posterior plane, like on CT or MRI images. At the same value of SAD, an increase of waist circumference may reflect increase of subcutaneous adipose tissue size.
Many studies confirmed strong association between anthropometrically assessed SAD and visceral adipose tissue area. Anjana et al. (2004), Sampaio et al. (2007) and Yim et al. (2010) www.intechopen.com reported stronger correlation between SAD and visceral fat area, comparing to waist circumference. Zamboni et al. (1998) found better association between SAD and visceral fat area in lean and moderately overweight subjects than in the obese. Regarding to gender, some studies have found better correlation in men, ranged between 0.61 and 0.82 (van der Kooy et al., 1993;Zamboni et al., 1998), while others have reported stronger relationship in women, with the range between 0.52 and 0.87 (Pouilot et al., 1994, Sampaio et al., 2007. Some studies demonstrated that SAD is a better predictor of visceral fat than waist circumference in men (Després et al., 1991;van der Kooy et al., 1993), while others gave opposite results in women (Sampaio et al., 2007). In the MRI study, van der Kooy et al. (1993) showed that SAD was superior to waist circumference and WHR in assessing visceral fat mass changes in men, while waist circumference and WHR were better measures in women. Comparing to other anthropometric measures, like waist circumference or WHR, SAD has been showed to have better correlation with biochemical and hemodynamic parameters associated with cardiovascular diseases and metabolic syndrome in both, lean and obese subjects: • Higher values of SAD correlate with atherogenic lipid profile including elevated triglycerides, reduced HDL-cholesterol, elevated apolipoprotein B levels, and atherogenic lipoprotein subfractions (Pouilot et al., 1994;Sjöstrom, 1994;Richelsen & Pedersen, 1995;Öhrvall et al., 2000;Turcato et al., 2000;Sampaio et al., 2007;Petersson et al., 2007;Nakata et al., 2010). • SAD is an important factor in prediction of glucose intolerance and insulin resistance (Pouliot et al., 1994;Öhrvall et al., 2000;Gustat et al., 2000;Risérus et al., 2004;Mazzali et al., 2006;Vasques et al., 2009a). Risérus et al. (2004) found that SAD was a strong predictor of hyperproinsulinemia, higher values of C-peptide and lower levels of insulin-like growth factor (IGF) binding protein-1. • SAD highly correlates with inflammatory and prothrombotic markers, like CRP (Mazzali et al., 2006;Petersson et al. 2007;Nakata et al., 2010) or PAI-1 (Öhrvall et al., 2000). According to Petersson et al. (2007), every one-centimetre increase in SAD is followed by an increase of C-reactive protein (CRP) by 0.41 mg/L. The same authors SAD Visceral adipose tissue Subcutaneous adipose tissue www.intechopen.com suggested that SAD may carry information concerning inflammatory status and possibly insulin resistance beyond that of other measures of obesity and fat distribution.
• SAD is associated with blood pressure and predicts hypertension (Öhrvall et al., 2000;Strazzulo et al., 2001). Gustat et al. (2000) highlight that SAD can predict blood pressure when other measures cannot.
Our previous results showed significantly higher values of SAD in obese women who displayed lipid and lipoprotein disturbances and hyperinsulinemia, comparing to healthy normal-weight women . According to our unpublished results (a group of 1090 men and 1231 women of different BMI-values, aged 18-79 years), SAD showed a significant correlation with sistolic and diastolic blood pressure and glycaemia in both genders, and with total cholesterol and triglycerides in men. In both, men and women, SAD showed best correlation with diastolic blood pressure (men: r=0.340, women:r=0.198). By discriminative analysis we determined range of SAD that correspond with lowest risk (men: 20.12-24.97 cm; women: 19.85-24.75 cm), while extremely high values were in the following ranges: 32.58-34.65 cm (men) and 29.87-31.80 cm (women).
In the large longitudinal study, Iribarren et al. (2006) confirmed utility of SAD in prediction of cardiovascular risk, independently of body mass index. Reed et al. (2003) found association between SAD and carotid artery intima-media thickness. Empana et al. (2004) established that age-adjusted risk of sudden death increases linearly with SAD increasement in both, normal-weight and overweight men. SAD has been shown to be an independent risk factor for death and morbidity in patients in the intensive care unit (Paolini et al., 2010).
There are also two indexes derived from SAD: • SAD-to-body height ratio (SAD/H) has been showed as slightly better predictor than SAD alone. Kumlin et al. (1997) reported that SAD/H is a strong predictor of Framingham coronary risk score. • SAD to mid-thigh circumference ratio, or abdominal diameter index (ADI), has been proposed by Kahn (1993) as even better predictor of cardiovascular risk, which was confirmed by Smith et al. (2005).

Application of sagittal abdominal diameter in elderly
Aging process is characterized by body composition changes that could not be captured by standard anthropometric measures like BMI. Increasing of total body fat occurs in both genders, which is followed by decreasing of muscle mass (sarcopenic obesity) and body fat redistribution in terms of changes from peripheral to central (abdominal) pattern (Prentice & Jebb, 2001;Greenlund & Nair, 2003;Davidson & Getz, 2004). In women, menopause plays important role in transitioning from a premenopausal gynoid (gluteo-femoral) to a postmenopausal central (visceral) pattern of body fat distribution and increase in total body fat (Movsesyan et al., 2003). Even in early menopause women have a 49% greater visceral fat mass comparing with premenopausal women (Toth et al., 2000). Together with other physiological and life style changes caused by aging, age-associated central fat distribution contributes to cardiovascular morbidity and mortality. That is why is highly recommended to assess central adiposity in older persons (Dorner & Rieder, 2011).
Some evidences pointed to better predictive value of SAD in younger individuals (Iribarren et al., 2006, Mukuddem-Petersen et al., 2004. However, SAD could be also very useful indicator in the elderly. According to Turcato et al. (2000), SAD and waist circumference are the anthropometric parameters which are the most closely related to cardiovascular risk factors in women and men aged from 67 to 78 years, independently of BMI. Harris et al. (2000) and Snijder et al. (2002) found that SAD was even better predictor of visceral fat area in subjects older than 70 years, comparing to waist circumference, while Mukuddem-Petersen et al. (2004) indicated that SAD had no advantages over simpler and more commonly used anthropometric measures such as waist circumference, regarding to their associations with components of the metabolic syndrome in older subjects.

Gender and ethnic specific usage of sagittal abdominal diameter
Men and women have different adipose tissue topography. Fat deposition is gluteo-femoral region is more typical for women, while men show preferential abdominal fat accumulation. Within abdominal region, visceral fat compartment is more predominant in men, while women have higher size of subcutaneous fat compartment (Anjana et al., 2004). Men and women also have different dynamics of losing visceral and subcutaneous fat during weight loss -men lose more visceral, and women lose more subcutaneous fat (van der Kooy et al., 1993).
It is assumed that SAD has a stronger capacity to predict visceral fat area, insulin resistance, and cardiometabolic risk in men, because they have higher visceral fat mass (Risérus et al., 2004). Vasques et al. (2009b)  Some ethnic groups show different pattern of body fat distribution and different susceptibility to insulin resistance. For example, Asian Indians have greater abdominal fat mass than Europeans of the same nutrition level (Anjana et al., 2004), while middle-aged and older African-American men and women have lower visceral fat than Hispanic and white men and women (Carroll et al., 2008). There are race and ethnical differences in the relationship between body fat distribution and health risk factors; thus, anthropometric measures could differ regarding the predictive capacity of cardiovascular risk factors. However, according to the results of several studies, SAD seems to be an excellent marker of metabolic and cardiovascular risk factors, irrespectively of national origin or ethnic background (Hwu et al., 2003;Valsamakis et al., 2004;Petersson et al., 2007, Iribarren et al., 2006.

Treshold values for sagittal abdominal diameter -Reflection of critical visceral fat mass or cardiometabolic risk
In spite of many evidences that SAD is very good in capturing the cardiometabolic risk, its use in clinical practice is limited due to a lack of specific cut-offs. Some authors have www.intechopen.com proposed cut-off values for SAD using different criteria, usually its correlation with cardiometabolic parameters and visceral fat area (Table 1). These results were mostly obtained using Receiver Operating Characteristics (ROC) curves, or linear regression analysis, and vary from 19.3 cm (Sampaio et al., 2007) to 27.6 cm (Valsamakis et al., 2004). Our results were obtained using the principles of rough set theory that will be described below. They were derived from evaluation of relationship between SAD and cardiovascular risk factors.
We produced "transparent", semantic model which can be easily analyzed. The most important information which can be extracted from semantic models is concerned with the meaning and importance of its elements, as well as with the relations between them. Data were represented in the form of a table with rows containing the objects and columns containing the attributes, and model was produced in the multiple sets containing If -Then rules.

Model for the better applicability of SAD in identifying patients at higher cardiovascular risk
Modern healthcare and computer science are fields that are interlaced to form the field of medical informatics. As mentioned by Øhrn (1999), Blois and Shortliffe define medical informatics as "the rapidly developing scientific field that deals with the storage, retrieval and optimal use of biomedical information, data, and knowledge for problem solving and decision making." In its broadest sense, medical informatics can be said to concern itself with the management of information in the context of modern healthcare. According to Øhrn (1999) current research in the field of medical informatics covers a wide array of topics, including: • Obviously, as a main prerequisite there is a existence of medical dataset or database. Medical datasets are often described as incomplete, sparse, vague, fuzzy, etc. According to Greco et al. (1998), the rough sets theory has often proved to be an excellent mathematical tool for the analysis of a vague description of objects.
On the base of the table-organized data it is possible to produce semantic model which provides information about meaning and importance of its elements, as well as the relationship between them (Brtka et al., 2008;Stokić et al., 2010). In order to investigate relationship between SAD and anthropometric and cardiovascular risk factors, we used methodology based on rough set theory (Pawlak et al, 1995, Pawlak & Skowron, 2007 applied to table-organized data with producing decision rules in the If -Then form. Our study included 1334 subjects (700 women and 634 men), aged 43.49±10.43 years. Following parameters were analyzed: age (years), body mass index (kg/m 2 ), SAD (cm), body fat mass (%), systolic and diastolic blood pressure (mmHg), total-, LDL-and HDLcholesterol (mmol/L), triglycerides (mmol/L), fasting plasma glucose (mmol/L), fibrinogen (g/L), uric acid (μmol/L), and 10-year Framingham Risk Score. The experiments were conducted by software system Rosetta -A Rough Set Toolkit for Analysis of Data. All numerical attributes were discretized using a simple "equal frequency binning" technique. The attribute SAD was chosen to be the decision attribute while all remaining attributes were chosen to form the set of condition attributes and the set of rules containing rules in the If -Then form was generated. The decision attributes (SAD) were classified into three classes: • 13.00-24.2 cm, • 24.3-31.6 cm and • 31.7-36.2 cm.

Rough-set theory principles
As the mathematical basis of the rough set theory there is the indiscernibility relation. Every object of the universe is described by certain amount of information expressed by means of some attributes used for that object description. The objects characterized by the same information are indiscernible in view of the available information about them.
As in Greco et al. (1998), Øhrn (1999) and Pawlak & Skowron (2007), let U be a universe (finite set of objects), Q={q 1 ,q 2 ,...,q m } is a finite set of attributes, V q is the domain of attribute q (attribute values) and V is the union of V q for every q∈Q. An information system is the 4tuple S=(U,Q,V,f) where f is a function such that f(x,q)∈V q for each q∈Q, x∈U, called information function.
Let x,y∈U (x and y are two objects e.g. patients), f is an information function and q∈Q. Every non-empty subset of attributes P determines an indiscernibility relation on U, denoted by The I P is an equivalence relation. The family of all the equivalence classes of the I P is denoted by U/I P and the equivalence class containing an element x by I P (x).
Let us consider a simple example of an information system based on the example from Greco et al. (1998), see Table 2.  Table 2. Simple example of an information system

Object
In the given table, there is a universe of six objects U={x 1 ,...,x 6 } and each object is described by means of four attributes: Age, Body Mass, Systolic Blood Pressure (SBP) and SAD.

The definition of the rough set
The rough set theory proved to be an excellent mathematical tool for the analysis of data in various domains. The information about the real world is given in a form of a decision system. The next definitions are based on Pawlak et al. (1995), Greco et al. (1998), Øhrn (1999) and Pawlak & Skowron (2007).

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Let C⊂Q and D⊂Q so that C∩D=∅, where Q is a set of attributes. The attributes from C are called the condition attributes and the attributes from D are called the decision attributes.
An information system where the set of condition attributes and the set of decision attributes are defined is called the decision system.
In most cases there is usually one binary decision attribute, while the other attributes are the condition attributes. In the previous example P might be the set of the condition attributes, and the set of decision attributes contains one element: D={SAD}.
Let X be a non-empty subset of U and ∅ ≠ P ⊆ Q. The set X is approximated by means of P-lower (2) and P-upper (3) approximations of X: The P-boundary region Bn(X) of X is defined by: For example, let us consider a case when the set X contains only those elements where the value of the decision attribute SAD is low: X={x 1 ,x 3 ,x 6 } (Table 2). Now, we can approximate the set X using only the information contained in P by constructing the P-lower (2) and Pupper (3) approximations of X: The P-boundary region (4) of X is: The reader may notice that the objects x 2 and x 3 have exactly the same values of the condition attributes but different value of the decision attribute. So, they constitute boundary region. We can say that the rough sets can be defined as follows (Pawlak et al., 1995;Pawlak & Skowron, 2007): The set X is rough (inexact) with respect to I P , if the boundary region of X is nonempty. The set X is crisp (exact) with respect to I P , if the boundary region of X is empty.

Data reduction
If we manage to identify equivalence classes then some savings (reductions) are to be made since only one element of the equivalence class is needed to represent the entire equivalence class. An issue of practical importance in reduction is to keep only those attributes that preserve the indiscernibility relation and consequently, the set approximation. The rejected attributes are redundant (superfluous) since their removal cannot worsen the classification (Greco et al., 1998). The calculation of all reducts is very complex but in many practical applications it is not necessary to calculate all the reducts, but only some of them.

Discretization
If we want numerical attributes to be properly incorporated into the classification rules, we should to discretize them. This enables the numerical attributes to be treated as categorical ones, and several algorithms for this purpose are available (Greco et al., 1998;Øhrn, 1999). The goal of the discretization process is to search for intervals or bins, where all cases that fall within the same interval are grouped together. This process can be also seen as the process of classification of the attributes' value set to some classes. The discretization is not specific to the rough set approach but is a pre -required step and is often performed implicitly, behind the scene, using human expert knowledge.

Decision rules
The expression a = v, where a is an attribute and v is an attribute value is called the descriptor. Now, it is possible to investigate the rules of the form: If Then . Here denotes a conjunction (AND logical operator) of descriptors that only involve attributes of some reduct (rule's antecedent) and (rule's consequent) denote a descriptor d = v, where d is a decision attribute and v is the allowed decision value.
For example, if we use the reduct R={Age, BM} from Table 2 and SAD as a decision attribute, then it is possible to generate the rules with two descriptors in the antecedent part and one descriptor in the consequent part of the rule. It is important to notice that a shorter reduct set means shorter decision rules in the rule set generated from that reduct.

Application of rough-set theory in identification of patients at higher cardiovascular risk using SAD
Our results showed that SAD could be a clinically useful marker for identification of combination and structure of risk factors by applying different rules in individuals of different BMI-categories.
Lower values of SAD in normal-weight individuals younger than 50 years always corresponded with Framingham risk score <9. However, in normal-weight subjects older than 50 years, SAD couldn't identify those at lower risk. SAD values between 24.3 and 31.6 cm, or even lower, between 13.0 and 24.2 cm, corresponded with Framingham risk score between 9 and 14 (  Table 3. Obtained rules for normal-weight subjects (BMI<26.43 kg/m 2 ) By examining the decision rules, SAD could point out a group of overweight patients with high level of visceral fat with different combination and composition of cardiovascular risk factors (Table 4). Thus, in overweight individuals aged 41-50 years, with higher fat mass, and SAD between 24.3 and 31.6 cm, we could expect higher values of diastolic blood pressure, total-and LDL-cholesterol, triglycerides, uric acid, as well as Framingham risk score over 14. The same range of SAD in older overweight individuals (>50 years) with higher fat mass, include higher systolic blood pressure, fasting plasma glucose and fibrinogen. On the other side, in younger overweight subjects with lower SAD (<24.3 cm) we could expect lower values of all atherogenic parameters, higher values of HDL-cholesterol and Framingham risk score <9, even if they have higher fat mass.
It means that SAD could identify metabolically healthy overweight individuals.

Conclusion
Many studies have proved that SAD is a good predictor of abdominal, especially visceral, fat mass, as well as of cardiometabolic risk. Several authors have suggested specific cut-off values for SAD that corresponded with cardiovascular and metabolic risk or with visceral www.intechopen.com fat area obtained by CT. Using the concept of a rough set, proved as a formal tool for modeling and processing information systems, we developed a useful model for identification of individuals with multiple cardiovascular risk factors using SAD.
Our results revealed connection between SAD and cardiovascular risk factors which showed dependence on age and nutrition level. We primarily recommend application of SAD in the assessment of the cardiovascular risk in overweight and obese individuals. SAD values ≥24.3 cm in overweight and obese subjects older than 41 years should correspond to increased risk, while values <24.3 cm in overweight subjects younger than 41 years could point to healthy metabolic profile.