**5. Novel findings in medical research and implications for an anthropometrically correct MI/CVD risk assessment**

It is well known BMI depends on weight and it strongly depends on metabolically healthy musculoskeletal components and body fat mass, especially subcutaneous, without discriminating the unhealthy intra-abdominal fat and their volume [2, 14, 23, 24, 37, 48]. Why to choose BMI to assess MI/CVD risk if it captures metabolically contradictory components? The consequence of this chimera is that to describe individuals' risks based on BMI is unfounded and potentially misleading. Accordingly, the concepts of ideal anthropometric health and BMI-classified obesity should not be considered synonymous or interchangeable, unless we accept misclassification and paradoxical information for biological risk assessment. BMI fails to discriminate between harmful body fat and healthy components and is an inappropriate formula to assess the association between excess fat mass and MI/CVD. Besides, while a part of the musculoskeletal component (mesomorphy) may be associated with MI, as %BF increases, a part of the association for BMI would capture a false risk and, therefore, information bias would occur for the true high risk BC in both sexes. The excessive body weight in individuals who have a high BMI and normal %BF (e.g., individuals/ athletes with high mesomorphy rating) would indicate a score of spurious risk, but

*Anthropometrics in Predicting Cardiovascular Disease Risk: Our Research Work Mathematically… DOI: http://dx.doi.org/10.5772/intechopen.105098*

never performing better than WC [24, 27, 37]. With respect to WHR, it is well known that it has demonstrated the highest predictive abilities for MI risk [4, 13, 17–21, 23]. Nevertheless, WHR may present bias with respect to WC when the risk assignment for both does not refer to the same risk, therefore reducing the quality of the comparison [24, 36, 37].

It is noteworthy that WC and HC only may coincide at the same estimation of risk when WC takes the same value as HC (WHR =1; X = 0, see **Figure 1**). Any WHR value of <1 (X > 0) demonstrates no cardiometabolic risk beyond that of WC alone or X. WHR as a proper fraction (<1) will never represent the entity of risk, and any risk-code selected for WHR between their risk cut-off values of <1 and 0.999 will be biased if WC or X receives no risk-code. There would only be a true risk for WHR with respect to WC when WC or X predicts the true risk from their defined risk cut-offs. If not, WHR may select true-negative values as false-positive ones when they merely represent protective overestimation for HC concerning WC and X.

Mathematically, between any WHR risk cut-off <1 (e.g., 0.95) and 0.999, we could always find different individuals and an infinite number of proper fractions whose decimal values receive a risk-code, but that do not refer to the same high risk BC as measured from the WC or X risk cut-off. This discovery arises from rigorous data analysis in the measurements for WC and HC, and where misclassification occurs for WHR-associated risk [23, 24, 36, 37]. As an example, 93.1/98 vs. 93.9/98 vs. 95/100, etc., =0.95: X between 5 and 4.1; 93/95.9 vs. 94.1/96.9 vs. 98/100.9, etc., =0.97: X between 3 and 2.1; 93.8/93.9 vs. 94.2/95 vs. 99/100 etc., =0.99: X between 1 and 0.1. Broadly, there would be five values for WHR between 0.95 and 0.99, and infinite fractions for values of X between 5 and 0.1; HC > WC in all and a WC risk cut-off ≥94.4 in each set. Equal values for WHR (e.g., between 0.82 and 0.999; X between 18 and 0.1) may be transferred to broader populations where the mean values for WC and HC were higher or lower than in the example. In any situation, WC and X values that depend on their own risk cut-offs would reflect different risk-codes in each fraction while WHR would support a unique value for the risk, but any mean value of WHR <1 precludes the same estimation of risk for WC and HC (HC ≠ WC), making the validity of WHR beyond that of WC alone anthropometrically impossible. These observations may help to explain a higher bias for WHR in predicting MI/CVD risk in women because the X positive value is always higher in women than in men. In fact, HC > WC at the baseline involves a positive X value, and the higher the X value, the higher the bias occurs by selecting a higher number of proper fractions and false-positives, so that the protective effect for HC would always be overestimated. Similarly, a higher bias for WHR would occur when the WC is taken at the minimum level vs. the maximum (e.g., at the umbilicus) due to a longer range between the lowest and 0.999 value (see **Figure 1**). "From a proper abstract fraction, if WHR risk cut-off is of <1 all WHR-associated risk above WC as being mathematically incorrect and anthropometrically unjustified provides epidemiological false inferences" [37].

In another mathematical consideration, our research has also revealed that WHR and WHtR contrast by suggesting the same true risk if HC and height present a relationship of height/HC =2. This ratio would occur if and only if WHR/WHtR = 2 (e.g., 0.90/0.45, 0.95/0.475, 1/0.5, 1.2/0.6 etc., HC = height/2 in all). This also appears anthropologically unlikely and selection bias occurred for WHR with respect to WHtR due to the protective overestimation for HC regarding height [23, 37].

As mentioned above, WC and WHtR may only be comparable if the equivalent relationship between WC and height refers to same estimation of risk for both (WC = height/2: WHtR risk cut-off =0.5). If not, between 0.51 and any WHtR

risk cut-off up to 1 (e.g., >0.55), we could always find different individuals and an infinite number of fractions receiving the same binary code for WHtR (no risk), but not referring to the same risk-code from the WC risk cut-off (see **Figure 3**). As an example, 82.8/162.4 vs. 88.6/174 vs. 80.6/158 vs. 95.4/187 etc., =0.51; 95.2/178.2 vs. 90/168 vs. 83/156, etc., =0.53; 96.7/178 vs. 92.5/168.2 vs. 98.8/179.6, etc., =0.55. Broadly, there would be no risk-code for WHtR ≤0.55 when the WC represents different risk-codes if their risk cut-offs were > 84 or > 95 on each set, and WC > height/2 in all. Thereby, the higher the WHtR, the higher the risk overestimation for WC occurs by selecting false-positive points as compared to those true-negatives below the WHtR risk cut-off. Equal values for WHtR (e.g., between 0.51 and 0.65) may be transferred to other populations where the mean values for WC and height were higher or lower than in the example. In any situation, WC values depending on their own risk cut-off would reflect different risk-codes into each fraction while WHtR would support a unique, continuous code (no risk) up to their own risk cut-off value. Hence, WC might present bias with respect to WHtR when the risk for both metrics does not refer to the same high risk BC, when compared either in men or in women. Thus, WC might capture risk if there are no differences in height between healthy and unhealthy cases (WHtR risk cut-off close to 0.5). In contrast, the risk captured from WC would be not equivalent when the mean height (WHtR risk cut-off much higher than 0.5) determines a significantly higher relative volume in cases, and therefore a different high risk BC when compared to healthy people (see **Figures 2** and **3**). Regarding this observation, the risk association for WC and WHtR will be equivalent if, and only if, the WHtR risk cut-off is very close to 0.5, but any value >0.5 precludes the same estimation of risk for WC and height (WC ≠ height/2), making the validity of WC alone beyond that of WHtR anthropometrically impossible. Thereby, "when WHtR risk cut-off is of >0.5 and <1 all WC-associated risk above WHtR … provides epidemiological false inferences" [37].

In another sense, a different cardiometabolic effect among visceral and extraabdominal fat has been argued when using WC to measure the total abdominal adipose tissue. However, there is evidence that the higher the intra-abdominal fat, the higher the WC value, irrespective of subcutaneous extra-abdominal fat [13–15, 22]. From the Framingham study, visceral fat has been strongly associated with a metabolic risk profile and MI in both sexes and technological studies have also observed that the ratio visceral fat/subcutaneous extra-abdominal fat presented a direct association with MI while subcutaneous area presented the inverse [12, 14, 16, 22, 37, 50]. The anthropometric explanation would be because, as intra-abdominal fat increases, subcutaneous adipose tissue of the extra-abdominal space suffers the mechanical effect of compression, which decreases their relative thickness and volume (tight fat) [37]. Moreover, it is noteworthy that %BF measured by DEXA strongly depends on WC and height rather than BMI in adult individuals [45]. In addition, MI men present high mesomorphy and low ectomorphy ratings, and %BF is more strongly correlated with WHtR than it is with WC (intra-abdominal + subcutaneous area). Therefore, WC does not necessarily refer to risk for an accurate comparison but considering it for a higher relative volume by unit of height, closely linked to a low ectomorphy [10, 24, 27, 31, 48]. Thereby, sophisticated volumetric imaging methods have demonstrated differences in the association of visceral and subcutaneous fat with an adverse metabolic risk profile in both sexes [50].

A novel insight in research, for the first time we have used a propensity score method to address selection biases in balancing the distribution of covariates between anthropometrically healthy subjects and MI cases [36]. It is well known in

#### *Anthropometrics in Predicting Cardiovascular Disease Risk: Our Research Work Mathematically… DOI: http://dx.doi.org/10.5772/intechopen.105098*

observational studies, treatment (or exposure) selection is often influenced by subject characteristics [51–53]. As a result, baseline characteristics of treated (or exposed) subjects often differ systematically from those of untreated (or unexposed) subjects. Therefore, one must account for systematic differences in baseline characteristics between treated and untreated (exposed or unexposed) subjects when estimating the effect of treatment (or exposure) on outcomes [53]. Based on our idea of how to reduce the effects of confounding in non-randomised anthropometric studies, we have applied the cited method. Thus, the conditional distribution of risk between groups (healthy and unhealthy cases) should be the same when observed baseline characteristics do not present standardised differences [37, 53]. Thereby, similar baseline characteristics for WHR and WC may provide bias in outcomes of both, if the risk assignment in both does not account for the covariates that predict the receiving true risk, WC as numerator and WHtR as measure volume, respectively. In this sense, as a result, risk assignment for WHR and WC may be systematically biased if values between WC, HC, height/2 and height show no balanced distribution and, therefore, the concerned metrics may not be directly comparable (see **Figure 3** and **Table 1**). Consequently, if the mathematical equivalence between covariates and propensity scores for metrics is not explored, it will be impossible to ensure a balanced distribution of risk between anthropometrics and groups. In agreement with the stratification method, all subjects who have (nearly) similar baseline characteristics and, therefore, similar propensity scores would have the same probability (nonzero) to receive a riskcode, making the risk assignment strongly ignorable [53]. Comparing the similarity of healthy and unhealthy cases in the same strata should begin with a comparison of the means or medians of the simple covariates and the distribution of their categorical counterparts between groups. If, after conditioning on the simple measurements, there remain systematic differences between means or medians, this would be an indication that the propensity score model has not been correctly specified for unbalancing the distribution of the measurements and the risk assignment. Thus, from our research, we have anthropometrically and mathematically demonstrated an association bias of WHR for unbalancing HC with respect to WC and height values in MI men [36, 37]. Besides, results from other larger studies [4–9, 14–22, 28–30, 32–35, 38–44] may be transferred to our analysis as appropriate. In revealing inequality between the simple measurements and risk cut-offs for metrics, our conclusions are not coincidental due to identifying biases and checking the lack of external validity. In brief, we have demonstrated association biases that are extendible to all previous studies and we have proposed the premises to avoid it.

## **6. Discussion**

The anthropometric robustness of BMI and WHR as a link to the true risk of the BC and MI/CVD is unclear and diffuse. Conceptually, each of these provides its own meaning without a verifiable associated risk beyond that of WC. Nevertheless, only a rigorous interpretation removing bias could avoid confusing or paradoxical information, independently focused on the number of lifestyle factors and other established risk factors that influence ideal cardiovascular health [11].

It is well known that BMI has significant association with MI in both sexes, but not the best, and unimportant differences were found when compared by sex [4, 17–19, 21]. From the UK Biobank results, the ratio of women-to-men's hazard ratios for incident MI for the comparison between BMI and WC demonstrated a higher hazard ratio of

association for WC in women, and no difference in men. Only WC and WHR, but not BMI and WHtR, were significantly associated with the risk of MI in women compared to men. Moreover, measures of central adiposity, particularly WHR as compared to BMI, showed a higher hazard ratio in women than in men [21]. However, when exploring the association between anthropometrics and obesity, novel findings have explained the reasons why both BMI and WHR are not optimal indicators in predicting MI risk, at least in men [23, 24, 27]. Thereby, it can be reasonably assumed that, since the musculoskeletal component may be artificially or indirectly associated to MI, BMI fails to reveal the true high risk BC by underestimating visceral fat volume and overestimating risk from the mesomorphy component. Thus, in two individuals with mesomorphy dominant and different high risk BC, the same BMI would underestimate the higher body fat volume in one of them. This observation means that BMI has the importance of producing a greater impact and bias in men due to it capturing a dimension of spurious risk beyond that of women. On this basis, from the UK Biobank, the comparison between BMI and WC by sex presented bias. This is because both metrics cannot refer to the same high risk BC when comparing men and women, and WC without accounting for the whole-risk (a 1-SD WHtR was >0.5 and < 1 in both sexes) [21, 37].

To our knowledge, body weight and HC have showed low predictive ability for MI and never justifying true biological plausibility for the risk. On the other hand, height and ectomorphy has been inversely associated to MI with a higher relative risk, although not necessarily referring to a causal relationship [10, 23, 24, 31, 48]. It is clear then that WC would be the only one among the simple measurements for reflecting both the cardiometabolic risk and the highest association discriminative for MI in both sexes [4, 7, 9, 12–21, 23, 24]. Besides, as %BF increases in vivo, the body fat storage is homogeneously distributed and WC, rather than BMI, becomes the best clinical expression of a body fat volume increase. Nevertheless, compound indexes such as WHR, conicity and WHtR have always captured a higher dimension of risk [4, 7, 9, 12, 16–19, 21, 23, 24, 27].

Surprisingly, most studies predicting MI/CVD risk always used a WHR cut-off <1 and/0r WHR/WHtR <2 in both sexes and different ethnicities while selection biases were never discussed [4, 5, 7, 13, 15, 17–19, 21, 28–30, 32, 35, 38–44, 54]. Why, when WHR <1, has the causal relationship between HC and adverse MI/CVD outcomes not clearly been elucidated? From the INTERHEART study [4], the median WHR in the overall population was 0.93 in cases and 0.91 in controls with a significant difference between both values, and therefore for the X distance, so the risk comparison was done without balancing between HC and WC. Besides, WC was obtained at the narrowest point (the longest X distance), and WHtR as entity of risk was not explored. On the other hand, the follow-up in the CONOR study [17] found, for WHR and WC, an association stronger in women and middle-aged than in men and elderly participants, respectively. However, the higher value of X for middle-aged (X = 21) and elderly women (X = 18) with respect to male counterparts (X = 11 and 8, respectively) was not kept in mind, and therefore, biases occurred with respect to WC and X in the risk comparison for unbalancing the mean HC and WC. Additionally, WC would appear to be found with classification bias for the risk in women compared to men if height was not accounted for in the data analysis and WHtR as an entity of risk was not well compared. Similarly, from the UK Biobank study [21], a 1-SD WHR was significantly associated with a higher hazard ratio of MI in women than in men, and with a corresponding women-to-men ratio of hazard ratios of 1.15. Nevertheless, the mean (SD) of WHR was <1 in both sexes (0.82: X = 18 in women, 0.93: X = 7 in men), so the false premise accepted in the risk assignment up to 0.999 value provided

#### *Anthropometrics in Predicting Cardiovascular Disease Risk: Our Research Work Mathematically… DOI: http://dx.doi.org/10.5772/intechopen.105098*

a selection bias for WHR when compared to WC or X. Thereby, having a baseline characteristic of WHR <1 either in healthy population or in cases, a different high risk BC as measured by WC and X will provide a higher WHR-associated risk due to the protective overestimation for HC where equal numbers of WHR <1 predict false-positives when accounting for an imbalance of the mean HC and WC or X. Besides, in data distribution and hazard ratios, WHR in the top was always <1 when WHtR in the bottom was >0.45–0.5 and < 1 in both sexes (WHR/WHtR <2), so the risk comparison between both indices was biased and demonstrated a protective overestimation for HC concerning height. Additionally, the strength of association for WC was significantly higher in women than in men while the hazard ratio for WHtR was similar in both sexes (1.34 in women, 1.33 in men). By deduction, height differences were higher in men than in women in occurring similar risk assignments for WC and WHtR in women (hazard ratio of 1.35 and 1.34, respectively), but not in men (hazard ratio of 1.28 and 1.33, respectively). This is because the mean WC and height demonstrated a different relationship, and WC and WHtR was not compared for the same risk [37]. Indeed, the mean (SD) of WHtR at the baseline in women (0.52 ± 0.1) was closer to 0.5 than that of men (0.55 ± 0.1) [21]. This means that, in the stratum between 0.5 and 0.52, WC and WHtR captured a similar dimension of risk in women due to a lower probability of selecting false-positives, while in a higher range up to 0.55, only WHtR captured the highest risk, as it happened in men. Thereby, height differences between women and men involve less chance of bias for WC in women when compared to WHtR, and WHtR more accurately predicts risk in men than WC [21]. By contrast, in the follow up of a Swedish cohort, WC presented less statistical significance for a recurrent MI in the female group [38]. However, the risk the WHtR measured was not explored and, therefore the risk comparison between sexes could not be referred to the same high risk BC and relative volume.

On the other hand, since short-stature has been associated with MI, the WC associated risk that is geometrically-derived from a two-dimensional area will be overestimated in taller individuals with respect to shorter people, including sex differences. In contrast, WHtR has the importance of corresponding to a relative volume where intra-abdominal risk components occupy all the space except for small peripheralsubcutaneous area, which is less deleterious [24, 37, 46, 47]. Unequivocally, WHtR gives us a relative risk volume and the higher the WHtR, the higher the risk. Besides, WHtR yields no bias with respect to others and it may capture a dimension of risk above WC. Obviously, this only happens when WHtR risk cut-off moves too far towards an excess of 0.5, as proven in men [21, 23, 24, 27]. It is also anthropometrically and mathematically demonstrable in most studies (**Table 1**).

In another consideration, some studies have signed a trend towards higher risk of MI as HC decreased (narrow hip) in a relationship with sarcopenia and deficiencies in physical activity [4, 19]. However, despite different values of HC either in the UK, Sweden, Norway, Spain or even in infarcted populations worldwide, studies have always found a WHR risk cut-off <1 and HC never takes the same value as WC [4, 18–21, 23]. On the other hand, HC-adjusted WC has demonstrated the strongest association with coronary disease and cardiovascular mortality [41–44, 53]. Nevertheless, by entering both WC and HC as independent markers of future CVD risk, the causal association for HC-adjusted WC in analytic models also appears to be wrong due to selection bias for the risk. The key lies in the discriminatory risk cut-offs for WC and HC, which reflect different sensitivity and specificity as well as different coherence and biological plausibility from each one. When using HC-adjusted WC, whether considering HC as a protective factor in a WHR risk cut-off of <1 (mean

HC > WC: X > 0) [39–42, 53], this argument becomes a false premise, because we will always find points of spurious risk in any WHR-associated risk above the WC, and therefore draw false conclusions for causation. It would occur even when X values are 0.1: WHR =0.999 (**Figures 1** and **3**). Hence, anthropometric risk evaluation is not subsumable by combining WC and HC data at the same level of equality (WC = HC instead of HC = WC + X), either for WHR <1 or HC-adjusted WC. That way, the paired comparison of two different biological factors would adulterate the associated joint risk and the real effect of HC, which takes a protective role falsely assigned. Then (and only then), when WC takes the same value as HC (risk equivalence) there will be the same (x, y) coordinates in the shared point where WC = HC: WHR = 1: X = 0, and, therefore, the same estimation of risk for WC and HC (**Figure 1**). In the same way, noting that anthropometrically healthy women significantly present lower WHR than men (higher X distance), a higher bias for WHR in predicting MI/CVD risk in women may be explained due to a higher selection of abstract fractions and spurious risk points where HC does not account for the same estimation of risk as WC. Similarly, higher bias would occur when the WC is taken at the minimum perimeter (both sexes), due to a higher X length (**Figure 1**). In this approach, the higher X value, the higher bias may occur. Thus, a higher HC in middle-aged people, physically active subjects or in women with higher gluteal–femoral fat deposits never justify a protective effect that influence MI/CVD, at least anthropometrically and while balancing the mean values of WC, HC, and X in any correct comparison between healthy and unhealthy cases including sex differences.

To our knowledge, using stratification for matching the selection bias of WHR has been demonstrated in men. This was because the same WHR risk-code (yes) on the same matched fractions between 0.95 and 0.999 always found different risk-codes for WC (yes/not) when conditioned on both WC < HC and WC receiving a true risk above their risk cut-off [36, 37].

In agreement with our observations, the strata between the WHR risk cut-off and 0.999 on the one hand, and from 0.51 up to any other WHtR risk cut-off of >0.5 on the other hand, usually coincide on the overlapping areas of the distributions for WHR and WHtR between healthy populations and MI/CVD cases. Thus, for the same binary code of no risk (true-negatives) between 0.51 and any other WHtR risk cut-off of >0.5, we could find the same WHtR value for different fractions from WC and height. However, WC might produce false-positives above their own risk cut-off if conditioned on WC > height/2 and WHtR received no risk (bias zone for WC as explained above). When unbalancing HC vs. WC and height mean values, or the mean WC vs. height/2 false-positive points for WHR and WC, respectively, might be selected for biasing any associated risk above WHtR. Besides, evidence states that, in any study population, HC and height/2 always present different mean values (HC > height/2: WHR/WHtR <2), so a risk assignment for WHR and WHtR always shows an imbalance for overestimating the protective effect of HC with respect to height, and therefore, comparing different risk [4–10, 14–30, 32–35, 38–40], (**Table 1**).

From a syllogistic approach, whether in any study population WHR (risk cutoff <1) shows a higher magnitude of association than WC (the first false major premise for a causal risk), while the mean HC is higher than WC (the second true minor premise), any WHR-associated risk above WC will occur for unbalancing the distribution of WC and HC as covariates. This fact determines false risk assignment for WHR (association bias) with respect to WC, which induces a false inference as the conclusion for causation. In no case WHR <1 would risk be captured above the WC because HC > WC is a natural inequality associated with a healthy population.

#### *Anthropometrics in Predicting Cardiovascular Disease Risk: Our Research Work Mathematically… DOI: http://dx.doi.org/10.5772/intechopen.105098*

Similarly, a WHtR risk cut-off >0.5 occurs, the WC shows higher magnitude of association than WHtR (the first false major premise for a causal risk) and when the mean WC > height/2 (the second true minor premise), any WC-associated risk beyond that of WHtR will occur for unbalancing the distribution of WC and height/2 as covariates. Thus, WC that captures a false risk (association bias) with respect to WHtR would induce a false inference as the conclusion for causation. In no case can WC alone capture the risk above WHtR because WC < height/2 is a natural inequality associated with an anthropometrically healthy population, and only up to a WHtR risk cut-off =0.5 (mean WC = height/2) would WC and WHtR capture the same risk. With the same premise, if any WHR risk cut-off is lower than that of WHtR × 2, and being the mean HC > height/2, any WHR-associated risk beyond that of the WHtR will occur for unbalancing the distribution of HC and height/2 as covariates, but WHR never captures the risk above WHtR. To clarify this, apply the results of the studies referenced in **Table 1** on **Figure 3** and once the simple measurements and their mathematical inequalities in the standard human body are well known, see **Figure 1**).

As a philosophically and anthropometrically correct reflection, not all subjects are at risk as according to their WHR measurement, and with similar baseline characteristics between their risk cut-off of <1 and 0.999 or twice the WHtR value that refer to the same risk as measured from WC or WHtR risk cut-off, respectively (bias zone for WHR). Similarly, not all subjects at risk according to their WC measurement, and with similar baseline characteristics for WC alone above their risk cut-off refer to the same risk as measured from WHtR between 0.51 and any other real risk cut-off >0.5 (bias zone for WC), (**Figure 3**).

Epidemiologically, while a shorter stature may be significantly associated to cases of MI/CVD (WHtR risk cut-off >0.5) and the mean values of HC higher than both WC and height/2 (WHR <1: WHR/WHtR <2: HC > WC > height/2, see **Table 1**), WHtR will always capture the highest dimension of risk above WC and WHR. This is because WHtR as a three-dimensional volume measure would always capture higher a biological risk than WC as a two-dimensional area. Similarly, when balanced distribution between the simple measurements may be checked and the risk may be conditioned on the real predictive variables (WC or WHtR >0.5 as appropriate) [36, 37], WHtR becomes the gold standard for risk assessment. It is geometrically clear. The same values of risk for WC between different individuals refer to a similar risk from WHtR as relative volume if the mean WC is ≤height/2 (WHtR ≤0.5 and unimportant differences for height), but never occur when individuals present a mean WHtR of >0.5 (significant differences for height). Thus, WHtR should be used as the optimal metric when making an anthropometrically and mathematically correct risk prediction, irrespective of the strength of association for other metrics in different studies. In such studies, a spurious risk might be artificially slanted towards the group of cases in the rest of compared metrics when specifically defined or universally categorised risk cut-offs were used [4–10, 14–30, 32–35, 38–44, 49, 54, 55].

Our demonstrations are a touchstone on the risk associated with WHR and WC from many studies, so universal recommendations made on the issues relating to WHR and WC alone for determining abdominal obesity and substantially increased risk of metabolic complications may turn out to be fallacious or at least have information bias [13, 14, 56]. Validity for both WHR and WC depends on the degree for measuring the risk. However, when having a WHR risk cut-off <1 as an abstract fraction or WC alone as a two-dimensional area, it will be impossible to discriminate the risk and relative volume, unlike WHtR, which is a more faithful measure. Thus, a true description of risk for WHR <1 requires of a categorical syllogism, where the

risk derives from an affirmative proposition for the WC value as a numerator. On the other hand, any association of risk for WC alone above WHtR will be a false conclusion, if the WHtR risk cut-off is of >0.5 and < 1. Since a part of the assigned risk for WHR and WC may be spurious, the conclusion for the risk will be in error due to a fallacious argument. Similarly, the assumption of risk for categorised risk cut-offs for overweight/obesity when not measuring the true high risk BC nor abdominal obesity volume will be a misleading proposition, which will provide a false conclusion for the associated real risk, or at least provide a conclusion with paradoxical information and bias. Therefore, in any study population, the risk captured by each metric depends on itself, its sensitivity and specificity, consistency, coherence, plausibility and anthropometric validity, rather than on its strength of association with respect to others, at least while predicting risk with simple measurements, where mathematical relationships of inequality provide imbalance and biases for the causal risk association.

In summary, BMI and WC will never refer to the same risk and high risk BC. Regarding that insight, while technological methods are clinically impracticable, to predict MI/CVD risk, WC should be the anthropometric reference for assessing the true high risk BC and risk beyond that of BMI.

It is worthy to note that the universally categorised risk cut-offs for metrics such as overweight/obesity [2], WHR ≥0.90 in men and ≥ 0.85 in women (<1 in both) [14], WC >94 (102) in men and > 80 (88) in women [13, 14, 56], and WHtR >0.5 and < 1 in both sexes, may provide confounding and association biases for causal risk. This occurs when the mathematical relationships are unbalanced between the simple measurements of healthy and unhealthy cases, and a spurious risk assignment being slanted in direction to the group of cases in the confounding metrics. At the same time, in the overlapping areas of the confounding metrics, subjects with similar baseline values must present different risk assignments when conditional on both imbalances between simple measurements and the real predictive variables [37]. Thus, regardless of WC, HC and height should be controlled in data analyses to preclude a different–equal risk assignment between subjects who have equal–different high risk BC and risk. Accordingly, a higher strength of association for WHR or WC with respect to WHtR does not mean higher risk, but association biases where both the high risk BC and relative volume were not well compared. In other words, WHR-associated risk above WC and WC-associated risk beyond that of WHtR were always a bias error, which is evidence that posed issues for the cardiovascular sciences for a long time due to the research process itself. Thus, when ignoring biases in research, false inferences could be drawn to predict MI/CVD risk in both sexes. On the contrary, only WHtRassociated risk above WC and WHR will hold true. Thereby, by identifying and removing biases in research, WHtR will always provide equality and balance between healthy populations and MI/CVD cases to be used as an entity of risk, while also having the importance of being cheap, accessible and easy to measure. Therefore, an appropriate ethnically-based and sex-specific WHtR risk cut-off would be the easiest and most definitive anthropometric tool to meet the best epidemiological criteria for the judgement of causal associations and to identify individuals at risk of MI/CVD. Broadly, it would occur while the degree of adiposity/overweight/obesity still has the importance of accumulating a homogenously distributed body fat volume. A continuous process of accumulating body fat over time provides changes in body shape and a higher degree of adiposity, even with fat flaps that would involve a higher risk and volume excess non-homogeneously distributed and, therefore, non-fully measurable from WC and height. In any case, a high degree of fatness will always keep a high correlation with WHtR, %BF and components of risk of the somatotype [10, 24, 27, 31, 45, 48].

*Anthropometrics in Predicting Cardiovascular Disease Risk: Our Research Work Mathematically… DOI: http://dx.doi.org/10.5772/intechopen.105098*

Lastly, after reviewing thousands of cases of MI/CVD, our findings have both internal and external validity, and therefore, they determine the generalisability to any ethnically-based or sex-specific population because they mathematically and epidemiologically satisfy our observations. On this issue, bias and causal associations in observational research must be well known [51–53], and overall, to avoid categorising as risk the value of each metric if their risk cut-off was not well verified and balanced with respect to others and specifically defined and checked in each study population. We also believe that an evolution of findings based on a balanced weighing of potentials for false-positive biases can produce scientific knowledge for the advancement of medical and cardiovascular sciences.

## **7. Conclusion**

Association biases for anthropometrics in predicting MI/CVD risk in both sexes have been demonstrated in anthropometric and mathematical terms. Regardless of BMI, which demonstrates either paradoxical or non-optimal MI/ CVD risk prediction in most studies, WHR-associated risk can lead to misleading evidence derived from a generalised mathematical misconception, which overestimates the protective effect of HC concerning WC and height. Until our discoveries by using matching in the overlapping zones between healthy population and cases, no other research has demonstrated biases by assigning spurious risk to true-negative values.

Epidemiologically, in the association of MI/CVD risk, WHR always appears to be a confounding variable with respect to WC and WHtR, due to differences in both the mean X value (HC–WC) and HC − height/2, respectively, either between groups or by sex. This is because there is always a WHR risk cut-off of <1 (mean HC > WC: natural inequality) and WHR/WHtR of <2 (mean HC > height/2: natural inequality). This, therefore, creates a protective overestimation for HC concerning WC and height. Similarly, WC may be a confounding variable with respect to WHtR due to differences for the mean WC and height/2, comparing either by group or by sex. This occurs if, and only if, the WHtR risk cut-off is >0.5 (mean WC > height/2), therefore creating an overestimation of risk for WC with respect to height in the tallest people and an underestimation of risk in the shortest, without accounting for a relative volume by unit of height.

Anthropometrically, the true risk exclusively derives from enlarged WC and abdominal obesity volume. However, accounting for body height as a volume modulator factor rends HC irrelevant or clinically useless, either in women or in men. Any association of MI/CVD causal risk for WHR beyond that of WC and WHtR becomes mathematically biased, anthropometrically inconsistent, biologically less plausible and epidemiologically false. WHtR as a proxy of adiposity and relative volume measure yields no bias and is biologically more plausible and consistent; it may capture a dimension of risk above WC as a two-dimensional transverse area. This only happens when height has an inverse association and the WHtR risk cut-off is >0.5. Thereby, in predicting MI/CVD risk, WHtR is the optimal anthropometric, rather than WC, WHR and BMI. Thus, quoting my own thinking: "Statistics confused medical science and cardiology, but mathematics does not fool the heart". Hence, researchers have the responsibility to design and conduct studies in a way that makes them capable of balancing the simple body measurements, ratios, ratios of ratios and risk cut-offs, as well as the high risk BC and true risk when predicting anthropometrically-measured

causal risk. Once the association biases for anthropometrics have been revealed, the worldwide focus of clinicians and scientists must shift.
