The Pennsylvania State University
The Graduate School
College of Engineering
STATISTICAL ANALYSIS OF THE POTENTIAL RISK FACTORS FOR ADULT
OBESITY IN THE UNITED STATES
A Thesis in
Industrial Engineering
by
Amey M. Farde
© 2012 Amey M. Farde
Submitted in Partial Fulfillment
of the Requirements
for the Degree of
Master of Science
August 2012
The Thesis of Amey M. Farde was reviewed and approved* by the following:
Andris Freivalds
Professor of Industrial and Manufacturing Engineering
Thesis Co-Adviser
Samuel A. Oyewole
Assistant Professor of Environmental Health and Safety Engineering
Thesis Co-Adviser
Paul C. Griffin
Peter and Angela Dal Pezzo Department Head Chair
Head of the Harold and Inge Marcus Department of Industrial and Manufacturing Engineering
*Signatures are on the file in the Graduate School
ii
Abstract
Obesity is a chronic physical condition which is characterized by high body fat, is accompanied
by health problems such cardiovascular disorders, musculoskeletal injuries, diabetes, high blood
pressure, high blood cholesterol, heart disease and stroke. In the United States, over 60% of the
population is at least overweight. Approximately $147 – $168 billion is spent annually on
obesity-related conditions and treatments. There have been studies related to the measure of
obesity based on Body mass index (BMI), weight, body fat, waist hip ratio and waist
circumference (WC). In this research, obesity was analyzed among men and women of varied
age groups, race, family income and education level using BMI cutoffs recommended by WHO.
The data used in the analysis was collected from National Health and Nutrition Examination
Survey (NHANES) from January 2009 to December 2010. From the 8,379 individuals used in
the study, a model was developed to predict the BMI of an individual using inverse
transformation. According to the analysis, 6.16% of the total female population (n=4184) were
extremely obese compared to 3.14% of male population. It was evident that the prevalence of
obesity was higher in female population than that in male. Amongst all the races, Non-Hispanic
blacks were in greater percentages in class I (16.72%), class II (8.17%) and class III (8.30%)
obesity. Class I and Class II obesity was more evident among individuals aged greater than 60
years. The analysis indicates rise in obesity with increasing age for the population with BMI
greater than 25. A predictable trend was visible in class I obesity, with the level of obesity
inversely related to the education level. No significant implications could be pointed out from the
analysis of the family income of the population. This research could provide a new approach in
the design of methods to prevent obesity and promote physical activity. The analysis could also
be used for health-care planning to estimate the cardiovascular risks among the population and
their costs implications.
iii
TABLE OF CONTENTS
List of Figures………………………………………………………………………….
vii
List of Tables…………………………………………………………………………...
viii
Acknowledgement……………………………………………………………………...
ix
Chapter 1 INTRODUCTION………………………………………………………...
1
Chapter 2 LITERATURE REVIEW………………………………………………...
5
2.1.1. Gender……………………………………………………………….
9
2.1.2. Age…………………………………………………………………..
10
2.1.3. Race………………………………………………………………….
11
2.1.4. Education Level ……………………………………………………….
14
2.1.5. Family Income………………………………………………………
15
2.2. Obesity Level and measurement of obesity………………………………...
16
Chapter 3 METHODOLODY AND RESEARCH DESIGN
3.1. Data Collection Method……………………………………………………
20
3.2. Experimental Design………………………………………………………
21
Chapter 4 ANALYSIS AND RESULTS
4.1. Analysis of Factors…………………………………………………………
23
4.1.1. Gender……………………………………………………………….
23
4.1.2. Age…………………………………………………………………..
24
4.1.3. Race………………………………………………………………….
25
4.1.4. Education Level ……………………………………………………….
26
4.1.5. Family Income……………………………………………………...
27
4.2. The Obesity Model…………………………………………………………...
29
4.3. Transformation Analysis……………………………………………………..
33
4.3.1. Square root transformation…………………………………………..
33
4.3.2. Inverse square root transformation…………………………………..
35
4.3.3. Log to the base 10 transformation…………………………………...
37
4.3.4. Natural log transformation…………………………………………..
39
4.3.5. Inverse transformation……………………………………………….
41
iv
4.4. Summary of Transformational Analysis……………………………………...
43
Chapter 5 CONCLUSION
5.1. Analytical Conclusion……………………………………………………
45
5.2. Future work and Recommendation……………………………………….
46
REFERENCES……………………………………………………………………………
49
Appendix……………….…………………………………………………………………..
57
v
List of Figures:
Figure1: Obesity Trends among U.S. Adults (1990 -2010)……………………………...
2
Figure 2: Prevalence of Overweight and Obesity among Young Adults (18 -24 year
olds)………………
3
Figure 3: Prevalence of obesity among Adults aged above 65 years…………………….
4
Figure4: Global obesity prevalence among males (above) and females (below) in 2008.. 7
Figure 5: Data distribution based on gender…………………………………………….. 23
Figure 6: Data distribution based on race………………………………………………...
24
Figure 7: Data distribution based on age…………………………………………………
25
Figure 8: Data distribution based on Education level……………………………………. 26
Figure 9: Data distribution based on Family income…………………………………….
27
Figure 10: Normal probability plot of the new model of BMI…………………………...
31
Figure 11: Normal probability plot of BMI for square root transformation……………... 35
Figure 12: Normal probability plot of BMI for inverse square root transformation……..
37
Figure 13: Normal probability plot of BMI for log to the base 10 transformation………
39
Figure 14: Normal probability plot of BMI for natural log transformation……………...
41
Figure 15: Normal probability plot of BMI for inverse transformation………………….
43
vi
List of Tables:
Table 1: World health organization cut off points and risk of metabolic complications.. 9
Table 2: Prevalence of Overweight, Obesity, and Extreme Obesity in Adults, by Age
and Racial/ Ethnic Group, 2003-2006…………………………………………………..
11
Table 3: Distribution of waist circumferences (in cm) among U.S. adults ( ≥20 years)
according to gender, race and age (1988-1994)…………………………………………
12
Table4: Distribution of waist circumferences (in cm) among U.S. adults (≥20 years)
according to gender, race and age (1999-2000)…………………………………………
13
Table 5: Sample population classified by gender, race, income, education and weight
category………………………………………………………………………………….
15
Table 6: Cutoff points for body mass index and waist circumference for obesity and
disease risk………………………………………………………………………………
18
Table 7:Classification of overweight and obesity beased on BMI……………………...
22
Table 8: Classification of the population on the basis of Education level………………
26
Table 9: Classification of the population on the basis of Family income………………. 27
Table 10: Summary of the analysis……………………………………………………... 28
Table 11: Table of Coefficients for the regression model………………………………. 30
Table 12: Analysis of variance for the regression model……………………………….. 30
Table 13: Table of Coefficients for the new regression model…………………………. 32
Table 14: Analysis of variance for the new regression model…………………………..
32
Table 15: Table of coefficients for the square root transformation model……………...
34
Table 16: ANOVA for square root transformation model………………………………
34
Table 17: Table of coefficients for the inversesquare root transformation model…….... 36
Table 18: ANOVA for inverse square root transformation model……………………...
36
Table 19: Table of coefficients for log to the base 10 transformation model…………...
38
Table 20: ANOVA for log to the base 10 transformation model……………………….
38
Table 21: Table of coefficients for the natural log transformation model………………
40
Table 22: ANOVA for the natural log transformation model…………………………... 40
Table 23: Table of coefficients for the inverse transformation model………………….. 42
vii
Table 24: ANOVA for the inverse transformation model………………………………
42
Table 25: Summary of the R2 and F values of the transformation models……………… 44
viii
ACKNOWLEDGEMENTS
First and foremost I would like to express my deepest gratitude to Dr. Andris Freivalds, who has
supported me with excellent guidance, patience and valuable inputs during this research. He
provided me a steadfast encouragement as well as friendly supervision in the completion of this
study.
I would like to Thank Dr. Samuel Oyewole, for his great support and willingness to provide the
best suggestions in developing this thesis. I would like to offer him my sincerest gratitude for
creating an excellent research atmosphere during my entire Master‟s program.
I would like to thank my family members, especially my dad, mom and brother for their endless
support and encouragement throughout my education. Lastly, I would also express my thanks to
all my friends here at Penn State for making this Masters journey a memorable one.
.
ix
Chapter 1
INTRODUCTION
Obesity is a condition characterized by excessive amount of body fat. It is a medical condition of
epidemic proportions that has rapidly plagued the global community over the last three decades
(Dixon, 2010). Obesity is also defined in terms of abdominal obesity. Abdominal obesity is
mentioned in individuals with waist–hip ratio above 0.90 for males and above 0.85 for females,
or a body mass index (BMI) above 30.0. In the United States, over 60% of the population is at
least overweight. Approximately $147 – $168 billion is spent annually on obesity-related
conditions and treatments (Sturm, 2002). According to Wolf et al., (1998), medical costs
associated with overweight and obesity may involve direct costs which include preventive,
diagnostic and treatment service and also indirect costs which include expenses related to
morbidity and mortality. On medical expenditures alone, the United States spent about $75
billion in 2003 (McMichael, 2001; Finkelstein et al., 2004; Finkelstein et al., 2010). In a recent
survey of hospitals in the University Health System Consortium and VHA Member Health Care
Organization, nearly 80% of those hospitals reported increased costs on special medical
equipment for obese patients.
The World Health Organization (WHO) defines obesity as abnormal or excessive fat
accumulation in the body that may impair human health. The number of obese individuals has
tripled in some areas of the world since 1980 (CDC, 2011). The WHO declared that obesity has
reached epidemic proportions around the world, as it has been reported that more than 1 billion
adults are at least slightly obese. In 2003-2006, more than one third adult population (35.7%)
was classified as obese. If current trends prevail, the national prevalence of obesity will exceed
1
51.1% by 2030. Also, 86.3% adults will be at least overweight with 96.9% black women and
91.1% Mexican-American men. It is estimated that the total health-care costs due to overweight
and obesity would double every decade to about $860.7 – $956.9 billion by 2030, responsible for
16 – 18% of the total healthcare costs (Wang et al., 2008).
Figure 1 shows percentage of adults within the United States and their BMI classification within
a twenty-year period (1990 – 2010) according to the United states Center for Diseases Control
and Prevention. Within the United States, Mississippi is the state with the highest prevalence of
obesity of 32.8%. The states having obesity over 30% also include Alabama, Oklahoma, West
Virginia, South Carolina and Tennessee. Colorado has the lowest prevalence with 18.5% (Flegal
et al., 2010).Earlier research claimed that the BMI-related prevalence of obesity among US adult
men was 35.5% and 35.8% for women.
Figure 1: Obesity Trends among U.S. Adults (1990 -2010)
2
Similarly, childhood obesity has more than tripled in the past 30 years (Ogden et al., 2010).
Currently, 10% of the world‟s adult population is considered as obese (WHO, 2008). Global
childhood obesity statistics indicate that approximately 43 million children under five years old
were considered to be overweight in 2010. In 1980, only 7% of children and adolescents were
overweight or obese (NCHS, 2011). Figure 2 shows the obesity among 18-24 years old in the
United States. In 2008, more than one third of children aged 18-24 years were either overweight
or obese. Over the past two decades, the percentage of overweight children (ages 6 - 11) has
more than doubled, rising to 15 percent in 1999 (CDC, 2010). On the other hand, there was a 5%
to 18% percentage increase in adolescents aged 12–19 years who were obese over the same
period.
Figure 2: Prevalence of Overweight and Obesity among Young Adults (18 -24 year olds)
3
Figure 3 shows the prevalence of obesity in the adult US population above the age of 65years
over the years 1995, 1999, 2003 and 2007. In 2007, the states with the greatest prevalence of
obesity among the elderly were Alaska (33.4%), Louisiana (29.9%), and Michigan (26.8%). The
states with the lowest level of elderly obesity were Hawaii (14.8%), Arizona (17.7%), and
Nevada (17.8%) (CDC, 2010). Over this period, twenty-three states experienced increases in
excess of 70%. The states to have more than 20% of their adult populations as obese were Iowa,
Illinois, Wisconsin, Nebraska, Kansas, Oklahoma and Texas. These rates of obesity may likely
indicate a trend in obesity based on the differences in race/ethnicity, income inequality, or
educational achievement.
Figure 3: Prevalence of obesity among Adults aged above 65 years (CDC, Behavioral Risk
Factor Surveillance System Survey Data. Atlanta, Georgia: U.S. Department of Health and
Human Services, Centers for Disease Control and Prevention, 1994-2007.)
4
Chapter 2
LITERATURE REVIEW
A severe increase in obesity is due to a combination of factors, including technological advances
that have more sedentary forms of employment, low costs of fast food and a decline in the
amount of leisure time adults spend engaging in physical activity (CDC, 2005). Obesity rates in
the United States may also be related to the increasing number of women who entered the
workforce in the late periods of the 20th century (Chou et al., 2004). There have been significant
changes in the eating patterns, with Americans consuming on average 300 calories more per day
in 2002 than in 1985 (Cutler et al., 2003). This prompted many families to rely on pre-packaged
meals or frozen dinners, and to start eating in restaurants more often.
Individuals usually consume larger portions and higher-calorie foods in restaurants than when
they eat meals at home (Young et al., 1995). Therefore, with time, there has been an increase in
the reliance on restaurants for meals which has had an impact on obesity rates (Young et al.,
2002). Physical effects of obesity are often seen in the form of back injuries at workspace,
fatigue, cumulative trauma disorders and other injuries. Adverse stereotyping typically includes
the perception that obese individuals are undisciplined, non-productive, inactive, unappealing
and responsible for their weight problem and is widespread in westernized countries (Hill, 2009).
Several research studies have highlighted overweight and obesity as a risk factor for several
other medical conditions such as liver diseases, gall bladder diseases, cardiovascular diseases,
type 2 diabetes mellitus, hypertension, heart and renal failure, cancers, chronic venous
insufficiency, gallbladder disease sleeping and breathing problems, deep venous thrombosis
5
(DVT), and arthritis, etc. (Adams & Murphy, 2000; Harney &Patijn, 2007; Bigal and Lipton,
2008; Oreopoulos et al., 2008; Sharifi-Mollayousefi et al., 2008; Tukker et al., 2008; Whitlock et
al., 2009). Some of the accompanying consequences of obesity have also been a reason for
mortality. In 2000, Obesity ranked the nation‟s second leading risk factor for mortality. Obesity
was associated with 112,000 deaths, well behind smoking (435,000 deaths) but somewhat greater
than alcohol consumption (85,000 deaths) (CDC, 2010). These include failure to control
smoking, inability to control hypertension, dyslipidemia and hyperglycemia, failure to control
weight loss with illness and failure to standardize for age (Weststrate et al., 1991). According to
Flegal et al. (2005), compared to the population with normal BMI (18.5 to ≤ 25), obesity (BMI
≥30) was associated with 111,909 excess deaths.
Fontaine et al. (2003) concluded that obesity could reduce life expectancy by as many as 20
years for some males and 5 years for females. Several research works have shown that obesity
accounts for almost 60% of the risk for developing type 2 diabetes (non-insulin dependent), over
20% of that for hypertension and coronary-heart disease, and between 10% and 30% for various
cancers (Hu, 2008; Williams and Fr ebeck, 2009). Figure 4 depicts the global prevalence of
obesity among adult males and females in 2008. Overweight and obesity has been considered the
fifth leading risk for global deaths. The prevalence of obesity was highest in the US among
males whereas it was least in Asia. According to Haslam & James (2005), Sub-Saharan Africa is
the only region of the world where obesity is not very common. The World Health Organization
(WHO) has estimated that at least 2.8 million adults die every year due to being overweight or
obese.
6
Additionally, overweight and obesity has accounted for approximately 44% of diabetes-related
deaths, 23% of global cardiovascular disease-related deaths, and between 7% - 41% of certain
cancer-related mortality. Obesity was declared a global epidemic by the WHO in 1997
(Caballero, 2007). In 2005, approximately 400 million adults worldwide (9.8%) were determined
to be obese. By 2008, roughly 1.5 billion adults were overweight, of which 500 million (200
million men and 300 million women) considered as obese.
Figure 4: Global obesity prevalence among males (above) and females (below) in 2008
Source: Global Prevalence of Adult Obesity (2008) – International Obesity Taskforce
In the North American continent, Mexico has become the second-fattest nation in the world, next
to the United States followed by Canada. In 1989, less than 10 percent of Mexican adults were
overweight. According to the latest national surveys in Mexico, more than 71 % of women and
7
66 % of men are now considered at least overweight (Monteverde et al., 2010). Approximately
24.1 % of adults in Canada were obese between 2007 and 2009. According to CDC (2011), in
2004, approximately 6.8 million Canadian adults aged 20 to 64 were overweight, and an
additional 4.5 million were obese (Statistics Canada, 2004).
The healthcare costs of obesity related diseases have been pegged at approximately $4.3 billion.
According to the report by US Department of Health and Human services (DHHS) (2001), the
federal government (through the Medicaid and Medicare programs) spends $84 billion annually
to improve the physical activity of individuals suffering from five major chronic conditions
which include diabetes, heart disease, depression, cancer, and arthritis. Obesity is associated with
a 36% increase in inpatient and outpatient costs and a 77% increase in medication costs over
those incurred by people within a normal weight range (Sturm, 2002). Studies suggest various
factors have contributed to the rise in obesity. Every individual can be associated with multiple
factors to like genetics, behavior, environment, culture, and socioeconomic status to predict
obesity. Findings by NIH (1998) suggest that although the nature of obesity-related health risks
is similar in all populations, the specific level of health risk for a given class of obesity may be
different depending on gender, race, age and socioeconomic conditions. In this study we study
the combinational effect of age, gender, race, family income and education level on the level of
obesity of an individual.
8
2.1.1. Gender:
The WHO (2008) recommendations for the waist and hip anthropometry are mentioned in the
table below.
Table 1: World health organization cut off points and risk of metabolic complications
Indicator
Cut-off points
Risk of metabolic complications
Waist Circumference
>90cm (M)
>80cm (W)
Increased
Waist Circumference
>102cm (M)
> 88cm (W)
Substantially Increased
Waist-hip ratio
>0.90cm (M)
> 0.85cm (W)
Substantially Increased
M-male, W-women
Women with similar waist circumferences and waist–hip ratios are reported to have larger
muscle masses and lower percentage body fat (Rush, et al., 2007). Obesity in women is more
prevalent at the foetal stage but the deposition of body fat is more evident during the puberty
(Wells, 2007).
Analysis of the data from NHANES III has shown that parity has been the reason for the change
in body shape (Lassek & Gaulin, 2006). It showed that women who had given birth had greater
waist circumference and lesser lower body fat. Men tend to have greater lean mass and bone
mineral mass and a lower fat mass than women. Distribution of mass, tissues, fat and bone
strength has had a major implication on an individual‟s obesity. Women have comparatively
more distribution of adipose tissue and peripheral distribution of fat while lesser arm muscle
strength than men in their early adulthood. Men have lesser limb fat and higher abdominal body
9
fat. (WHO, 2008) The level of testosterone has been inversely proportional to the level of
obesity. In men the reduction of free testosterone, increases the body fat and hence reduces the
muscle mass (Derby et al., 2006). According to the study by the Baltimore Longitudinal Study of
Aging on the effect of weight change on fat obesity, men have larger waist changes than hip
changes, whereas in women they were similar. The study shows that with a 4.5 kg weight gain,
men had a 4 cm and women had a 3.3 cm increase in waist circumference. Similarly, it showed
that men had a 2.5 cm increase in hip circumference compared to a 3.6 cm increase in women
(Shimokata, et al., 1989). Flegal et al., (2012) considering obesity for BMI ≥ 30 found that
between NHANES III and NHANES 1999 to 2000, increased from 20.2% to 27.5% among men
and from 25.4% to 33.4% among women.
2.1.2. Age:
NHANES data show that waist circumference increases with age for both sexes up to the age of
70 years (Ford et al., 2003). Flegal et al. (2010) found that the prevalence of obesity in the
United States is roughly 68% among adults (18 years and above). Ford et al., 2003 stated that
increase in waist circumference was not significant in men 30 to 59 years old, women 40 to 59
and more than 70 years old. The analysis proved that women between the age 20-29 years
showed the largest increase in waist circumference. According to the Salinsky et al., (2003), in
both the genders, the prevalence of obesity increases with age until the age of 69, after which it
starts to decline. Recently, there has also been a noticeably sharp increase (70%) in rates of
overweight and obesity among adults aged 18 through 29.
10
Table 2: Prevalence of Overweight, Obesity, and Extreme Obesity in Adults, by Age and
Racial/Ethnic Group, 2003-2006 (Sommers, 2009)
2.1.3. Race:
Consequences of obesity can affect some races more than others (Fontaine et al., 2003). Flegal
et al. (2010) found that African-Americans had the largest prevalence of obesity in the United
States. Table 2 shows that the prevalence of overweight, obesity, and extreme obesity among
non-Hispanic blacks and Mexican Americans exceeds that of non-Hispanic whites in most age
11
categories. One of the study reported that at a given waist circumference, the Hispanics and
whites have almost equal visceral adipose tissue (Carroll et al., 2008). Ford et al., (2003)
analyzed the changes in waist circumference in NHANES III among U.S. adults from 1988 to
1994 through NHANES 1999 to 2000. The percentile distribution of the waist circumference
among US adults according to race, gender and age for the years 1998-1994 and 1999-2000 is
shown in Table 3 and Table 4.
Table 3: Distribution of waist circumferences (in cm) among U.S. adults (≥20 years)
according to gender, race and age (1988-1994) (Ford et al., 2003)
12
Table 4: Distribution of waist circumferences (in cm) among U.S. adults (≥20 years)
according to gender, race and age (1999-2000) (Ford et al., 2003)
From the 15,454 participants analyzed from (1988 to 1994) and 4024 participants from 1999 to
2000, the unadjusted waist circumference increased from 95.3 to 98.6 cm among men and from
88.7 to 92.2 cm among women. From table 2, the high risk waist circumference values are ≥102
cm in men and ≥88 cm in women. The above results also showed an increase in the high risk
waist circumference in all subgroups between the two surveys except in Mexican- American
women. The tables also show that the largest mean waist circumference for men was among
whites and was among African Americans women in both surveys.
13
2.1.2. Education level:
Research has shown that the prevalence of obesity declines with increase in education. Studies
estimate that 26% of high school dropouts were obese in 2000, versus 22% of individuals with a
high school diploma and 15% of college graduates (Baum II & Ruhm, 2009). Higher education
seems to correlate with lower rates of obesity. According to U.S. Department of Health and
Human Services (2001), those with less than a high school education are more likely to be obese
(24%) than those with a high school diploma (19%).
However, Salinsky et al. (2003) claim that the greatest increase of obesity (67%) within the last
decade have occurred among individuals with some college education. The findings by
Paeratakul et al., (2002) on the relation of gender, race and socioeconomic status to obesity are
shown in the Table 5. According to the study, the prevalence of obesity was higher among
Hispanic subjects compared to blacks and whites. The obesity level was also higher among
individuals with lower income and lower education compared to the rest of the population.
14
Table 5: Sample population classified by gender, race, income, education and weight
category (Paeratakul et al., 2002)
2.1.3. Family Income:
Studies have shown that the prevalence of obesity is inversely related to income (Mokdad et al.,
2011). In 1999-2002, 23% of white women with family incomes greater than 400% of the
federal poverty level (FPL) were obese, compared to an obesity rate of 40% among white women
who were living in poverty (at or below the FPL). Analogous obesity figures for white males
during this period were 14% and 34%. Irrespective of the racial groups, women of lower
socioeconomic status, with an income of less than 130% of the FPL, are 50% more likely to be
obese than those with higher incomes. Conversely, men are equally likely to be obese, regardless
of their socioeconomic group (Salinsky et al., 2003). The reason for increase in the obesity in the
lower income population may be due to limited access to cheap healthy food and the
consumption of low cost, energy dense foods. It has been noted that obesity is not only prevalent
15
in high income countries, but is on a rise in low and middle income countries possessing urban
conditions.
Studies by the U.S. Department of Health and Human Services (DHHS) have also reported that
family income is not the predictor of overweight among Mexican American, black children and
adolescents. However, in the case of non-Hispanic white adolescents, family income is inversely
related to the prevalence of obesity. Due to the high level of poverty in developing countries, the
rate of obesity among children in these nations could be correlated to substantial low family
income. Approximately, 35 million overweight children are living in developing countries and 8
million in developed countries.
2.2.Obesity level and measurement of obesity:
In adults, obesity is generally classified using Body mass index (BMI) and is one of the most
common measure of the excessive accumulation of body fat. It is a ratio relating height and
weight of an individual and is mostly measured in kg/m². Recently, increased BMI has been
associated with increased morbidity and higher health risks in adults which has justified for the
use BMI to assess the level of obesity. BMI has been a consistent measure in predicting the risk
of cardiovascular disease (CVD) and type 2 diabetes.
Most of the sources have identified obesity on the basis of BMI, waist circumference and waist
hip ratio (Lean et al, 1995, Ford et al, 2003, Zimmet and Alberti, 2006). Waist circumference
has been a measure to predict intra-abdominal fat mass and total fat. It has been a consistent
measure in predicting the health risks and hence has been provided with cut off points to estimate
the risk in an individual (see table 6). Along with reflecting the level of risk for CVD, waist
16
circumference is closely correlated with both BMI and WHR (Lean et al, 1995). Waist Hip Ratio
(WHR) is measured by an individual‟s ratio of the waist circumference to the hip circumference
and is a useful health risk indicator. According the research by Dalton et al. (2003) on the
correlation of BMI, waist circumference and waist hip ratio (WHR) on cardiovascular disorders
(CVD), waist hip ratio is the most useful measure of obesity to use to identify individuals with
CVD risk factors.
National heart, lung and blood institute (NHLBI) of National institute of health (NIH) provides
certain guidelines for the classification of obesity on the basis of body mass index and waist
circumference and its association with health risks. The classification takes into consideration
that increase in BMI is reflected with an increase in health disorders and waist circumference is a
predictor of abdominal fat which is the major risk factor than fat free mass. The population is
classified in 6 categories based on BMI and the health risk for individuals with BMI greater than
25 is specified depending on the waist circumference. Individuals with BMI greater than 40 are
subjected to extremely high health risk irrespective of their WC. The recommendations for the
Cut-off points for BMI and waist circumference for obesity and disease risk are shown in the
Table 6.
17
Table 6: Cutoff points for body mass index and waist circumference for obesity and disease
risk according to NIH guidelines
Source: NHLBI Obesity Education Initiative (2000)
In the study conducted by Janssen et al. (2004), a comparison between normal, overweight,
obese men and women was categorized in normal and high waist circumference. In their study,
they identified that obesity related disease risk can be predicted using WC than BMI. BMI
predicted non abdominal fat and abdominal subcutaneous fat, whereas waist circumference
predicted the visceral fat. (Janssen et al., 2002) Research conducted by Biggard et al. (2003) on
BMI and waist circumference indicates that both these measures are highly correlated and
measure different characteristics of obesity. Their analysis shows that for given value of BMI,
waist circumference is an indicator of abdominal fat deposit while for a given waist
circumference, BMI predicts the fat free mass as well as fat deposits in higher BMI values.
Although Clinical Guidelines on the Identification, Evaluation, and Treatment of Overweight
and Obesity in Adults (2007), indicated that men and women with WC values above 102 and 88
cm, respectively, are at a higher risk of health disorder compared with men and women with WC
values below these cutoff points, studies did not take into consideration the effect of BMI on the
health risks in individuals of variable WC. There hasn‟t been any research that justifies that the
18
WC cut-offs implemented by NIH predict health risk better than the ones predicted by BMI.
Although there has been a prevalence of other measures for predicting obesity, BMI has been a
reliable and clinically used on a global scale. Hence in this research we take into consideration
BMI as a measuring unit for the assessment of obesity.
19
Chapter 3
Methodology and Research Design
`
3.1.Data Collection Method
The data used in the analysis was collected from National Health and Nutrition Examination
Survey (NHANES). This survey is structured to examine the health and nutritional standards of
United States population. The Data used in the research were collected between January 2009
and December 2010. Since the research is oriented toward the adult population, the base age was
assumed as 18 years.
The information of eight thousand three hundred and seventy nine individuals was used in the
analysis. The data was selected such that it consisted of considerable population representing
both the genders (50.07% male, 49.92%female). Five factors which are the potential reasons for
the obesity were extracted from the universal data for the analysis. The factors are mentioned
below:
(A) Age
(B) Gender
(C) Race
(D) Family Income
(E) Educational level
Each of these factors (except gender) was divided on a level from 1-5 to provide a quantitative
significance for the analysis. Each of these factors corresponds to x1, x2, x3, x4 and x5. These
factors (x1, x2, x3, x4, and x5) are regarded as the independent variables. The dependent variable is
20
the BMI of individuals used for the analysis which is denoted as (y). Based on this, a statistical
relationship could be derived between the independent and dependent variables as shown in
Equation (a)
y = f (x1, x2, x3, x4, x5, ε)
... (a)
In the above function, ε denotes the residual error which includes the uncontrollable and
nuisance factors.
3.2. Experimental Design
WHO states that BMI is an important measure to determine overweight and obesity and
determine the risks of disorders associated with those conditions (WHO, 2010). Although,
recently waist circumference, body fat, neck circumference, hip ratio are used for the estimation
of obesity, BMI has been a traditional and an accurate measure to predict obesity. The
experimental data is analyzed to predict the obesity in the population. The given data is divided
based on the BMI in six levels. This data was further sorted out to calculate the individuals in
each level of the factors. The percentage of population represented in the classification provided
a trend of obesity in these factors.
For this distribution of the data based on BMI, we take into consideration WHO guidelines as
well as the clinical guidelines for obesity in adults as a standard as shown in the table 7 below.
Individuals with BMI greater than 30 were considered as obese. This data was further used to
develop a regression model to predict the relation between these factors. Regression was carried
in Minitab and normal probability plot of BMI was plotted against the residuals.
21
Table 7: Classification of Overweight and obesity based on BMI (WHO, 1997)
Obesity class
BMI ( Kg/m²)
Underweight
<18.5
Normal
18.5-24.9
Overweight
25-29.9
Obesity
Extreme Obesity
I
30-34.9
II
35-39.9
III
>40
22
Chapter 4
Analysis and Results
4.1. Analysis of factors:
Statistical analysis of the data was conducted using MINITAB and Microsoft Excel. The data
was analyzed through certain graphs and model adequacy testing. The five factors discussed
earlier were considered in order to determine the level of obesity level in an individual.
4.1.1. Gender:
Data distribution based on Gender
Percentage of Sample data
35
30
25
20
15
Male
10
Female
5
0
< 18.5
18.5-25
25 - 30
BMI
30 - 35
35 and
above
> 40
Figure 5. Data Distribution based on Gender
From the distribution of data based on the gender as indicated in figure 5, 6.16% of the total
female population (n=4184) was class III obese compared to 3.14% of male population (n=
4183). A similar trend was visible in class II obesity (5.69% male, 7.84% female). There is not
much significant difference in the percentage of male and female population in class I obesity. A
23
higher number of male population was overweight (27.96%) compared to the females (22.37%).
If we consider the cumulative of the obese population, it is evident that the prevalence of obesity
is higher in females than in males.
4.1.2. Race:
The US population was divided in five categories based on race/ethnicity which included
Mexican American (n=1839), Non-Hispanic white (n= 824), Non-Hispanic black (n=3673),
other (n= 1543) Hispanic and others (n=501). Among both the genders, Non-Hispanic blacks
were in greater percentages in class I, class II and class III obesity. 8.3% of the Non-Hispanic
blacks were extremely obese followed by 4.46 % Non-Hispanic white. Similar trends were
evident in class II obesity which was dominated by Non-Hispanic black (8.17%) followed by
Non-Hispanic white (7.11%) and Mexican American (6.92%). Non-Hispanic blacks and
American Mexican were in higher percentages amongst the overweight population. (See figure
6).
Data distribution based on race
Percentage of sample data
40.00
35.00
30.00
25.00
Mexican American
20.00
Other Hispanic
15.00
Non-hispanic White
10.00
Non-hispanic Black
5.00
Others
0.00
<18.5
18.5-25
25 - 30
30 - 35
BMI
35 - 40
> 40
Figure 6. Data Distribution based on Race
24
4.1.3. Age:
The sample data is distributed in five groups from age 18. Figure 7 clearly indicates rise in
obesity with increasing age for the population with BMI greater than 25. Class I and Class II
obesity was more evident among individuals aged greater than 60 years followed by individuals
between 50-59 years and 40-49 years group (See figure 7). 6.47 % of the population in the age
group between 50-59 years were extremely obese followed by 5.51% of the 60 plus years
individuals. Under Class I obesity, the percentage of individuals aged greater than 60 years were
twice compared to the ones within 18-29 years.
Data distribution based on age
40.00
Percentage of sample data
35.00
30.00
25.00
18-29
20.00
30-39
15.00
40-49
50-59
10.00
60+
5.00
0.00
<18.5
18.5-25
25 - 30
30 - 35
35 - 40
> 40
BMI
Figure 7. Data distribution based on Age
25
4.1.4. Educational level:
The sample data was classified in five levels on the basis of the education background as shown
in the table below.
Table 8: Classification of the population on the basis of educational level
1
2
3
4
5
Less Than 9th Grade
9-11th Grade (Includes 12th grade with no diploma)
High School Grad/GED or Equivalent
Some College or AA degree
College graduate and above
From the data distribution based on obesity (figure 11), about 30.98% of the population educated
under less than 9th grade (n=978) were overweight. There was no significant comparison of
obesity on the basis of education level under class II and class III obesity though it is worth
mentioning that College graduated were amongst the least in these classes Class I obesity was
more prevalent among individuals with education less than grade 9th (19.33%). A predictable
trend was visible in class I obesity, with the level of obesity inversely related to the education
level (See figure 8).
Percentage of sample data
Data distribution based on Education level
40.00
35.00
30.00
25.00
20.00
15.00
10.00
5.00
0.00
1
2
3
4
5
<18.5
18.5-25
25 - 30
30 - 35
35 - 40
> 40
BMI
Figure 8. Data distribution based on Education Level
26
4.1.5. Family Income
The population was divided in five levels based on the family income as shown in the table
below.
Table 9: Classification of the population on the basis of Family Income
1
2
3
4
5
$75,000 +
$55,000 to $74,999
$35,000 to $54,999
$10,000 to $34,999
$0 to $9,999
The distribution of data based on family income did not indicate a trend in the obesity. The
richest section of the society (n= 1830) was least amongst class III obesity followed by the
poorest section (n= 820). Population with income between $55k and $74,999 were in higher
percentage (13.40%) with extreme obesity. Population with family income between 35k to
$54,999 were in higher percentages in both class I obesity was well as amongst the overweight.
(See figure 9)
Data distribution based on Family Income
Percentage of sample data
35.00
30.00
25.00
$75,000 +
20.00
$55,000 to $74,999
15.00
$35,000 to $54,999
10.00
$10,000 to $34,999
$0 to $9,999
5.00
0.00
<18.5
18.5-25
25 - 30
30 - 35
35 - 40
> 40
BMI
Figure 9. Data distribution based on Family Income
27
Table 10: Summary of the analysis
Male
Female
19.62
18.46
BMI levels
18.5 25 30 35 24.9
29.9
34.9
39.9
Percentages in each category
27.96
27.96
15.61
5.70
30.24
22.38
14.92
7.84
Race
Mexican American
Other Hispanic
Non-Hispanic White
Non-Hispanic Black
Others
22.13
19.66
16.63
17.95
27.54
25.23
29.61
30.49
27.41
37.33
27.24
26.70
25.97
21.45
20.56
16.42
14.32
15.19
16.72
8.98
5.71
6.92
7.11
8.17
3.59
3.26
2.79
4.60
8.30
2.00
Age ( years)
18 - 29
30 - 39
40 - 49
50 -59
> 60
29.18
32.66
20.54
10.08
3.05
31.97
27.90
32.86
27.82
25.19
18.59
20.13
22.32
30.84
34.46
10.69
10.79
12.86
17.56
22.41
5.67
5.10
6.38
7.23
9.38
3.90
3.42
5.03
6.47
5.51
Education level
Less Than 9th Grade
9-11th
High School Grad
Some college degree
College Grad & above
16.05
20.63
20.75
17.82
19.20
23.21
27.41
26.42
30.22
35.23
30.98
24.49
24.36
23.70
25.34
19.33
14.94
15.29
15.35
13.10
6.24
7.65
7.67
7.59
4.25
4.19
4.88
5.51
5.33
2.87
Family Income
$75,000 +
$55,000 to $74,999
$35,000 to $54,999
$10,000 to $34,999
$0 to $9,999
19.13
17.56
17.45
19.68
20.37
32.13
29.77
27.73
27.01
32.80
24.97
25.27
26.53
25.30
22.80
14.97
14.00
16.68
15.26
14.76
5.41
9.49
7.11
7.01
5.37
3.39
3.91
4.50
5.74
3.90
Factors
Sub-factors
>18.5
Gender
> 40
28
3.15
6.17
4.2. The Obesity Model:
Obesity level on the basis of BMI could be predicted from the input variables and the regression
model could be developed to recommend policies for obesity control based on these factors and
interactions. Regression models were developed to analyze the relation of various factors
affecting the class of obesity. Forward regression method is commonly used in multiple
regression analysis. Initially, a model containing all the factors previously discussed was
developed (equation b). The model was significant with p value less than 0.05. Although a
higher R2 value is preferred in data analysis, it is impractical to achieve it for human population
data involving a large amount of data. As seen from the table of coefficients (table 11), the
insignificant factor in the model is family income (p>0.05). Model terms are considered
significant if their p-values are less than 0.05.
If non-significant variables were allowed to come into the model, the R-squared would continue
to increase, even though the predictive capability of the regression gets worse. Thus nonsignificant variables definitely should not be allowed into the model. Values greater than 0.1
indicate the model terms are not significant. If there are many insignificant model terms, model
reduction may improve the model. The regression equation with all the factors is shown along
with the table of co-efficients followed by the analysis of variance. (Refer Table 8 and 9 for the
classification of education level and family income)(Race is classified in the order of the legend
in figure 6)
BMI =
+
+
+
+
17.6 + 0.110 Age (yrs) - 0.639 Gender (1=m, 2=f)_1 + 1.69 Race_1
1.70 Race_2 + 2.16 Race_3 + 3.05 Race_4 + 1.54 Education Level_1
1.13 Education Level_2 + 1.24 Education Level_3
1.36 Education Level_4 + 0.093 Family Income_1
0.568 Family Income_2 + 0.500 Family Income_3 + 0.652 Family
Income_4
…. (b)
29
Table 11: Table of Coefficients for the regression model
Predictor
Constant
Age (yrs)
Gender (1=m, 2=f)_1
Race_1
Race_2
Race_3
Race_4
Education Level_1
Education Level_2
Education Level_3
Education Level_4
Family Income_1
Family Income_2
Family Income_3
Family Income_4
Coef
17.6015
0.109850
-0.6394
1.6902
1.7045
2.1566
3.0495
1.5391
1.1277
1.2422
1.3633
0.0930
0.5680
0.4997
0.6525
SE Coef
0.4920
0.005227
0.1609
0.3817
0.4186
0.3528
0.3819
0.3408
0.2902
0.2574
0.2413
0.3288
0.3667
0.3278
0.2867
T
35.77
21.02
-3.97
4.43
4.07
6.11
7.99
4.52
3.89
4.83
5.65
0.28
1.55
1.52
2.28
P
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.777
0.121
0.127
0.023
Table 12: Analysis of variance for the regression model
Source
DF
SS
MS
Regression
14.00
35247.80 2517.70
Residual error 8363.00 451129.50 53.90
Total
8377.00 486377.30
F
46.67
P
0.00
R-Sq
7.20%
R-Sq (adj)
7. 1%
A new model without family income was developed to better predict the level of obesity
(equation c). The normal plot of residuals of the new model shown in Figure 10 shows a high
level of adequacy in normality of the model. In order to determine the normality of the new
model, the normal plot of residuals was analyzed to determine whether the normal probability
plot passes the “fat pencil” test. The “fat pencil” test is a terminology used to determine the level
of closeness of the data points to a straight line. The normal plot of BMI is shown in the figure
below.
30
Figure 10
The new regression model along with the Table of coefficients and analysis of variance is shown
in Table 13 and 14 respectively. The model is significant with p values of the factors less than
0.05. The „fat pencil test‟ shows that there is a fair amount of non-normality in the model. Data
transformation would be required to improve it and analyze its adequacy.
BMI = 17.9 - 0.653 Gender (1=m, 2=f)_1 + 0.110 Age (years) + 1.68 Race_1
+ 1.67 Race_2 + 2.11 Race_3 + 3.02 Race_4 + 1.70 Education Level_1
+ 1.28 Education Level_2 + 1.39 Education Level_3 + 1.47 Education
Level_4
…. (c)
31
Table 13: Table of Coefficients for the new regression model
Predictor
Constant
Gender (1=m, 2=f)_1
Age (yrs)
Race_1
Race_2
Race_3
Race_4
Education Level_1
Education Level_2
Education Level_3
Education Level_4
Coef
17.9392
-0.6528
0.110439
1.6822
1.6691
2.1053
3.0245
1.6965
1.2758
1.3910
1.4667
SE Coef
0.4277
0.1607
0.005192
0.3813
0.4183
0.3520
0.3819
0.3222
0.2740
0.2461
0.2358
T
41.94
-4.06
21.27
4.41
3.99
5.98
7.92
5.27
4.66
5.65
6.22
P
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
Table 14: Analysis of variance for the new regression model
Source
DF
SS
MS
Regression
10.00 34729.80 3473.00
Residual error 8367.00 451647.50 54.00
Total
8377.00 486377.30
F
64.34
P
0.00
R-Sq R-Sq (adj)
7.10%
7%
32
4.3. Transformation Analysis:
Transformation analysis is used in situations where there is low level of accuracy in the model or
if the model fails to pass the fat-pencil test. Transformation makes the given data appear close
and enhances the interpretability of the graph. Since in our results, the model was not highly
accurate, it was transformed to enhance the correlation between the factors. We transformed the
data using the square root, inverse square root, log to the base 10, natural log, and inverse of the
BMI. Transformation of the dependent variable (y) was considered in this analysis. We then
compared the R2 and the F values of these transformations to the previous model to predict the
best transformation.
4.3.1. Square root transformation:
The mathematical representation of the square root transformation is shown in the equation
below. The square root transformation of the BMI (y) is given as (y‟). The table of coefficients
and the table of analysis of variance are shown in Table 15 and 16.
y‟ =
y
…. (d)
33
Table 15: Table of coefficients for the square root transformation model
Predictor
Coef
SE Coef
T
P
4.22914
0.04104
103.06
0.000
-0.05377
0.01541
-3.49
0.000
0.0114778
0.0004981
23.04
0.000
Race_1
0.16783
0.03658
4.59
0.000
Race_2
0.16646
0.04013
4.15
0.000
Race_3
0.20387
0.03377
6.04
0.000
Race_4
0.28402
0.03664
7.75
0.000
Education Level_1
0.15866
0.03091
5.13
0.000
Education Level_2
0.11445
0.02629
4.35
0.000
Education Level_3
0.12721
0.02361
5.39
0.000
Education Level_4
0.13820
0.02262
6.11
0.000
Constant
Gender (1=m, 2=f)_1
Age (yrs)
Table 16: ANOVA for square root transformation model
Source
DF
Regression
10
SS
F
P
354.555 35.456 71.36 0.000
Residual Error 8367 4157.414
Total
MS
R-Sq R-Sq(adj)
7.90%
7.70%
0.497
8377 4511.969
The table of coefficients shows that all the factors in the model are significant with p value lesser
than 0.05. The ANOVA for the square transformation depicts that the model is significant along
with better R2 value of 7.9 % compared to the R2 value of 7.1 % of the new model developed
previously. The model even provided a better F value of 71.36 compared to 64.34 of the new
model. The normal plot of residuals showed in the Figure 11 in not accurate enough with several
outliers. The „fat pencil‟ test shows a fair amount of non-normality in this model.
34
Figure 11
4.3.2. Inverse square root transformation:
The mathematical representation of the inverse square root transformation is shown in the
equation below. The inverse square root transformation of the BMI (y) is given as (y‟). The table
of coefficients and the table of analysis of variance are shown in Table 17 and 18.
y’ =
1
y
…. (e)
35
Table 17: Table of coefficients of the inverse square root transformation model
Predictor
Coef
SE Coef
T
P
0.237311
0.001644
144.34
0.000
0.0014973
0.0006176
2.42
0.015
-0.00051204
0.00001996
-25.66
0.000
Race_1
-0.006927
0.001466
-4.73
0.000
Race_2
-0.006953
0.001608
-4.32
0.000
Race_3
-0.008082
0.001353
-5.97
0.000
Race_4
-0.010615
0.001468
-7.23
0.000
Education Level_1
-0.005828
0.001239
-4.71
0.000
Education Level_2
-0.003845
0.001053
-3.65
0.000
Education Level_3
-0.0043845
0.0009460
-4.63
0.000
Education Level_4
-0.0051292
0.0009062
-5.66
0.000
Constant
Gender (1=m, 2=f)_1
Age (yrs)
Table 18: ANOVA for inverse square root transformation model
Source
DF
SS
MS
F
P
Regression
10
0.654686
0.065469
82.09
0.000
Residual Error
8367
6.672844
0.000798
Total
8377
7.327530
R-Sq R-Sq(adj)
8.90%
8.80%
The ANOVA shows that the model provided a better F value of 82.09 compared to 64.34 of the
new model. The model even shows a better R2 value of 8.9% compared to 7.1% of the new
model. The normal plot of residuals showed in the figure 12 in quite accurate with a few
outliers. The „fat pencil‟ test shows a fair amount of normality in this model. The model is
significant since the table of coefficients show that the p value of all the factors is less than 0.05.
36
Figure 12
4.3.3. Log to the base 10 transformation:
The mathematical representation of log to the base 10 transformation is shown in the equation
below. The log to the base 10 transformation of the BMI (y) is given as (y‟). This transformation
is used for analysing growth measurements as log function reduces the bigger values and
enhances smaller values.The table of coefficients and the table of analysis of variance are shown
in Table 19 and 20.
y’ = log10(y)
…. (f)
37
Table 19: Table of coefficients of log to the base 10 transformation model
Predictor
Coef
SE Coef
T
P
1.25103
0.00704
177.72
0.000
-0.007758
0.002644
-2.93
0.003
0.00209440
0.00008545
24.51
0.000
Race_1
0.029432
0.006275
4.69
0.000
Race_2
0.029315
0.006884
4.26
0.000
Race_3
0.034938
0.005793
6.03
0.000
Race_4
0.047234
0.006284
7.52
0.000
Education Level_1
0.026207
0.005303
4.94
0.000
Education Level_2
0.018101
0.004510
4.01
0.000
Education Level_3
0.020416
0.004051
5.04
0.000
Education Level_4
0.022958
0.003880
5.92
0.000
Constant
Gender (1=m, 2=f)_1
Age (yrs)
Table 20: ANOVA for log to the base 10 transformation model
Source
DF
Regression
10
SS
MS
F
P
11.3122 1.1312 77.37 0.000
R-Sq
R-Sq(adj)
8.50%
8.40%
Residual Error 8367 122.3315 0.0146
Total
8377 133.6437
The p values shown in the table of coefficients are less than 0.05 indicating the significance of all
the factors in the model. The ANOVA for the log to the base 10 transformation model shows a
good significance with better R2 value of 8.5 % compared to the R2 value of 7.1 % of the new
model developed previously. The model even provided a better F value of 77.37 compared to
64.34 of the new model. The normal plot of residuals showed in the Figure 13 is somewhat
accurate enough with few outliers. The „fat pencil‟ test shows some amount of non-normality in
this model.
38
Figure 13
4.3.4. Natural log transformation
The mathematical representation of the natural log transformation is shown in the equation
below. The natural log transformation of the BMI (y) is given as (y‟). The table of coefficients
and the table of analysis of variance are shown in Table 21 and 22.
y’ = ln( y)
…. (g)
39
Table 21: Table of coefficients of the natural log transformation model
Predictor
Coef
SE Coef
T
P
2.88060
0.01621
177.72
0.000
Gender (1=m, 2=f)_1
-0.017863
0.006088
-2.93
0.003
Age (yrs)
0.0048225
0.0001968
24.51
0.000
Race_1
0.06777
0.01445
4.69
0.000
Race_2
0.06750
0.01585
4.26
0.000
Race_3
0.08045
0.01334
6.03
0.000
Race_4
0.10876
0.01447
7.52
0.000
Education Level_1
0.06034
0.01221
4.94
0.000
Education Level_2
0.04168
0.01038
4.01
0.000
Education Level_3
0.047009
0.009327
5.04
0.000
Education Level_4
0.052862
0.008934
5.92
0.000
Constant
Table 22: ANOVA for the natural log transformation model
Source
DF
SS
MS
F
P
Regression
10
59.9761
5.9976
77.37
0.000
Residual Error
8367
648.5894
0.0775
Total
8377
708.5654
R-Sq
R-Sq(adj)
8.50%
8.40%
The table of coefficients shows that all the factors in the model are significant with p value lesser
than 0.05. The statistical characteristics of ANOVA for the square transformation show that the
model is significant. The model has a better R2 value of 8.5 % compared to the R2 value of 7.1 %
of the new model developed previously. The model even provided a better F value of 77.37
compared to 64.34 of the new model. The normal plot of residuals showed in the Figure 14 is
not accurate enough with several outliers. The „fat pencil‟ test shows does not show a fair
amount of normality in this model.
40
Figure14
4.3.5. Inverse transformation
The mathematical representation of the inverse transformation is shown in the equation below.
The inverse transformation of the BMI (y) is given as (y‟). The table of coefficients and the table
of analysis of variance are shown in Table 23 and 24.
y’ = 1
y
…. (h)
41
Table 23: Table of coefficients of the inverse transformation model
Predictor
Coef
SE Coef
T
P
Constant
0.0565544
0.0006838
82.70
0.000
Gender (1=m, 2=f)_1
0.0005077
0.0002569
1.98
0.048
-0.00021982
0.00000830
-26.48
0.000
Race_1
-0.0028696
0.0006096
-4.71
0.000
Race_2
-0.0029102
0.0006688
-4.35
0.000
Race_3
-0.0033073
0.0005628
-5.88
0.000
Race_4
-0.0042245
0.0006105
-6.92
0.000
Education Level_1
-0.0022855
0.0005152
-4.44
0.000
Education Level_2
-0.0014365
0.0004381
-3.28
0.001
Education Level_3
-0.0016505
0.0003935
-4.19
0.000
Education Level_4
-0.0020194
0.0003769
-5.36
0.000
Age (yrs)
Table 24: ANOVA for the inverse transformation model
Source
DF
SS
MS
F
P
Regression
10
0.117753
0.011775
85.34
0.000
Residual Error
8367
1.154434
0.000138
Total
8377
1.272187
R-Sq
R-Sq(adj)
9.30%
9.10%
The ANOVA for inverse transformation depicts a significant model which shows a better R 2
value of 9.3% compared to 7.1% of the new model. All the factors in the model are significant
with p value less than 0.05. The model provides a better F value of 85.09 compared to 64.34 of
the new model. The normal plot of residuals showed in the Figure 15 is quite accurate with a few
outliers. The „fat pencil‟ test shows a fair amount of normality in this model.
42
Figure15
4.4. Summary of Transformational Analysis:
Transformational analysis served the purpose of providing a better obesity model than the new
model developed in equation (c). Table 25 briefly summarizes all the transformation considered
in the analysis. The adequacies of each of the models were analyzed on the basis of their
respective R2 and F values as well as on the basis of the normality of the probability plots. All
the transformed models had higher R2 and F values but only the inverse transformation and
inverse square root transformation depicted a fair amount of normality on the basis of „fat pencil
test‟. Comparing the inverse transformation and inverse root transformation model on the basis
of their statistical characteristics of the model, the inverse transformation seems to be the best
model with the highest R2 and F values of 9.3% and 85.34 respectively. The regression equation
for the inverse transformation model is shown below.
43
Table 25: Summary of the R2 and F values of the transformation models
Transformation
New
Model (y)
Square
Root of (y)
Inverse
Square
Root of (y)
Log to the
base 10 of
(y)
Natural
log of (y)
Inverse of
(y)
R2 value (%)
7.1
7.9
8.9
8.5
8.5
9.3
F-Value
64.34
71.36
82.09
77.37
77.37
85.34
1/BMI = 0.0566 + 0.000508 Gender (1=m, 2=f)_1 - 0.000220 Age (years)
- 0.00287 Race_1 - 0.00291 Race_2 - 0.00331 Race_3
- 0.00422 Race_4 - 0.00229 Education Level_1
- 0.00144 Education Level_2 - 0.00165 Education Level_3
- 0.00202 Education Level_4
…. (i)
44
Chapter 5
Conclusion
5.1. Analytical Conclusion
According to the analysis, the inverse transformation model of BMI was significant with p value
< 0.05 and R-square of 9.3%. The statistical behavior of the Obesity model reveals that the RSquared (9.3%) of the model is almost same as that of the Adj R-Squared (9.1%). The results
show that factors age, race, gender and education level are the significant factors since their pvalues are less than 0.05. As predicted in the model, research has supported the effect of age,
race, gender and education level on the variation in BMI. Previous studies by DHHS have shown
that there hasn‟t been a correlation between obesity and the family income among Mexican
American, black children and adolescent. Paeratakul et al. (2002) found that greater percentage
of population in higher income class falls under the overweight category. A study conducted by
Salinsky et al. (2003) did not shown any significant trend between obesity and social status
amongst men. Hence, it is not quite surprising to find that family income is not a significant
factor.
According to the analysis shown in Table 12, 6.16% of the total female population (n=4184) was
class III obese compared to 3.14% of male population (n= 4183). Prevalence of obesity was
higher in females than in males in class II obese as well as extremely obese population. Amongst
the races, non-Hispanic Blacks were in higher percentages in class I, II and III obesity. 8.3% of
the Non-Hispanic blacks were extremely obese followed by 4.46 % Non-Hispanic white.
Percentage of population aged above 60 years was highest in class I and class II obesity. For the
population with BMI greater than 25, there was evident rise in percentage of obese individuals
with an increase in age. Class I and Class II obesity was more evident among individuals aged
45
greater than 60 years followed by individuals between 50-59 years and 40-49 years group. The
percentage of individuals who are at least college graduates is the minimum under extreme
obesity. Although there is not much significant data comparison in class II and III obesity on the
basis of education level, it is noticeable that class I obesity was more prevalent among population
with education less than 9th grade. The percentage of the richest section (3.39%) of the society
was least amongst class III obesity followed by the poorest section (3.90%). No significant
relations could be pointed out from the analysis of the family income of the population. This was
also evident from the obesity model as family income was not a significant factor with p value
greater than 0.05.
Although there has been a steep rise in the obesity, none of the studies have tried to mention the
relation of the level of obesity based on other non-BMI-related measures. There needs to be a
spread of awareness on the social as well as personal front on the control of obesity through
various health control programs. Assessing the trends in the rise in the obesity levels, adequate
education of the preventive measures, food intake control, and physical activities could provide
the much needed information for the development of obesity control programs to effectively
tackle this epidemic.
5.2.Future Improvements and Recommendations:
Obesity is a very complex problem that cannot be solved through any particular solution. There
should also be an initiative from every individual on the personal front. With the augment of
technology in household chores, there has been an increasing trend towards sedentary lifestyles.
Children and adolescents spend more than 2 hours watching television every day. Currently, the
government is working on areas which include formal regulations related to food labeling to
convey nutritional content, dietary guidelines to promote healthy eating habits, public awareness
46
campaigns, curricula development, and model educational programs to facilitate behavioral
change. Efforts relying primarily on information dissemination and education to change attitudes
and behaviors related to nutrition and physical activity are a major emphasis of government
activity to control obesity (Salinsky et al., 2003). Although there are various initiatives from the
government, an effective response is required action on many fronts of the society. Information
that facilitates healthy food and lifestyle choices, public awareness levels regarding the
importance of these choices, and behavioral and motivational programs to aid in weight control
and management are critical components for an effective strategy to reduce obesity. Whether
education is through labeling, mass media, professional guidelines, or community outreach
programs, all these efforts represent population-based attempts to increase awareness and support
healthy behaviors.
Companies have started promoting health care programs for employees and have started
evaluating the return on investment (ROI) on the basis of work productivity as well as employee
absenteeism. On the research front, efforts need to be taken to concentrate on the determination
of the prevalence of obesity among children (from birth to 18 years old). Other potential risk
factors such as health condition, physical activities, smoking, etc. can be considered in the
subsequent intervention efforts. Additionally, the effect of weight gain and the frequency of
diabetes, cardiovascular disorders, musculoskeletal injuries on healthcare costs and hospital
utilization must be adequately investigated.
BMI is not a reliable measure for children and may not be as useful for athletes or muscle-fit
individuals (military population). According to Biggard et al. (2003), analysis involving the
47
combination of BMI and waist circumferences strongly predicted all-cause mortality in middleaged men and women. Further efforts should be made to analyze obesity using other measuring
units of obesity like waist circumference, body fat index, waist-hip ratio and neck circumference.
A research on BMI cut-off values should be carried out to improve discrepancies in the study of
anthropometric data. Investigation should also be carried out to build sensitive cut-offs for the
recently used measuring units of obesity.
48
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7. Appendix:
Abbreviations:
ANOVA - Analysis of Variance
BMI – Body Mass Index
CDC – Center of Disease Control
DHHS – Department of Health and Human Services
NHANES - National Health and Nutrition Examination Survey
NHLBI - National Heart, Lung, and Blood Institute
NIH - National Institutes of Health
NCHS – National Center for Health Statistics
WC – Waist Circumference
WHO – World Health Organization
56