MARY MAYENGO BIOSTATISTICS MIDTERM. SECTION 005
Case Study 1
According Stefano lazar et al (2010) as individuals age there is a decline in fat free mass
or muscle and therefore basal metabolic rate. Based on this finding one can assume that a
slower metabolic rate as one ages will result in increase in Body Mass Index (BMI).
However, other factors such as stress both emotional and work related have been associated with variations in BMI, Ariana M Chao et al 2017 found that chronic stress, high
cortisol and insulin were associated with weight gain. The presence of social support is
thought to mitigate chronic stress and thus influence BMI.
In this study we investigate the null hypothesis “BMI does not increase with increase in
age” and the alternative hypothesis “BMI increases with increase in age,” while controlling for confounders such as stress, emotional support. The confounder stress is represented by jobs demand and emotional support represented by family social support from
family and sympathy scale. The information from this study is from the National Survey
of Midlife Development in the United States (MIDUS II) for 2004-2006. Analysis is done
with multivariate regression with BMI as the dependent variable and centering of all independent variables using an alpha of (0.05).
Equation for model: 1; b+ b1 (age_centred) + b2 (job demands_centred) + b3 (sympathy_centred)
Equation for model 2: b+ b1 (age_centred) + b2 (job demands _centered) + b3 (sympathy
_centered) + b4 (social support _centered)
Key
b – the BMI for the average age at average job demand, average sympathy and social
support in the sample.
b1- the change in BMI for a unit change in age when other factors are constant.
b2 - the change in BMI for a unit change in job demands when other factors are constant.
b3 - the change in BMI for a unit change in sympathy when other factors are constant..
b4 - the change in BMI for a unit change in social support when other factors are constant..
METHODS AND ANALYSIS
The information in the MIDUS II was obtained through phone interviews conducted by
the University of Wisconsin, information for a total of 1876 individuals was used in this
analysis before data cleaning and 1850 after data cleaning.
Univariate Analysis
The BMI was determined using the weights and heights of individuals. The average
BMI was 27.6 with a range of 14.23 – 45.19 and standard deviation of 4.98. the age was
determined from the date of birth, the average age was 52.6 ,and range was 32- 82 years
MARY MAYENGO BIOSTATISTICS MIDTERM. SECTION 005
and standard deviation 10.20. Jobs demands were assessed on a scale of 5 – 25 the mean
for this variable was 14.8 with a standard deviation of 3.24. The sympathy determined
from a sympathy scale that ranged between 1-7 with an average
4.6 and standard deviation of 0.93. Social support from family was assessed using a social support scale with a range of 1-4 ,the mean social support was 3.5 and standard deviation 0.59.
Table 1
variable
mean
Standard
deviation
Range
BMI
27.6
4.98
14.23-45.19
Age
52.6
10.20
32-82
Sympathy
4.6
0.93
1-7
Job demands
14.8
3.24
5-25
Social support
3.5
0.59
1-4
Bivariate Analysis
The bivariate analysis was done using Pearson’s correlation given that this was continuous data that satisfied assumptions of linearity. There was a small insignificant positive
correlation between BMI and Age ( r = 0.0154 p = 0.506), small significant positive correlation between BMI and Job Demands (r = 0.05 p = 0.031), small significant negative
correlation between BMI and social support ( r = -0.084 p = 0.0003), and a small insignificant negative correlation between BMI and sympathy ( r = -0.029, p = 0.208).
Table 2
variable
Pearson’s correlation
P value
Age
0.0154
0.506
Sympathy
-0.029
0.208
Job demands
0.05
0.031
Social support
-0.084
0.0003
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Multivariate Analysis
After centering of all independent variable; age, sympathy, job demands and social support, two models of models of multivariate regression were run with BMI as the outcome
variable. The first model consisted of centered age, sympathy and job demands as the independent variables to give the intercept relevance during interpretation. Model assumptions such as of data points linearity, normal distribution of residuals, homoscadasity
and absence of multicollinearity were tested as shown in fig 1, fig 2, fig 3, fig 4 respectively. Absence of influential outliers , independence of data points and absence of multi
linearity were met after dropping 25 values that were Influential outliers; with standardized residuals greater than cooksd. The second model was run using 4 independent variables including social support. All model assumptions that is normality of residuals, homoscadascity and absence of multicollinearity were tested only as shown in fig 5, fig
6 ,fig 7 and fig 9 respectively. Absence of influential outliers , independence of data
points and absence of multi linearity were met.
Interpretation for model 1
The multilinear regression with standardized beta coefficients was significant ( F(3,
1847)= 3.3 p = 0.0188 adjusted R squared = 0.0038). the constant is the BMI at average
age, job demand and sympathy was 27.6 significant with ( p < 0.01, SE = 0.116 ). The
increase in BMI for every unit change in age while controlling for other variables was an
insignificant 0.018 (p = 0.124, SE = 0.011 beta = 0.038). when other variables are kept
constant there is a significant increase in BMI for every unit change in job demands of
0.104 (p = 0.005 SE = 0.037 beta = 0.067). There is a decrease in BMI with every unit
change in sympathy of -0.193( p = 0.123 , SE = 0.125 beta = -0.036) that is insignificant
while other factors are kept constant. Job demand is the best predictor of BMI given that
it has the highest beta coefficient of 0.067. the variance in BMI accounted for by this
model is 0.38%. The unique contributions of all the independent variables are insignificant as shown in table 3 below.
Equation ; BMI = 27.6 + 0.104(job demands_centred) + 0.018(age_centred) –
0.193(sympathy_centred).
Table 4
variable
coefficient Standardized P value
coefficients
Standar
d error
Semi
partial
correlation
&(pvalue)
MARY MAYENGO BIOSTATISTICS MIDTERM. SECTION 005
Age
0.018
0.038
0.124
0.005
0.036
(p=0.124)
Job demands
0.104
0.067
0.005
0.011
-0.0358
(p= 0.123)
sympathy
-0.193
-0.036
0.123
0.125
0.065
(p = 0.006)
F
statistic(3,1847)
= 3.3
Adjuste
dR
squared
= 0.0038
P value =
0.0188
Model 2
variable
coefficient Standardized P value
coefficients
Standar
d error
(SE)
Semi
partial
correlation
&(pvalue)
Age
0.019
0.039
0.109
0.120
0.044
(p = 0.060)
Job demands
0.088
-0.026
0.018
0.037
0.056
(p =0.016)
Social support
-0.639
-0.077
0.001
0.196
-0.081
( p=0.0005)
sympathy
-0.143
-0.027
0.256
0.126
-0.029
(p = 0.204)
F
statistic(3,1847)
= 5.16
Adjuste
dR
squared
=
0.0089
P value =
0.0004
The model of multivariate regression with standardized beta coefficients with BMI as the
outcome variable and centered ;social support, job demands, sympathy and age is signif-
MARY MAYENGO BIOSTATISTICS MIDTERM. SECTION 005
icant ( F(4,1846) = 5.16 , p = 0.0004 , R squared = 0.0089). The intercept is the BMI at
average age, job demand, social support and sympathy is 27.6 and
significant. There is a non-significant increase in BMI of 0.019(p = 0.109, SE = 0.120,
beta = -0.039) for every unit increase in age when other factors are constant. When Job
demands increases by 1 unit there is significant 0.088 ( p = 0.018 ,SE = 0.037 beta =
0.039) in BMI when other variables are controlled for. There is a significant negative relationship between social support and BMI with -0.639(p = 0.001 SE = 0.196 beta = 0.077) decrease in BMI for every unit increase in social support when other factors are
controlled for. The unit decrease of BMI of -0.143( p = 0.256 , SE = 0.126 beta = -0.027
) for every unit change in sympathy was insignificant. Overall social support is the beat
predictor of BMI with highest standardized beta of – 0.077. The variance in BMI accounted for by the model is o.89%. The unique contributions of each variables are indicated by the semi partial correlation shown in the table above.
Equation; BMI = 27.6 + 0.088(job demands_centred) + 0.019(age_centred) – 0.143(sympathy_centred) - 0.639 (social support_centred)
CONCLUSION
We cannot reject the null hypothesis, there is no significant relationship between age and
BMI. Social support from family improves the model fit as indicated by the increment in
adjusted R squared from 0.0038 to 0.0089. social support and jobs demands are the only
significant predictors of BMI.
MARY MAYENGO BIOSTATISTICS MIDTERM. SECTION 005
APPENDIX
q-q plot shows tailing and absence of normal distribution of residual for model 1
Fig 1
!
scatter plot shows absence of absolute homoscadasity for model 1
fig 2
!
multicollinearity test ( assumption met)
fig 3
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!
fig 4
table of VIF & 1/VIF for model 1.
variable
VIF
1/vif
Age centered
1.12
0.892
Job demands centered
1.09
0.915
Sympathy centered
1.03
0.972
1.08
MARY MAYENGO BIOSTATISTICS MIDTERM. SECTION 005
q-q plot shows tailing and absence of absolute normal distribution of residual for
model 2
Fig 5
!
!
scatter plot shows absence of absolute homoscedasity for model 2
fig 6
MARY MAYENGO BIOSTATISTICS MIDTERM. SECTION 005
fig 7
table of VIF & 1/VIF for model 2.
variable
VIF
1/vif
Age centered
1.12
0.891
Job demands centered
1.11
0.900
Social support
1.04
0.960
Sympathy centered
1.04
0.966
Mean vif
1.08
REFERENCES
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Between Basal Metabolic Rate, Gender, Age, and Body Composition in 8,780 White
Obese Subjects
Obesity Reasearch Journal vol 18 issue 1 P 71-18 derived from
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Ariana M. Chao,
Ania M. Jastreboff ,Marney A. White,
Carlos M. Grilo,
Rajita Sinha 2017 Stress, cortisol, and other appetite-related hormones: Prospective prediction of 6-month changes in food cravings and weight. Obesity Reasearch Journal/
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