Biostatistics Assignment 2: Investigating the Relationship between Pulse Rate and BMI

CURTIN UNIVERSITY
SCHOOL OF PUBLIC HEALTH
Epidemiology & Biostatistics
Epidemiology & Biostatistics (MPH406)
Index No. EPID6001 (EPID6002)
Assignment 2 Semester/Session 2, 2018
Declaration
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not previously been submitted for assessment. I have carried out the analyses, interpreted and
answered all questions in this assignment myself. This work complies with Curtin University rules
concerning plagiarism and copyright. I understand that all forms of plagiarism, cheating and
unauthorised collusion are regarded seriously by the University and could result in penalties
including failure and possible exclusion from the University. I have retained a copy of this
assignment for my own records.
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Assignment 2: BIOSTATISTICS
(Total marks 50 - to be scaled to 25%)
Question ONE
(Total: 23 marks)
In a study a fictitious random sample (Assign2Pulse2018S2.dta) was obtained with information of
pulse rate, gender, smoke status, level of activity, and BMI measured for 80 subjects. One of the
aims for the study is to understand the difference in pulse rate between overweight and non-
overweight people, and subjects’ gender differences need to be accounted for as well. In this
question, you are given one continuous dependent variable Y (pulse) and two categorical
independent variables (gender and BMICat) as follows:
Table 1
Variable Description
pulse Pulse rate beat per minute
gender 1 = male, 2 = female
BMICat 1 = non-overweight, 2 =overweight
Your task is to investigate the relationship between pulse and BMICat using appropriate procedures
and techniques, accounting for gender in the analyses as a potential effect modifier. Use a
significance level α of 5%.
Hint:
 You may find helpful to follow the instructions in Lab 1 for t test.
 You may find helpful to follow the strategy for analyses given in Module B6 and
Computing Lab 6.
1. (2 marks) Obtain the sample mean pulse rate, standard deviation (both with 3 decimal
places) and number for each BMICat group against each gender group and fill the following
table. Calculate and Comment on the difference in the mean pulse between non-overweight
and overweight subjects for each gender group in relation to a possible interaction between
gender and BMICat. (No Stata output(s) are required for this question)
Pulse
Gender BMI Mean SD N
Female Non-overweight 75.793 11.245 29
Overweight 91.000 7.071 2
Total 76.774 11.581 31
Male Non-overweight 71.056 11.115 36
Overweight 66.462 6.839 13
Total 69.837 10.294 49
Total Non-overweight 73.169 11.337 65
Overweight 69.733 10.872 15
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2. (4 marks) Test the hypothesis that the population mean pulse rate is the same for non-
overweight and overweight subjects.
(No Stata output(s) are required for this question)
i) Hypotheses: (1 mark)
HO: The average pulse rate is not significantly different for non-overweight and
overweight subjects.
HA: The average pulse rate is significantly different for non-overweight and
overweight subjects.
ii) Name the t test you used for the hypothesis (0.5 marks): Independent Samples t-test
iii) P value of the t test you used (0.5 marks): 0.2898
iv) Conclusion of the hypothesis test: (2 marks)
Since the p-value (0.2898) is greater than the 5% significance level, we fail to reject the
null hypothesis and conclude that the average pulse rate is not significantly different for
non-overweight and overweight subjects. That is, there is no significant evidence to
conclude that the average pulse rate for non-overweight and overweight subjects are
different.
3. (7 marks) Now assess the difference the population mean pulse rate between non-
overweight and overweight subjects using a multiple regression model, accounting for
gender in the analyses as a potential effect modifier.
i. Name the multiple regression model which is appropriate for this question. Why?
Linear regression; this is because the dependent variable (pulse rate) is continuous.
(1 mark)
ii. The mean plots for this question are given below:
65 70 75 80 85 90
(mean) pulse
Non-OW OW
BMICat
male female
65 70 75 80 85 90
(mean) pulse
Male Female
gender
non-overweight overweight
Based on the mean plots given, make a justification on whether the interaction term
between BMICat and gender should be included and assessed in your model. (1 mark)
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The interaction term between BMICat and gender should be included and assessed in
the model since the interaction seems to be significant.
iii. Fit the model you recommended for pulse on BMICat and gender. (2 marks)
Attach relevant Stata output (eg., ANOVA table) here
_cons 75.7931 1.96104 38.65 0.000 71.88735 79.69885
1 1 -9.331565 3.524841 -2.65 0.010 -16.35189 -2.311236
1 0 15.2069 7.720624 1.97 0.053 -.170059 30.58385
0 1 -4.737548 2.635069 -1.80 0.076 -9.985743 .5106468
male
overweight#
pulse Coef. Std. Err. t P>|t| [95% Conf. Interval]
Total 10023.95 79 126.885443 Root MSE = 10.561
Adj R-squared = 0.1211
Residual 8475.87828 76 111.524714 R-squared = 0.1544
Model 1548.07172 3 516.023907 Prob > F = 0.0050
F( 3, 76) = 4.63
Source SS df MS Number of obs = 80
. reg pulse overweight# male
iv. Based on the ANOVA table in Question iii, test the hypothesis that there is no
interaction in the population between BMICat and gender, including your interpretations
and conclusions (1 mark).
The ANOVA table clearly shows that there is significant interaction in the population
between BMICat and gender (p < 0.05). The p-value for the ANOVA test is less than 55
level of significance hence leading to rejection of the null hypothesis thus we conclude
that there is significant interaction in the population between BMICat and gender.
v. Comment on whether a further model is necessary by selecting an answer below (2
marks):
a) Yes, then which variable should be removed from the model? Why?
Attach Stata output (eg., parameter estimation table) here
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b) No, there is not necessary to have a further model. Why?
Attach Stata output (eg., parameter estimation table) here
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