From the Introduction to Modern Statistics (IMS) textbook, complete
the following exercises:
- Ch 5.10, exercises: 5.6, 5.14, 5.22
Also complete the additional questions given below:
Question #1: Researchers recruited 451 patients with
a high level of cardiovascular risk. They split these patients into two
groups, a treated group that received stents (small mesh tube placed
inside of vulnerable arteries) and medical management (medications,
lifestyle coaching, etc.), and a control group that only received
medical management. Of the 224 patients in the treatment group, 45
suffered a stroke within the first year of the study, while only 28
patients in the control group had a stroke during this time.
- Part A: Use the given information to find the
odds of stroke in each group
- Part B: Find the odds ratio comparing the odds of
stroke in the treatment (stent) group compared to the odds of stroke in
the control group. Using this descriptive statistic, treated patients
were how many times more likely to have a stroke in the first year of
the study?
- Part C: Find the odds of “no stroke” in each group,
then calculate the odds ratio comparing the odds of “no stroke” in the
control group relative to the treatment group. Using this descriptive
statistic, control patients were how many times more likely to not have
a stroke in the first year of the study?
- Part D: Use the given information to find the risk
of stroke in each group.
- Part E: Calculate the relative risk of
stroke in the treated group compared to the control group. Using this
descriptive statistic, treated patients were how many times more likely
to have a stroke in the first year of the study?
- Part F: Use the given information to find the risk
of “no stroke” in each group. Then, calculate the relative risk
of “no stroke” in the control group compared to the treated group. Using
this descriptive statistic, control patients were how many times more
likely to not have a stroke in the first year of the study?
- Part G (optional, extra credit): The odds ratio is
known as a symmetric measure of association (you
may read this link for details). Is relative risk a symmetric
measure? How do Parts A-F relate to the symmetry of the odds ratio and
possible symmetry of relative risk.
Question #2: The data read into R by
the code given below contains the results of a randomized experiment
conducted by surgeons at Harvard Medical School to compare a “low-flow
bypass” and “circulatory arrest” surgical approaches in the treatment of
infants born with congenital heart defects. The study’s recorded
outcomes are Psychomotor Development Index (PDI), a composite score
measuring physiological development, with higher scores indicating
greater development, and Mental Development Index (MDI), a composite
score measuring mental development, with higher scores indicating
greater development.
inf_heart = read.csv("https://remiller1450.github.io/data/InfantHeart.csv")
- Part A: Create a two-way frequency table displaying
the relationship between the variables
Sex and
Treatment. Does the infant’s sex appear to be associated
with the treatment they received? Support your answer using an
appropriate descriptive statistic calculated from your frequency
table.
- Part B: Create a data visualization showing the
distribution of PDI scores for all infants in the study. Briefly
describe this distribution, being sure to address all of the important
characteristics discussed in our data
visualization lecture
- Part C: Create a data visualization showing the
distributions of PDI scores for each type of surgery. Does there appear
to be an association between type of treatment and PDI?
- Part D: Find the mean, median, standard deviation,
minimum, and maximum of the variable PDI for both groups (types of
surgery).
- Part E: Filter the data to only include male
infants, then recalculate the mean PDI scores in each group. How do
these means compare to those found using the entire data set In Part D?
Based upon your findings in Part A, is this surprising?
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Submission instructions
- Use R Markdown to create a document containing your answers and any
R code used.