Lab 5 - Health Risks - Instructions-3

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University of Illinois, Urbana Champaign *

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Statistics

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Apr 3, 2024

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Lab 5 – Comparing Health Risks NAME 1 – NETID NAME 2 – NETID [if applicable] NAME 3 – NETID [if applicable] Formatting Instructions - Please submit your lab report as a pdf to Gradescope. - When you upload to Gradescope, please match pages with the question number . - Be sure that all group members are added in your submission to Gradescope (click view/edit group on the top right of the page once shown your final submission after matching pages). Assignment Overview - We’ll be investigating the heart dataset, which collected data on the health factors of 303 patients being screened for heart disease. We’ll use this data to address the following three research questions (one on each page): o Do people with fasting blood sugar levels above 120 mg/dL have a higher risk for heart disease? o Do people who have experienced an exercise induced angina have a higher risk for heart disease? o Do people who experience exercise induced anginas have different cholesterol levels on average? STEP 0 - Pre-lab work o Complete the pre-lab tutorial (Comparing Groups) for Lab 5 first: https://stat212-learnr.stat.illinois.edu/ - Download the heart.csv file to your computer and then import into your RStudio session. - Create a new R script (or use the RMarkdown file if you are using that option) - Remember to library(tidyverse) so that you can use the ggplot function! Variables Each row of this dataset represents one patient being screened, and the following variables were documented for each patient: - age: age in years - sex: biological sex (0 if female, 1 if male) - cp : chest pain type (0 if typical angina, 1 if atypical angina, 2 if non-anginal pain, 3 if asymptomatic) - exang: binary variable documenting whether patient experienced exercise induced angina - trestbps: resting systolic blood pressure (in mm/Hg on admission to hospital) - chol: serum cholesterol (mg/dL) - fbs: binary variable documenting whether fasting blood sugar was high (“yes” if > 120 mg/dL and “no” if <= 120 mg/dL) - restecg: resting electrocardiographic results (0 if normal, 1 if having ST-T wave abnormality, 2 if showing probable or definite left ventricular hypertrophy) - thalach: maximum heart rate achieved - oldpeak: ST depression induced by exercise relative to rest - slope: the slope of the peak exercise ST segment - ca: number of major vessels (0-3) colored by flourosopy - target: Whether patient was found to have angiographic disease status (heart disease) as determined by amount of blood vessel narrowing (“positive” if heart disease diagnosis, “negative” if no heart disease diagnosis)

Research Question 1: Do people who are diabetic (fasting blood sugar levels above 120 mg/dL) have a higher risk for heart disease? Question 1 (5pts) : Let’s first investigate visually. Create a 100% stacked barplot to compare the proportion of patients with heart disease based on whether their fasting blood sugar level was above 120 mg/dL. Include an image of your barplot in the report and Include your R code - One bar should represent those who are diabetic, and the other should represent those who are not. The bar should be shaded to reflect what proportion in each group have heart disease. - Give the bars a black border, and adjust the width to be between 0.2 and 0.5 - Add an appropriate x axis label, y axis label, and title. Question 2 (5pts) : Now, let’s use a test for two proportions to make a statistical inference. Using a pipe, create a frequency table to get counts of how many people have or don’t have heart disease based on whether they are diabetic or not. Copy or screenshot the frequency table into your report and Include your R code - If done correctly, this table will have 4 rows. - You can screenshot in the table exactly as it appears in R output, or you can re-format it in your document if you wish to. Run a proportions test to answer research question 1 and Include your R code. - Tip: Is this a directional or non-directional test? Read the research question again! - Remember that you need to enter two vectors into your code, the first vector includes the numbers in each group who have heart disease, and the second vector includes the totals for each group. - Copy+paste or screenshot the summary output from your proportions test. In your own words , interpret the results and make a conclusion in context. A full response should: - Identify the proportion with heart disease in each group - Identify the p-value - Briefly summarize your answer to our first research question using these results.

Research Question 2: Do people who have experienced an exercise induced angina have a higher risk for heart disease? Question 3 (5pts) : Repeat the procedures for Question 1, but with this new predictor variable. Include an image of your 100% stacked barplot in the report and Include your R code Question 4 (5pts): Follow the same procedures in Question 2 to address our second research question statistically. Copy or screenshot the frequency table into your report and Include your R code Run a proportions test designed to answer your second research question and Include your R code. In your own words , interpret the results and make a conclusion in context (same as Question 2). Question 5 (5pts): Let’s now estimate the relative risks for heart disease for the two situations we explored. Rather than code this computationally in R, we will use an online calculator ! See Calculator link below: Report the relative risk (and 95% confidence interval) for heart disease when patient is diabetic as compared to when they are not diabetic. Report the relative risk (and 95% confidence interval) for heart disease when the patient had experienced an exercise induced angina as compared to if they hadn’t. Use any online calculator you’d like, but here is the calculator we used in class : https://istats.shinyapps.io/Association_Categorical/ . Web search “Art of Stat Web Apps” and choose “Association Between Two Categorical Variables”.  Choose contingency table setup in the first drop-down.  Have your rows represent your explanatory variables (diabetes status, or angina status), and columns represent your response variable (heart disease status). Labels are optional, but might be helpful to keep track of what to plug in!  Be sure to choose ratio of proportions from the drop-down and check the “95% confidence interval” option below.

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Let’s next consider cholesterol levels as our target response variable. Notice that cholesterol will be a numeric variable, so our approach to this question will be slightly different. Research Question 3 : Do people who experience exercise-induced anginas have different cholesterol levels on average? Let’s say the researchers believe either a drop or an increase in cholesterol is possible and noteworthy to report! Question 6 (5pts) : Create a jittered plot to compare cholesterol levels between the angina and no angina groups. Include an image of your jittered plot in the report and Include your R code - Keep the width of your jitter small (like between 0.02 and 0.10) - Color each group of points differently (one color for “No” and one color for “Yes”) - Add an appropriate x axis label, y axis label, and title Question 7 (5pts) : Complete a t-test to address the research question posed. Even though we have enough observations such that a z-test would be reasonable, it’s easier in R to just run a t-test, and the results will be approximately the same! We will not assume equal variances (software can handle this situation easier, and this is the “safer” testing option). Copy or screenshot the summary output from your t-test In your own words , interpret the results and make a conclusion in context. A full response should: - Identify the average cholesterol level for each group - Identify the p-value - Briefly summarize how this result helps you address research question 3.