Intensive Care Unit

The Intensive Care Unit (ICU) is the specialized unit of a hospital that focuses on extremely severe and life-threatening medical issues (septic shock, organ failure, major trauma, etc). Patients admitted to the ICU require constant care and monitoring by highly-trained medical professionals and the use of advanced equipment.

Researchers are interested in the survival of patients admitted to the ICU. Patients with a low predicted probability of survival can be triaged to more medical resources and care, and patients with a high predicted probability of survival can be triaged to another unit of the hospital.

The file icu.csv contains information for a random sample of 150 patients at an Intensive Care Unit. Researchers are interested in predicting patient survival. This data is from the Data and Story Library (DASL).

• id: patient ID code
• survive: survival status (0 = patient died, 1 = patient survived to discharge)
• age: age (years)
• sex: sex (0 = male, 1 = female)
• infection: infection status (0 = no infection, 1 = infection suspected)
• sysbp: systolic blood pressure (mm of Hg)
• pulse: heart rate (beats per minute)
• emergency: admission status (0 = elective admission, 1 = emergency admission)

Exercises

1. Create three effective, well-labeled visualizations to explore the relationship between the variables below. Provide a brief one or two sentence comment on each.

   • age and survive
   • emergency and survive
   • sysbp and survive

2. Fit a logistic regression model with survive as the response variable with the predictors age, sysbp and emergency. Report the model output in tidy format.

3. Write out the equation of the fitted logistic regression model. You can use “pred-log-odds” for the response variable.

4. Provide an interpretation of \(\hat{\beta}_{\text{emergency}}\) in the context of the problem. Your interpretation should involve odds or odds ratios, not log odds.

5. Provide an interpretation of \(\hat{\beta}_{\text{age}}\) in the context of the problem. Your interpretation should be in terms of odds or odds ratios, not log odds.

6. An 87 year old patient is admitted in an emergency situation with a systolic blood pressure of 88 mm of Hg. What is this patient’s predicted log-odds of survival?

7. What is this patient’s predicted probability of survival?

8. The patient described in Exercises #6 and #7 survived. Is this result surprising? Answer with justification.

9. A patient is admitted in an emergency situation with a systolic blood pressure of 80 mm of Hg. How young must the patient be in order to have a predicted probability of survival at least 0.50 based on the logistic regression model?

10. The file icu_test.csv contains a test dataset of 50 patients not included in the original data. Fill in the code below to find the model predictions for the 50 patients, and then calculate their predicted probabilities.

icu_test <- read_csv("data/icu_test.csv")
_____ <- augment(_____, newdata = icu_test)

Submission

Knit to PDF to create a PDF document. Knit and commit all remaining changes, and push your work to GitHub. Make sure all files are updated on your GitHub repo.

Please only upload your PDF document to Gradescope. Associate the “Overall” graded section with the first page of your PDF, and mark where each answer is to the exercises. If any answer spans multiple pages, then mark all pages.