# Logistic Regression/Odds Ratio

1. A random sample of 200 patients admitted to an adult intensive care unit (ICU) was collected to examine factors associated with death during hospital stay for ICU patients. Data was also collected on patient's age (in years), race, whether the patient had an infection at the time of ICU admission, and whether the patient had CPR administered prior to the hospital admission. Of specific interest is whether or not infection at the time of admission is associated with increased probability of death during hospital stay. Logistic regression was employed to help answer the substantive question. Below find the estimated coefficients for infection status at time of admission from 4 different logistic regression models all relating the probability of death in the ICU to patient characteristics.

a. What is the direction of the relationship between the probability of death and patients infection status in this sample of 200 patients? Is this direction consistent across the four logistic regression models presented above?

b. Compute a 95% CI for the (unadjusted : ie, from the first model listed) coefficient of infection status (at the population level) based on the above results.

c. Compute the estimated unadjusted odds ratio of death in the ICU for patients admitted with an infection relative to patients admitted with no infection. Give a 95% confidence interval for this odds ratio, and interpret in words.

d. For all 3 regression models which include infection status and other patient characteristics as predictors/covariates:

i. estimate the adjusted odds ratio of death for patients with infection at the time of ICU admissions relative to patients without infection at the time of admission

ii. compute the 95% confidence interval for the relative odds (odds ratio) of death for patients with an infection at time of admission as compared with those without an infection.

See attached file for full problem description.

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#### Solution Preview

1. A random sample of 200 patients admitted to an adult intensive care unit (ICU) was collected to examine factors associated with death during hospital stay for ICU patients. Data was also collected on patient's age (in years), race, whether the patient had an infection at the time of ICU admission, and whether the patient had CPR administered prior to the hospital admission. Of specific interest is whether or not infection at the time of admission is associated with increased probability of death during hospital stay. Logistic regression was employed to help answer the substantive question. Below find the estimated coefficients for infection status at time of admission from 4 different logistic regression models all relating the probability of death in the ICU to patient characteristics.

a. What is the direction of the relationship between the probability of death and patients infection status in this sample of 200 patients? Is this direction consistent across the four logistic ...

#### Solution Summary

The probability relationship of death and patients infection status is discussed. The 95% confidence interval for the relative odds is found.