# Logistic Regression

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.

e. Which of the 3 adjusted odds ratios computed in part (d) are "statistically significant"?

f. How do the resulting adjusted odds ratio estimates and confidence intervals from part (d) compare across the 3 sets of logistic regression models with additional predictors?

g. How could you use these results to assess whether the relationship between death in ICU patients and infection at the time of admission is confounded by other patient characteristics?

h. What type of study design is this? Would it be possible to use the results from the 4th logistic regression model (with infection status, age, CPR, and race as predictors) estimate the probability (risk) of death for various groups of patients based on the reported patient characteristics?

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e. Which of the 3 adjusted odds ratios computed in part (d) are "statistically significant"?

Parts a - d can be found in posting 108519. Part d is included below in italics:

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.

For the other 3 regression models, we will calculate the odds ratio and the CI for it using the methods from parts b and c.

95% CI odds ratio 95% CI for odds ratio

Model 2 (0.0703, 1.5297) 2.2255 (1.0728, 4.6168)

Model 3 (-0.0494, 1.4494) 2.0137 (0.9518, 4.2606)

Model 4 (-0.0894, 1.4094) 1.9348 (0.9145, 4.0935)

Each of the ...