# Lecture: Multilevel Regression

• Read Chapter 14 in Statistical Analysis of Electronic Health Records by Farrokh Alemi, 2020
• Practice based multilevel regression Read►

## Assignment

Submit assignments in Blackboard. Include in the first page a summary page.  In the summary page write statements comparing your work to answers given or videos.  For example, "I got the same answers as the Teach One video for question 1."

Question 1: The following simulated data show the survival of patients in two tertiary medical centers and 3 community hospitals.  Should ambulances take trauma victims to tertiary medical centers, by passing community hospitals? Data► R Code► Answer by Debora Vittorio►

1. Predict patient survival rates using patient-level variables:  (a) Presence of severe burns, (b) Head injury, (c) More than 65+ years old, (d) Male gender.  Identify the intercept for each hospital
2. Regress unexplained variation in survival probability on features of the hospital, including whether it is a tertiary medical center (Yes=1, No=0), or has a dedicated burn unit (Yes=1, No=0).

 Hospital Tertiary Center Has Burn Unit A 1 0 B 1 1 C 0 0 D 0 0 E 0 0
3. Report the meaning of these two related regressions.

Question 2: In this problem, we approach multi-level modeling through SQL.  In particular, we address question 1 but this time we use SQL instead of regression.  These steps could be helpful:

• Select the data for one of the medical centers and contrast it to the average of other centers.
• Use SQL to calculate survival rate for the hospital and the average of other hospitals across strata.  Each stratum is a combination of patient conditions.
• Estimate the survival rate for each hospital at the situation where all patient conditions are absent.  This is done in two steps.  First, regress survival at one hospital on survival at other hospitals.  The intercept for this regression is the estimated survival for the hospital when all patient conditions are absent.
• Regress survival rates at different hospitals on distance and percent satisfied at the hospital.
• Examine mortality rates at the center as a function of center's distance to referral source and satisfaction of the patients in the center.
 Medical Center Average Travel Distance Percent Satisfied Hospital 1 50 79 Hospital 2 80 82 Hospital 3 70 80 Hospital 4 70 79 Hospital 5 80 79 Hospital 6 70 83 Hospital 7 80 81

Use the instructor's last name as the password for the data.

Question 3:  Using multi-level modeling, calculate the expected length of stay for the clinician and peer group, after removing the effects of previous Myocardial Infarction (MI) and Congestive Heart Failure (CHF).  Compare the performance of the clinician to the peer provider using the intercepts estimated for each group.

 Clinician's Patients Peer Provider's Patients Case Previous MI CHF Length of stay Case Previous MI CHF Length of stay 1 MI CHF 6 1 MI CHF 5 2 MI No CHF 5 2 MI CHF 5 3 MI CHF 6 3 No MI CHF 4 4 MI CHF 6 4 No MI No CHF 3 5 MI CHF 6 5 No MI CHF 4 6 MI No CHF 5 6 No MI CHF 4 7 MI CHF 6 7 MI CHF 5 8 MI No CHF 5 8 MI CHF 5 9 MI CHF 6 9 MI CHF 5 10 MI No CHF 5 10 MI CHF 5 11 MI CHF 6 11 MI CHF 5 12 No MI CHF 4 12 No MI No CHF 3 13 No MI CHF 4 13 No MI CHF 4 14 No MI CHF 4 14 No MI CHF 4 15 MI CHF 6 15 No MI CHF 4 16 MI CHF 6 16 No MI CHF 4 17 MI CHF 6 17 No MI CHF 4 18 MI No CHF 5 18 No MI No CHF 3 19 MI No CHF 5 19 MI No CHF 4 20 MI CHF 6 20 MI CHF 5 21 MI CHF 5 22 MI CHF 5 23 MI No CHF 4 24 No MI CHF 4