# Supplement to Multilevel Regression Chapter

## Assignment

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►

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.  In particular, for each 2 medical centers follow these steps:

1. Select the data for the medical center.
2. Use SQL for Level 1 model:
• In temporary table #Cancer, calculate the probability of mortality for patients with cancer at different combination of comorbidities (called strata).  Call the probability "Probability of Strata + Cancer".  You can accomplish this by selecting the probability where lung cancer =1 and grouping by concatenation of all comorbidities.  To concatenate string variables you can use the + sign.
• In temporary table #NoCancer, calculate the probability of mortality for patients without cancer at different strata.  Call the probability "Probability of Strata + No Cancer".
• Join the tables #Cancer and #NoCancer on Strata.
3. Use Regression for Level 2 model:
• Regress the "Probability of Strata + Cancer" on "Probability of Strata + No Cancer".
4. Use the intercept as the impact of cancer in the Medical Center.
5. 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 Distance % Satisfied Center1 50 79 Center2 80 82 Center3 70 80 Center4 70 79 Center5 80 79 Center6 70 83 Center7 80 81

Use the instructor's last name as the password for the data. Data► Shukri's Video Part 1► Shukri's Video Part 2► Shukri's SQL Code► Answer by Jehanzeb► Answer by Shukri & Lavanya►

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 clincian to the peer provider using the intercepts estimated for each group.  Answer by Jehanzeb► Answer by Shukri & Lavanya►

 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

## More

For additional information (not part of the required reading), please see the following links:

1. A practical guide to multi-level modeling PubMed►