﻿ Multi-Level Regression

Lecture: Multilevel Regression

• Read Chapter 14 in Statistical Analysis of Electronic Health Records by Farrokh Alemi, 2020

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? Please note that because of sample size issues, the purpose of this analysis is not to generalize to all tertiary centers or burn units but to estimate the probability of the survival at the five hospitals listed, after controlling for case mix differences.  In this sense, this is a study of the entire population and not a study of a sample of the population.

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). Hospitals A and B are part of tertiary centers. Hospitals C, D, and E are not tertiary centers. Hospital B is the only hospital with a burn unit.
 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.

Resources for question 1:

Optional Question 2: In this problem, we approach multi-level modeling through SQL, preferrably within R. In particular, we address question 1 but this time we use SQL instead of regression. This is an optional assignment that you can do to understand better the purpose of multi-level analysis.  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 by examining survival in a strata where all conditions are absent.  If the hospital's probability of survival cannot be estimated in this stratum, then measure it as the average of probabilty of survival for the hospital in strata with one more, or one less, condition.
• Examine mortality rates at the center as a function of center's distance being above average and satisfaction of the patients in the center being above average.
 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

Resources for question 2:

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.

Resources for question 3:

 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