Lecture: Multilevel Regression
Assigned Reading
- 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.
- 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
- 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 |
- 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
|
More
For additional information (not part of the required reading), please see the following links:
- A practical guide to multi-level modeling
PubMed►
This page is part of the HAP 819 course on Advanced Statistics organized by Farrokh Alemi PhD
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