Lecture: Multilevel Regression  

 

Assigned Reading

  • Multilevel regression Video► Read►

Assignment

Question 1: The following data provides information on long cancer mortality at different medical centers on a large set of patients.  Medical centers claim that they have higher or lower risk for lung cancer mortality because of patients' comorbidities.  Use multi-level analysis to establish if any particular medical center has a statistically significant excess mortality rate beyond what could be expected from patients' comorbidities:

  1. Identify the intercept for each medical center in a regression of 6-month mortality on patients comorbidities
  2. Regress mortality at the centers (intercepts estimated in previous step) on patients satisfaction with the services and travel distance from referral to 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
  3. Report the meaning of these two related regressions 

Use the instructor's last name as the password for the data. Data► CSV► Wan-Chu's Teach One► R code► Answer by Jehanzeb► Answer by Shukri & Lavanya►

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►

This page is part of the course on Comparative Effectiveness by Farrokh Alemi PhD Home►  Email►