Michael Griswold Biostats Retreat 2003

1
Clear-Cut Logging?
A Discussion on Model Evaluation for Complex
Distributions

• Michael Griswold Biostats
  Retreat 2003

2
Clear-Cut Logging
3
Complex Distributions
4
SEERMED DATA
End of Life Colorectal Cancer Costs
5
SEERMED DATA
Truncated Below 50,000
6
SEERMED DATA
Truncated Above 50,000
7
Covariate Sets

• Basic Set 
• The Basic Covariates of Interest 
• Full Set 
• Basic Set interactions, spline-terms, etc
• Significance Set 
• .05 Significant Covariates from the Full Model
• Modified Significance Set
• Significance Set without collinear variables
• Gender Ethnicity, adjusted for Age Geography
• Gender Ethnicity groups

8
Regression Models

1. LogNormal
2. LogNormal with Smearing
3. Logistic P(gt0)
4. Two-Stage LogNormal
5. Two-Stage LogNormal with Smearing
6. Gamma (GLM log-link)
7. Two-Stage Gamma
8. Cox PHM
9. Normal
10. Two-Stage Normal

9
Evaluation Design
Validation Sample (10)
Training Sample (90)
10
Evaluation Design
Validation Sample (10)
Training Sample (81)
11
Evaluation Statistics

• BIAS(Model,Cov)
• MAE(Model,Cov)
• RMSE(Model,Cov)
• LS-Rule(Model,Cov)

12
PHM Density Estimate

•  Cox PHM Survival Function   S(c)   S0(c)(
  )   
•  Cox PHM Density Function
• f(c)    -S?(c)
• -e(X?) ? S0(c)(1- ) ? S0?(c)
•   e(X?) ? S0(c)(1- ) ? f0(c)
•  Estimate f(c)   e(X ) ? S0(c)(1- ) ?
  f0(c)

13
PHM Baseline Survival
B-Splines 1) Local support computation 2)
Monotonic Coefficients ? Monotonic Smooth 3)
Derivative of a B-Spline of degree 'p' 
B-Spline of degree ('p'-1) 
S0(c)
Great Resource C.K. Shenes Webpage
Cost (c)
14
Results distbs
Colorectal Cancer Costs



15
Validation Results
16
Validation Results
17
Validation Results
18
Complex Longitudinal Data
Cost 1
Cost 2
19
Bivariate Mixtures
Sample Sizes
Cost 2
Cost 1
20
My Statistician said Get More Data
21
Q-Q plots
22
SQUARE QQ-Plot
23
SQUARE log -Plot
s(p) smooth function of percentile
24
MSQUARE QQ-Plots
25
MSQUARE log(QR)-Plots
26
Analogy

• SQUARE 2-groups t-test
• IMSQUARE k-groups ANOVA
• URSQUARE2 Continuous Reg.

27
(No Transcript)
28
(No Transcript)