Michael Griswold Biostats Retreat 2003

Clear-Cut Logging

Complex Distributions

SEERMED DATAEnd of Life Colorectal Cancer Costs

SEERMED DATATruncated Below $50,000

SEERMED DATATruncated Above $50,000

Covariate Sets

1. Basic Set  • The Basic Covariates of Interest 

2. Full Set  • Basic Set + interactions, spline-terms, etc…

3. Significance Set  • .05 Significant Covariates from the Full Model

4. Modified Significance Set • Significance Set without collinear variables

5. Gender & Ethnicity, adjusted for Age & Geography6. Gender & Ethnicity groups

Regression Models1. LogNormal

2. LogNormal with Smearing

3. Logistic: P($>0)

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

Evaluation Design

Training Sample:

(90%)

Validation

Sample

(10%)

Evaluation Design

Training Sample:

(81%)

Validation

Sample

(10%)

Training Cross-Validation samples

(10% of 90% = 9%)

Evaluation Statistics

• BIAS(Model,Cov) =

• MAE(Model,Cov) =

• RMSE(Model,Cov) =

• LS-Rule(Model,Cov) =

n

iiin 1

Cov)(Model,CC1

n

iiin 1

Cov)(Model,CC1

n

iiin 1

2Cov)(Model,CC1

n

iif

n 1

Cov)(Model,)C(ˆlog1

 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)

PHM Density EstimateXe

Xe

Xe

Xe???

Need estimate of the baseline Density function

Cost (c)

S0(c)

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) 

*Great Resource: C.K. Shene’s Webpage

f0(c) = s( S0(c) )

Results: distbsColorectal Cancer Costs

$$

$$

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Validation Results

Validation Results

Validation Results

Complex Longitudinal Data

Cost 2 Cost 1

Cost 1

Cost 2

SampleSizes

Bivariate Mixtures

My Statistician said “Get More Data”

Q-Q plots

SQUARE: QQ-Plot

SQUARE: log -Plot

s(p) = smooth function of percentile

)(Q

)(Q

wf

bf

p

p

E(Cwf) – E(Cbf)

1

0 wf1} - {

1

0 wf

1

0 bf

)(Qe

)(Q)(Q

dpp

dppdpp

s(p)

MSQUARE: QQ-Plots

MSQUARE: log(QR)-Plots

S1(p)

S2(p)

S3(p)

S4(p)

S5(p)

S6(p)

Analogy

SQUARE 2-groups t-test

IMSQUARE k-groups ANOVA

URSQUARE2 Continuous Reg.