Michael Griswold Biostats Retreat 2003
Feb 02, 2016
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
$$
$$
$$
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.