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Model and Variable Selections for Personalized Medicine

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Title: Model and Variable Selections for Personalized Medicine


1
Model and Variable Selections for Personalized
Medicine
Lu Tian (Northwestern University) Hajime Uno
(Kitasato University) Tianxi Cai, Els
Goetghebeur, L.J. Wei (Harvard University)
2
Outline
  • Background and motivation
  • Developing and evaluating prediction rules based
    on a set of markers for
  • Continuous or binary outcome
  • Censored event time outcome
  • Evaluating the incremental value of a biomarker
    over
  • the entire population
  • various sub-populations
  • Incorporating the patient level precision of the
    prediction
  • Prediction intervals/sets
  • Remarks

3
Background and Motivation
  • Personalized medicine using information about a
    persons biological and genetic make up to tailor
    strategies for the prevention, detection and
    treatment of disease
  • Important step develop prediction rules that can
    accurately predict health outcome or diagnosis of
    clinical phenotype

4
Background and Motivation
  • Accurate prediction of disease outcome and
    treatment response, however, are complex and
    difficult tasks.
  • Developing prediction rules involve
  • Identifying important predictors
  • Evaluating the accuracy of the prediction
  • Evaluating the incremental value of new markers

5
Background and Motivation AIDS Clinical Trial
ACTG320
  • Study objective to compare
  • 3-drug regimen (n579) Zidovudine Lamivudine
    Indinarvir
  • 2-drug regimen (n577) Zidovudine Lamivudine
  • Identify biomarkers for predicting treatment
    response
  • How well can we predict the treatment response?
  • Is RNA needed?

6
Background and Motivation
Is RNA needed?
Predictors
7
Background and Motivation AIDS Clinical Trial
Regression Coefficient
  • Coefficient for ?RNAweek 8 highly significant ?
  • RNA needed for a more precise prediction of
    responses??

8
Background and Motivation
Is RNA needed?
Y ?CD4week 8
ZPredictors
9
Developing Prediction RulesBased on a Set of
Markers
  • Regression approach to approximate Y Z
  • Continuous or binary outcome Generalize linear
    regression
  • Survival outcome
  • Proportional Hazards model
  • Time-specific prediction models
  • Regression modeling as a vehicle
  • the procedure has to be valid when the imposed
    statistical model is not the true model!

10
Developing and Evaluating Prediction Rules
  • Predict Y with Z based on the prediction model
  • Evaluate the performance of the prediction by the
    average distance between and Y
  • The utility or cost to predicting Y as
    is
  • The average distance is
  • Examples
  • Absolute prediction error
  • Total Cost of Risk Stratification

11
Evaluating and Comparing Prediction Rules
  • The performance of the prediction model/rule with
    can be estimated by
  • Prediction Model/Rule Comparison
  • Prediction with E(Y Z) g1(aZ) vs E(Y W)
    g2(bW)
  • Compare two models/rules by comparing

12
Variability in the Estimated Prediction
Performance Measures
  • Variability in the prediction errors
  • Estimate ? 50, SE 1? SE 50?
  • Inference about D and ? D1 D2
  • Confidence intervals based on large sample
    approximations to the distribution of

13
Bias Correction
  • Bias issue in the apparent error type estimators
  • Bias correction via Cross-validation
  • Data partition? Tk, Vk
  • For each partition
  • Obtain based on observations in Tk
  • Obtain based on observations in Vk
  • Obtain cross-validated estimator

14
Example AIDS Clinical Trial
  • Objective identify biomarkers to predict the
    treatment response
  • Outcome Y ?CD4week 24
  • Predictors Z Age, CD4week 0, ?CD4week 8,
  • RNAweek 0, ?RNAweek 8
  • Working Model E(YZ) ?Z

15
Example AIDS Clinical TrialIncremental Value of
RNA
Estimates
95 C.I.
Std Error Estimates
16
Incremental Value of RNA within Various
Sub-populations
17
Trandolapril Cardiac Evaluation Study(Kober et
al 2005, NEJM)
  • Prognostic importance of the left ventricular
    dysfunction
  • Thune et al (2005) Diamond study
  • Trace study (Kober et al 2005, NEJM)
  • Designed to determine whether patients w/ left
    ventricular dysfunction soon after myocardial
    infarction benefit from long-term oral ACE
    inhibition
  • Between 1990 and 1992, a total of 6676 patients
    with myocardial infarction were screened with
    echocardiography
  • A total of 5921 subjects had available data

18
Trandolapril Cardiac Evaluation Study (Kober et
al 2005, NEJM)
  • Routine Markers include
  • Age
  • creatine (CRE)
  • occurrence of heart failure (CHF)
  • history of diabetes (DIA),
  • history of hypertension (HYP),
  • cardiogenic shock after MI (KS)
  • We are interested in evaluating in the
    incremental value of wall motion index (WMI)

19
Trandolapril Cardiac Evaluation Study (Kober et
al 2005, NEJM)
  • Does WMI improve the prediction of 5-year
    survival?

20
Population Average Incremental Value of
WMIPredicting 5-year Survival
5-year mortality rate 42
21
D1
D2
22
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23
Gain Due to WMI
24
? 1
? 4
? 9
Gain Due to WMI with respect to D?
25
ExampleBreast Cancer Gene Expression Study
  • Objective construct a new classifier that can
    accurately predict future disease outcome
  • vant Veer et al (2002) established a classifier
    based on a 70-gene profile
  • good- or poor-prognosis signature based on their
    correlation with the previously determined
    average profile in tumors from patients with good
    prognosis
  • Classify subjects as
  • Good prognosis if Gene score gt cut-off
  • Poor prognosis if Gene score lt cut-off
  • van de Vijver et al (2002) evaluated the accuracy
    of this classifier by using hazard ratios and
    signature specific Kaplan Meier curves

26
ExampleBreast Cancer Gene Expression Study
  • Data consist of 295 Subjects
  • Outcome T time to death
  • Predictors Lymph-Node Status, Estrogen Receptor
    Status, gene score
  • We are interested in
  • Constructing prediction rules for identify
    subjects who would survive t-year, Y I(T ?
    t)1.
  • Evaluating the incremental value of the Gene
    Score.

27
Example Breast Cancer DataPredicting 10-year
Survival
28
Evaluating the Prediction RuleBased on Various
Accuracy Measures
  • For a future patient with T0 and Z0, we predict
  • Classification accuracy measures
  • Sensitivity
  • Specificity
  • Prediction accuracy measures

29
Example Breast Cancer DataPredicting 10-year
Survival
30
Example Breast Cancer Data
  • To compare
  • Model II g(a Node ER)
  • Model III g(a Node ER Gene)
  • Choosing cut-off values for each model to achieve
    SE 69 which is an attainable value for Model
    II, then
  • Model II ? SP 0.45, PPV 0.35, NPV 0.77
  • Model III ? SP 0.75, PPV 0.54, NPV 0.85
  • 95 CI for the difference in
  • SP 0.11, 0.45, PPV 0.01, 0.24, NPV
    0.06, 0.19

31
Prediction IntervalAccounting for the Precision
of the Prediction
  • Based on a prediction model
  • predict the response
  • summarize the corresponding population average
    accuracy
  • What if the population average accuracy of 70 is
    not satisfactory? How to achieve 90 accuracy?
  • What if can predict Y0 more precisely
    for certain Z0, while on the other hand fails to
    predict Y0 accurately?
  • Account for the precision of the prediction?
    Identify patients would need further assessment?

32
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33
Prediction Interval
  • To account for patient-level prediction error,
    one may instead predict
    such that
  • The optimal interval for the population with Z0
    ?? is
  • estimated conditional density
    function

34
Example Breast Cancer Study
  • Data 295 patients
  • Response 10 year survival
  • Predictors Lymph-Node Status, Estrogen Receptor
    Status, Gene Score
  • Model
  • Possible prediction sets ?, 0, 1, 0,1
  • Classic prediction considers 0, 1 only.

35
90 Prediction Set 0,1
90 Prediction Set 0
Predicted Risk 0.04
Predicted Risk 0.51
36
Example Breast Cancer Study Prediction Sets
Based on Clinical Gene Score
37
Remarks
  • Proper choice of the accuracy/cost measure
  • Classification accuracy vs predictive values
  • Utility function what is the consequence of
    predicting a subject with outcome Y as
  • With an expensive or invasive marker
  • Should it be applied to the entire population?
  • Is it helpful for a certain sub-population?
  • Should the cost of the marker be considered when
    evaluating its value?
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