How do we know whether a marker or model is any good?

A discussion of some simple decision analytic methods

Carrie Bennette

(on behalf of Andrew Vickers)

University of Washington

Overview of talk

• Marker research in cancer: state of the science

• Traditional statistical methods for evaluating predictions

• Decision analytic approaches

Overview of talk

• Marker research in cancer: state of the science

• Traditional statistical methods for evaluating predictions

• Decision analytic approaches

A combination of common and minor variations in five regions of DNA can help predict a man’s risk of getting prostate cancer, researchers reported Wednesday. A company formed by researchers at Wake Forest University School of Medicine is expected to make the test available in a few months …. It should cost less than $300. This is, some medical experts say, a first taste of what is expected to be a revolution in medical prognostication

SNP panel

• Predictive accuracy of SNP panel: 0.57

• Predictive accuracy of single PSA in middle age: 0.75

• Doesn’t add to standard predictors (Nam et al.)

Systematic review of molecular markers in cancer

• 129 papers published in 2005 and 2006 eligible for analysis

• More markers than papers

• 97% included inference statistics

• 36% included marker in a multivariable model

• 11% measured predictive accuracy

• 0 used decision analytic techniques

Overview of talk

• Marker research in cancer: state of the science

• Traditional statistical methods for evaluating predictions

• Decision analytic approaches

Example: Binary test for cancer on biopsy

• Patients with high PSA are referred to biopsy

• But most patients with high PSA don’t have prostate cancer

• Could a second marker help?

• Study of biopsy cohort: 26% had cancer

– Assess presence of two markers

Traditional biostatistical metrics

  Sensitivity Specificity PPV NPV LR+ LR- AUC (Youden)

Brier(mean squared error)

 Test A 91% 40% 35% 92% 1.52 0.23 0.65 0.47

 Test B 51% 78% 45% 82% 2.32 0.63 0.64 0.29

Which test is best?

• Sensitivity / specificity insufficient to determine which test should be used:

– “Depends on whether sensitivity or specificity is more important”

Conclusion about traditional metrics

• Traditional biostatistical techniques for evaluating models, markers and tests do not incorporate clinical consequences

• Accordingly, they cannot inform clinical practice

Overview of talk

• Marker research in cancer: state of the science

• Traditional statistical methods for evaluating predictions

• Decision analytic approaches

A hierarchy of evidence

• Inference statistics

– Marker “not unassociated with outcome”

• Predictive accuracy

– How much information does the marker give you?

• Decision analytic techniques

– Do you make better decisions on the basis of the marker?

Threshold probability

• Predicted probability of disease is p=

• Define a threshold probability of disease as pt

• Patient accepts treatment if p= ≥ pt

• pt describes how patients values relative harm of false positive and false negative

Decision theory

“I would biopsy a man if his risk of prostate cancer was 20% or more, that is, I would conduct no more than 5 biopsies to find one cancer. I consider the harms associated with delaying the diagnosis of prostate cancer to be four times worse than the harms, risks and inconvenience of biopsy.”

 Treat: Sens. Spec. Prev. Net benefit

Test A 91% 40% 26%91% × 26% - 

(1 – 40%) × (1 – 26%) × (0.2 ÷ 0.8) = 0.1256

Test B 51% 78% 26%51% × 26% - 

(1 – 78%) × (1 – 26%) × (0.2 ÷ 0.8) = 0.0919

Everyone 100% 0% 26%100% × 26% - 

(1 – 0%) × (1 – 26%) × (0.2 ÷ 0.8) = 0.075

No-one 0% 100% 26%0% × 26% - 

(1 – 100%) × (1 – 26%) × (0.2 ÷ 0.8) = 0

Worked example at pt of 20%

Net benefit has simple clinical interpretation

• Net benefit of 0.126 at pt of 20%

• Using the model is the equivalent of a strategy that led to 126 patients per 1000 with cancer being biopsied with no unnecessary biopsies

Net benefit has simple clinical interpretation

• Difference between model and treat all at pt of 20%.

– 0.051

• Divide by weighting 0.051/ 0.25 = 0.204

– 204 fewer false positives per 1000 patients for equal number of true positives

– E.g. 204 fewer patients undergoing biopsy without missing any cancers

Decision curve analysis

4. Vary pt over an appropriate range

Vickers & Elkin Med Decis Making 2006;26:565–574

1. Select a pt 2. Positive test defined as 3. Calculate “Clinical Net Benefit” as:

tppˆ

Decision analysis

All markers

PSA

Free, Total PSA

Biopsy all

Biopsy none

Vickers JCO 2009

Parry-Jones A R et al. Stroke. 2013;44:1840-1845

Conclusion

• Huge number of markers proposed

• Evidence base is very weak for most

• Traditional biostatistical methods do not assess clinical value of a marker

• Simple decision analytic methods can distinguish potentially useful from useless models and markers