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PSI 2014 ConferenceThe Tower Hotel, Tower Bridge, London

Risk Calculation in Screeningwith Biomarkers

Nick CowansStatistical Programmer

Veramed Limited

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Biomarkers

Something we measure in order to predict risk of a disease/syndrome in a subject

Cholesterol: coronary/vascular diseaseCA-125: ovarian cancer PAPP-A, Free hCGβ: Carrying a Trisomy 21 fetus

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Characteristic of BiomarkersConcentrations bound at zeroNo upper limit

0 “”

Log transform

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Mean()

Variance(2)

= [ , 2 ]

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Unaffected PopulationN(U, 2

U)Affected Population

N(A, 2A)

AU

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Calculating RiskLikelihood affected: 2l

Likelihood unaffected: l

X = x U/l

Likelihood ratio = 2

TWICE as likely to be

from affected population

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Estimating parameters,

We cannot know , population parametersA conventional method :

Collect some data in each population, ZUse Maximum Likelihood Estimation to estimate , call it Ignore uncertaintyUse in risk calculation

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Making predictions

p(X=x| A)

p(X=x| U)new data

parameter estimates

Your prediction is conditional on your parameter estimates, which are

uncertain

LikelihoodRatio

=

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Estimating parameters

Not a problem when sample size is largeIf sample size is small, repeating experiments can result in very different estimates:

10 samples (or experiments)

True mean = 10n = 10,000:

n = 10:more uncertainty

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Predictive approach

Rather than predict conditional on uncertain estimated parameters as in the estimative approachObtain predictive density functionBayesian concept; parameters given own distributions

parameter estimates from data Zp(X|)estimative approach:

^

Just data Zpredictive density function: p(X|Z)

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Predictive approach

With Normally distributed data, the predictive density function becomes a scaled and shifted central t-distributionNumber of samples in original data, Z, is no longer ignored, and is incorporated via degrees of freedom

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Predictive approach

Estimative Method

2l

l

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Predictive approach

Estimative Method

Predictive Method

2l

l

l

1.6l

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Case study

Screening for trisomy 21In trisomy 21 pregnancies:

PAPP-A decreasedFree hCGβ increased

Bivariate Normal distributionRisk calculated based upon maternal age, biochemistry and nuchal fold thickness

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Marker distribution

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Results

Risk ROC Curves

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Summary

Fallacy of estimative approach: takes no account of sampling variability of the estimatorPredictive approach weighs possible distributions of new data according to the various plausible values for More likely to see differences in risks with small sample sizes

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Acknowledgments

Professor Kevin Spencer (Barking Havering and Redbridge University NHS Trust)Professor David Wright (University of Plymouth)Dr Kevin Walters (University of Sheffield)

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Thank you