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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