An example of using BFDP for identifying noteworthy associations Joan Dong

Recent technological advances allow the huge numbers of genetic information for analysis. Produces new challenges in terms of statistical analysis and interpretation. Some reports of associations between genetic variants and common cancer sites and other complex diseases are false positives. A major reason for this unfortunate situation is the strategy of declaring statistical significance based on a P value alone.

The P-value is by far the most commonly used measure, but requires careful calibration when the a priori probability of an association is small.

Standard statistical decision making α=0.05 is universal Analysis – Prior probability not considered formally – Loss from bad decisions not considered – probability that positive report is a false positive is not considered

A false discovery is the result of the Type I error of rejecting the null hypothesis stating that the marker has no effects, when in fact it has. To prevent false discoveries, one can propose stringent criteria (critical P-values, independent replications, etc).

Controlling the false discovery rate for multiple testing: - Adjusting for multiple testing is typically based on the number of the tests that are performed (the Bonferroni correction). A disadvantage of these kind of family-wise correction is that when many tests are performed, the critical P value becomes very small, resulting in a low statistical power to detect the true effects.

This presentation will introduce the BFDP method proposed by Jon Wakefield and show how to assess the BFDP and how to use it to decide whether a finding is deserving of attention or noteworthy. BFDP – Bayesian False Discovery Probability

Bayes’s theorem gives the probability of the hypothesis H0 given data y as Pr (H0 |y,H0 ∪ H1)=p(y|H0)Pr (H0|H0 ∪ H1)/p(y|H0 ∪ H1 ) Where p(y|H0 ∪ H1 )=p(y|H0 )Pr (H0 |H0 ∪ H1 )+p(y|H1 )Pr (H1 |H0 ∪ H1 ) Then Pr (H0|y)=p(y|H0)pi0/p(y|H0 )pi0 + p(y|H1 )(1-pi0 ) Pi0=Pr(H0) is the prior on the null Pr(H0|y)=BF*PO/BF*PO+1 Where BF=p(y|H0)/p(y|H1) - Bayes factor PO=pi0/1-pi0 Use ABF (approximate Bayes factor) for BF ABF=p(theta|H0 )/p(theta|H1) BFDP=ABF*PO/ABF*PO+1

Example of how to us the BFDP program

SAS macro was developed for calculating BFDP. %macro cal_BFDP(dataout,datain,pi1,pi2,pi3,pi4,rcost,upodd); data &dataout; set &datain; rcost=&rcost;*ratio of costs; BFDPt=rcost/(1+rcost);*BFDP threshold; pi1=&pi1;pi2=&pi2;pi3=&pi3;pi4=&pi4;*prior; upOdd=&upodd; w=round((log(upOdd)/1.96)**2,0.001); r=w/(w+se**2); z=log(or)/se; ABF=exp(-Z*Z*r*0.5)/sqrt(1-r); priorOdds1=(1-&pi1)/&pi1; priorOdds2=(1-&pi2)/&pi2; priorOdds3=(1-&pi3)/&pi3;priorOdds4=(1-&pi4)/&pi4; BFDP1=ABF*priorOdds1/(ABF*priorOdds1+1); BFDP2=ABF*priorOdds2/(ABF*priorOdds2+1); BFDP3=ABF*priorOdds3/(ABF*priorOdds3+1); BFDP4=ABF*priorOdds4/(ABF*priorOdds4+1); Run; %mend;

An example – Four levels of prior probability for SNP analysis have been suggested: (i) prior probability 0.01 (ii) prior probability 0.03 (iii) prior probability 0.05 (iv) prior probability The upper OR was set at 3, and the selected levels of noteworthiness for BFDP at 0.8, as recommended in the original papers.

Results

Conclusion BFDP can be used for reducing the number of false positive discoveries.

REFERENCES Wakefield, J. (2007). A Bayesian measure of the probability of false discovery in genetic epidemiology studies. American Journal of Human Genetics, 81,

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