Sequential Multiple Decision ProceduresSequential Multiple Decision Procedures (SMDP) (SMDP)

For PGRN mini-GAW DataFor PGRN mini-GAW Data

Q. Zhang and M.A. Province Q. Zhang and M.A. Province

Division of BiostatisticsDivision of BiostatisticsWashington University School of MedicineWashington University School of Medicine

PGRN AWSII, ChicagoPGRN AWSII, Chicago April 28, 2005April 28, 2005

Brief History of SMDPBrief History of SMDP

Sequential Probability Ratio Test (SPRT), Wald 1947Sequential Probability Ratio Test (SPRT), Wald 1947

SMDP, Bechhoffer, Kiefer, Sobel, 1968SMDP, Bechhoffer, Kiefer, Sobel, 1968

SMDPSMDP Haseman-Elston Method (ASP), Province 2000 Haseman-Elston Method (ASP), Province 2000

Idea 1: SequentialIdea 1: Sequential

nn00Start from a small sample size

Increase sample size one by one

Use sequential information

Do analysis at each time

Stop when conclusion is reached

nn00+1+1

nn00+2+2

nn00+i+i

…

Plan experiments in next stage and save resources

Use residual/extra data to do validation

…

Idea 2: Multiple DecisionIdea 2: Multiple Decision

SNP1SNP1

SNP2SNP2

SNP3SNP3

SNP4SNP4

SNP5SNP5

SNP6SNP6

……

SNPnSNPn

Multiple DecisionMultiple DecisionIndependent TestIndependent Test

Test 1

Test 2

Test 3

Test 4

Test 5

Test 6

Test n

SNP1SNP1

SNP2SNP2

SNP3SNP3

SNP4SNP4

SNP5SNP5

SNP6SNP6

……

SNPnSNPn

Tradeoff between false positive rate and false negative rate.

SMDP divides populations into two groups and guarantees that there is a real difference (D) between the two groups with probability P*.

Model: Model: Regression ModelRegression Model

SNP GenotypesSNP Genotypes

11 => 011 => 012 => 112 => 122 => 222 => 2

PhenotypesPhenotypes

NPUBSNPUBS

NDRIVEL NDRIVEL

PCTDRIVELPCTDRIVEL

RIVALSIDERIVALSIDE

GOTGRANTSGOTGRANTS

YY = = αα+ + ββX X ++ ЄЄ

SNP x Drug/TreatmentSNP x Drug/Treatment

11 => 0 ALCOHOL11 => 0 ALCOHOL

12 => 1 X 12 => 1 X OROR

22 => 2 IVY22 => 2 IVY

SNP Main effectsSNP Main effects SNP-Drug interactionsSNP-Drug interactions

MethodsMethodsFixed sample Fixed sample RegressionRegression(Entire data)(Entire data)

Regular P value Regular P value

Bonferroni corrected P valueBonferroni corrected P value

FDR corrected P valueFDR corrected P value

SMDPSMDP(Sequential)(Sequential)

nn00

nn00+1+1

nn00+h+h

…

Q[h]1Q[h]1

Q[h]2Q[h]2

Q[h]3Q[h]3

Q[h]4Q[h]4

Q[h]5Q[h]5

……

……

nn00+2+2

…

Sequential sum of squares of Sequential sum of squares of regression errorsregression errors

StoppingStopping

rulerule

PPProbability thatProbability that

a real differencea real difference

(D) between two(D) between two

groups existsgroups exists

Region 3 (86 SNPs), GOTGRANTS

Region 2 (28 SNPs, IVY-SNP), RIVALSIDE

Region 1 (74 SNPs, ALCOHOL-SNP), PCTDRIVEL

SMDP SummarySMDP Summary

Test, identify all signals simultaneously Test, identify all signals simultaneously No multiple comparisonsNo multiple comparisons

Tight control statistical Tight control statistical errors (Type I, II)errors (Type I, II)

Efficient, Sequential information Efficient, Sequential information “Minimal” N to find significant signals“Minimal” N to find significant signals

Reliable, Save rest of N for validationReliable, Save rest of N for validation

Thanks !Thanks !

Fixed sample regression Fixed sample regression

Region 3 (86 SNPs), GOTGRANTS

Fixed sample regressionFixed sample regression Region 2 (28 SNPs, IVY-SNP), RIVALSIDE

Fixed sample regressionFixed sample regression Region 1 (74 SNPs, ALCOHOL-SNP), PCTDRIVEL

Fixed sample regression of 5 phenotypes on genotypes of 188 SNPsFixed sample regression of 5 phenotypes on genotypes of 188 SNPs