likelihood ratio testing under non-identifiability: theory and biomedical applications

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Likelihood Ratio Testing under Non-identifiability: Theory and Biomedical Applications. Kung-Yee Liang and Chongzhi Di Department Biostatistics Johns Hopkins University July 9-10, 2009 National Taiwan University. Outline. Challenges associated with likelihood inference - PowerPoint PPT Presentation

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  • Likelihood Ratio Testing under Non-identifiability: Theory and Biomedical ApplicationsKung-Yee Liang and Chongzhi DiDepartment BiostatisticsJohns Hopkins University

    July 9-10, 2009National Taiwan University

  • OutlineChallenges associated with likelihood inferenceNuisance parameters absent under null hypothesisSome biomedical examplesStatistical implicationsClass I: alternative representation of LR test statisticImplicationsClass IIAsymptotic null distribution of LR test statisticSome alternativesA genetic linkage exampleDiscussion

  • Likelihood InferenceLikelihood inference has been successful in a variety of scientific fieldsLOD score method for genetic linkageBRCA1 for breast cancerHall et al. (1990) SciencePoisson regression for environmental healthFine air particle (PM10) for increased mortality in total cause and in cardiovascular and respiratory causes Samet et al. (2000) NEJM ML image reconstruction estimate for nuclear medicineDiagnoses for myocardial infarction and cancers

  • Challenges for Likelihood InferenceIn the absence of sufficient substantive knowledge, likelihood function maybe difficult to fully specifyGenetic linkage for complex traitsGenome-wide association with thousands of SNPsGene expression data for tumor cellsThere is computational issue as well for high-dimensional observationsHigh throughput data

  • Challenges for Likelihood Inference (cont)Impacts of nuisance parametersInconsistency of MLE with many nuisance parameters (Neyman-Scott problem)Different scientific conclusions with different nuisance parameter valuesIll-behaved likelihood functionAsymptotic approximation not ready

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    0.38100.3510

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    1.0570.2690.9930.307

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    Dominant1_HLOD

    recessive1_HLOD

    dominant2_HLOD

    recessive2_HLOD

    genetic distance in CentiMorgans

    HLOD

    Parametric Linkage Analyses - 123 multiplex families - 4 models

    Sheet1

    JHU Data from Collaborative SZ SNP scan - 4 paraemtric Models -- chromosome 8 - Merlin analysis, adjusted for Ld (r2=.16) -

    all subjects coded either 2=affected or 0=unknown (no one is coded 1=unaffected)

    MODELMODELMODELMODEL

    Doug - dominantDoug - recessiveAravinda- dominantAravinda recessive

    POSITIONLODALPHAHLODPOSITIONLODALPHAHLODPOSITIONLODALPHAHLODPOSITIONLODALPHAHLOD

    0-12.4130.1550.3810-46.265000-25.130.1130.3510-25.81300

    0.001-12.4860.1510.3640.001-46.421000.001-25.2070.1110.3380.001-25.95700

    0.002-12.5740.1470.3470.002-46.662000.002-25.2980.1080.3240.002-26.17500

    0.003-12.6830.1430.330.003-47.263000.003-25.4110.1060.3110.003-26.63200

    1.69-11.4450.1810.5141.69-44.7170.0070.0021.69-24.3920.1310.4571.69-24.98100

    2.4-11.6690.1790.5092.4-45.420.010.0042.4-24.7880.1290.4542.4-25.20800

    2.53-11.7840.1770.5022.53-45.7220.010.0042.53-24.9470.1280.4492.53-25.32600

    2.69-11.620.180.5152.69-45.6430.0110.0062.69-24.3580.130.4592.69-25.1110.0010

    3.73-10.4280.2190.7423.73-43.7020.0490.1073.73-22.7080.1590.6463.73-23.090.0520.08

    4.35-10.6990.2130.6944.35-43.7280.0510.1174.35-23.4140.1510.5824.35-22.9620.0590.102

    4.5-10.6790.2170.7354.5-43.9350.0540.1344.5-23.5350.1530.6234.5-23.1360.0620.116

    4.63-10.710.2150.7254.63-44.4690.0530.1284.63-23.5850.1520.6154.63-23.6210.0590.107

    5.18-10.7520.2080.6755.18-43.6650.0610.1755.18-23.5160.1470.5745.18-23.3970.0670.142

    6.45-11.6460.1720.476.45-43.010.0710.2746.45-24.4560.1210.4036.45-22.9830.0790.221

    7.81-12.7080.1410.337.81-42.470.0740.3557.81-26.1620.0970.287.81-22.6810.0850.299

    9.69-12.2880.150.3659.69-41.2190.0840.4439.69-25.3720.1030.3039.69-21.9650.0970.378

    12.29-12.4190.1540.39312.29-41.4550.1010.62212.29-25.2350.1070.33112.29-21.5810.1210.573

    13.39-13.1110.1490.37713.39-42.670.1010.63313.39-26.3010.1050.32113.39-21.8960.1230.594

    13.83-13.120.1510.38513.83-42.2490.1030.65113.83-26.3070.1060.32913.83-21.550.1260.618

    14.86-14.1540.1310.29514.86-44.3080.0850.47114.86-27.7610.0940.26914.86-22.7270.1030.436

    15.09-13.4880.1410.33415.09-43.0380.0870.48715.09-26.4350.1030.30915.09-22.0550.1060.452

    15.64-12.9710.160.42615.64-42.6870.090.51515.64-25.8280.120.40415.64-21.8140.110.479

    16.061-13.0010.1670.47216.061-42.8420.0930.54916.061-25.9020.1270.45816.061-21.8640.1140.512

    16.31-13.150.1640.45216.31-42.8190.0940.55716.31-26.0270.1250.44116.31-21.8440.1140.518

    16.72-14.0080.1450.3616.72-44.2520.0920.53516.72-27.0060.1120.36316.72-22.5660.110.494

    21.74-15.820.0990.18221.74-47.4020.0850.52821.74-29.3550.0720.1721.74-24.3030.1060.522

    22.15-16.2430.0980.18122.15-48.5590.0810.48822.15-29.9770.0720.17122.15-24.8340.10.478

    22.17-16.5290.0870.14522.17-49.5940.0710.39122.17-30.2720.0650.14322.17-25.690.0870.379

    22.22-16.5610.0840.13322.22-49.6440.0690.37922.22-30.1870.0630.13322.22-25.7350.0860.366

    22.795-17.7460.010.00122.795-49.080.0670.35622.795-32.2150.001022.795-25.4130.0810.331

    23-15.6570.0650.06223-46.1260.0860.51423-28.7640.0410.04123-22.9570.1070.499

    23.15-14.5980.1050.15723.15-46.1740.0970.62723.15-27.3690.0680.10823.15-22.2850.1220.625

    23.19-14.4040.1110.17623.19-46.2240.0980.63123.19-27.0380.0730.12123.19-22.2910.1230.632

    23.58-15.3810.0930.13723.58-49.1560.0720.

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