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4. Gene Sets for Breast Cancer Prognosisset t-statistic showed similar or just slightly lower AUC than that of individual genes. Theset PC, and set U-statistic showed statistically significant reductions in AUC, compared withindividual genes (Figure A.6).While the AUC does not seem to improve, on average, by using set statistics rather thanindividual genes, Figure 4.4 shows that the variance of the AUC is lower for the set t-statisticthan for individual genes. This observation is consistent with the expectation that creatingnew features by averaging over individual genes reduces the variance of the input andconsequently that of the classifier’s prediction.Further, we observed that the discrimination of metastasis good/poor outcome from thegene sets statistics were similar in the internal and external validation, indicating that thecentroid classifier did not significantly over- or under-fit the data, and that the AUC estimatesfrom internal validation, which are easier to obtain since only one dataset is required, arerepresentative of the external validation which is more complicated since at least two datasetsare required.4.3.2. Stability of Feature RanksWe were interested in how the ranks of a single feature vary, since we prefer features that arehighly ranked on average and have small variability about that average. If a feature has lowaverage rank and large variability, it may sometimes appear at the top of the list simply bychance when the experiment is repeated, indicating that it is not a reliable predictor. On theother hand, features with high average rank and large variability may still be good predictorson average but will create unstable gene lists, manifesting as different datasets producingdifferent gene lists of similar predictive ability.To evaluate the variability of the ranks, we used the percentile bootstrap to sample theobservations with replacement, generating a bootstrap distribution for the centroid weights forgenes and gene sets in one dataset (GSE4922). Since there are 22,215 genes and only 5414 genesets, a reduced gene list was produced by training a centroid classifier on the GSE11121 datasetand selecting the top 5414 genes based on their absolute centroid weights ∣w j ∣ (Eqn. 4.2); thegene list was fixed across the bootstrap replications.In many cases we are interested in a small signature comprised of the most useful orpredictive features. Therefore, we selected the top 15 genes and gene sets based on theirmean rank. Figure 4.5 shows the mean, 2.5%, and 97.5% percentiles from 5000 bootstrapreplications, for these top features (shown from highest to lowest) using the set centroidstatistic. It is clear that the top gene sets have lower variation than the top genes. In light ofthese results, it is not surprising that lists of prognostic genes show little overlap, as even thebest ranked genes vary considerably within the same dataset, let alone between them; geneset features are more stable.74
4.3. Results0.012Var(AUC)0.0100.0080.006●rawset.centroidsset.mediansset.medoidsset.medoids2set.t.stat●0.004●0.002●● ● ● ● ● ● ● ● ● ● ●1248163264128256512102420484096541481921638422215FeaturesFigure 4.4.: Variance and 95% confidence intervals of the AUC from external validation betweenthe five datasets, n = 2 × ( 5 )2= 20 (train,test) pairs, for different numbersof features. The confidence intervals are [(n−1)s 2 /χ 2 α/2,n−1 , (n−1)s2 /χ 2 1−α/2,n−1 ],where χ 2 α is the α = 0.05 quantile for a chi-squared distribution with n − 1 degreesof freedom, and s 2 is the sample variance.75
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Scalable Approaches for Analysis of
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DeclarationThis is to certify that1
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AcknowledgmentThanks are due to my
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ContentsList of Abbreviationsxxix1.
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Contents8.3. Methods . . . . . . .
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List of Figures3.1. An illustration
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List of Figures5.2. Left: LOESS-smo
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List of Figures7.12. Top 5 principa
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List of FiguresB.1. APRC for HAPGEN
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List of FiguresC.1. Time to run fmp
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List of Tables6.2. List of independ
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List of AbbreviationsAUCFNFPGEOGiBG
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1. Introductionmolecular marker dat
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1. IntroductionThesis Outline and C
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1. IntroductionChapter 7 — Charac
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2Biological BackgroundIn this chapt
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2.2. The Molecular Basis for Diseas
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2.3. Gene Expression• mRNA extrac
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2.3. Gene Expressionanalyses, and s
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2.3. Gene Expression• Tissue spec
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2.3. Gene ExpressionepigeneticsDNAm
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REVIEWS2.4. The Genetic Basis of Di
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Page 65 and 66: 3Review of the Analysis of Gene Exp
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Page 129 and 130: 5.2. BackgroundThe lasso can be for
Page 131 and 132: 5.3. Design Considerations5.3. Desi
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Page 149 and 150: 6Sparse Linear Models Explain Pheno
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6.3. Results6.2.5. Data and quality
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6.3. Results1005000.80.60.40.22500+
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6.3. ResultsDisease Abbrev. Cases C
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6.3. Results0.9AUC0.80.70.6DatasetB
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6.3. Results1.00.8PPV0.60.4●●
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6.3. ResultsT1D models trained on t
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6.4. Discussionconfidence — cases
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6.5. ConclusionsFrom a computationa
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7. Genetic Control of the Human Met
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8Fused Multitask Penalised Regressi
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8.2. BackgroundRecently, Kim and Xi
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8.3. Methodsβ−0.20 −0.10 0.00
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8.4. Simulationwhere L is the loss
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8.4. Simulation• The fused ridge
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8.4. Simulation30Same sparsity, sam
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8.5. Resultslikely due to random va
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●●●●●●●Lasso●●Rid
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8. Fused Multitask Penalised Regres
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9. ConclusionsThis assumption is ne
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9. Conclusionsof results. There is
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9. Conclusionsin general, since the
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A. Supplementary Results for Gene S
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BSupplementary Results for Sparse L
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B.2. Real Dataare highly unlikely
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B.2. Real Data• differential miss
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B.2. Real Datafor Celiac1/Celiac2-U
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B.2. Real Data1005000.80.60.40.2250
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B.2. Real Data(a) Original Celiac1
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B. Supplementary Results for Sparse
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BibliographyK. L. Ayers and H. J. C
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BibliographyH. Brentani, O. L. Caba
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BibliographyH. Dai, L. van’t Veer
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BibliographyC. M. van Duijn, Y. S.
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BibliographyV. Guerrero. Time-serie
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BibliographyA. V. Ivshina, J. Georg
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BibliographyT. A. Mckinsey, K. Kuwa
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BibliographyL. Pusztai, C. Mazouni,
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BibliographyD. Botstein, P. E. Løn
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BibliographyP. J. van Diest, E. van
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BibliographyZ. Wei and H. Li. Nonpa
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