New Statistical Algorithms for the Analysis of Mass - FU Berlin, FB MI ...

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78 CHAPTER 4. (BIO-)MEDICAL APPLICATIONS and φ being the CDF of a standard normal random variable. To check the requirements of normality we use established standard tests, such as Lilliefors test ((Lilliefors, 1967), needs a large sample), Anderson-Darling test ((Anderson and Darling, 1952), for small to medium sample size, e.g. 10-200), Shapiro-Wilk test (Shapiro and Wilk, 1965), or the Jarque-Bera ((Bera and Carlos, 1980), highly attentive to outliers) test. (2) If Tn is not a normal distribution the Pivotal Intervals method can be used. A 1 − α bootstrap pivotal confidence interval can be calculated by: � Cn = � 2 · ˆ θn − θ ∗ ((1−α/2),B) , 2 · ˆ θn − θ ∗ ((α/2),B) where θ ∗ β,B is the β sample quantile of (ˆ θ ∗ n,1 , . . . , ˆ θ ∗ n,B ) and ˆ θn = T (X1, . . . , Xn) Model Validation by Cross-Validation Cross-validation is one of several approaches to estimating how well the model just learned from some training data is going to perform on future (yet unseen) data. It is better than the widely used residuals approach. The problem with residual evaluation is that it just gives a indication on how well a model fits the given data opposed to the a predictions for the performance on data it has not already seen. Other (more complex) method include Akaike Information Criterion (AIC, asymptotically equal to CV with k = n − 1) or Bayesian Information Criterion (BIC, asymptotically equal to CV with k ≈ 10). Cross-validation (Stone, 1974) partitions the original sample into (two or many) subsets. The analysis (e.g. model parameter estimation) is initially performed on one of these subsets (often denoted training set), while the other subsets (test sets) are used to confirm and validate the initial analysis. A widely used method is the so called k-fold cross-validation. Here, the original sample is partitioned into k sub-samples. The cross-validation process is then repeated k times: in each step one of the k sub-samples (each sample is used exactly once) is used as the test set and the remaining k − 1 sub-samples as the training set. The final results is usually computed by taking the average from the k single results. 4.3 Study Results This section will explain the results of the algorithmic pipeline described in the previous chapter when analyzing data such as introduced in section 4.1. The outcome of the first stage of the analysis pipeline are lists of peaks that occur in a significant portion of a group at the same m/z value. These peaks are the basis for further analysis stages that yields three distinct classes of results: Correlations: If patient meta-data are available (such as age, weight, blood parameters etc., see for example Figure 4.3.2) (cor-)relations can be sought for between peak properties (such as height) and meta-data properties (see section 4.3.1). Fingerprints: Peaks of two groups (e.g. cancer vs. healthy) are compared to find peaks having the same m/z value in both groups but differ in properties. More formally, peaks in group A at position X that are similar
4.3. STUDY RESULTS 79 Figure 4.3.3: Left: Masterpeaks of two groups (top: men; bottom: woman) at m/z 2274da. Obviously the average height of a peak in the woman’s group is lower than in the men’s group. This is also clearly shown in the chart of the height distributions (right): the two distributions do overlap between 400-800, but outside this area there is a clear domination of one group. with respect to a property P but differ to peaks in group B at position X (again with respect to property P ) are sought for. An example is shown in Figure 4.3.3: two masterpeaks and their respective height distributions (of their single peaks) are shown. The best combinations of these distinguishing peaks are then used to create fingerprints. Thus, a fingerprint is basically a list of m/z values. Each list entry has attached the considered property (e.g. peak height or peak width) and the average value of this property for each group. A fingerprint can be used to classify unknown spectra (see Sec 4.3.2). Difference Analysis: Based on the distinguishing features found during the fingerprint detection stage, further investigations can be done that analyze these differences. For example, using tandem mass spectrometry, the underlying proteins can be determined (see section 4.3.4). Clustering: Spectra of one groups can be clustered using the fingerprint features to detect sub-groups within a group, e.g. a particular sub-group of cancer type X (see section 4.3.3). 4.3.1 Correlation of Patient Meta Data to Peaks This analysis finds correlations of certain meta-data such as blood parameters to peak properties. These correlations are found between properties of peaks (e.g. height) from a particular group of patients (e.g. 20 year old men from a blood donator study) and available meta-data for these patients (e.g. blood parameters such as FT3). The actual analysis computes the correlation corXi,j between a peak property i (e.g. peak height, peak area, peak width, peak shape) and some parameter j which can be almost anything that is related to a patient (e.g. sex, age,
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New Statistical Algorithms for the
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Contents Acknowledgments . . . . .
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New Statistical Algorithms for the
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Extended Abstract English Version M
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German Version Das Gebiet der Prote
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Chapter 1 Introduction and Survey 1
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1.2. GOALS, OBJECTIVES AND TASKS 7
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1.2. GOALS, OBJECTIVES AND TASKS 9
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Chapter 2 Preliminaries 2.1 Topic O
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2.1. TOPIC OVERVIEW 13 Figure 2.1.1
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2.1. TOPIC OVERVIEW 15 completeness
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2.2. AN EXAMPLE 17 (a) Opera A (b)
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2.2. AN EXAMPLE 19 Figure 2.2.6: Tw
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2.2. AN EXAMPLE 21 successes. We ca
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Chapter 3 Mathematical Modeling and
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3.2. INTRODUCTION TO MALDI TOF MS 2
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Page 37 and 38: 3.3. PREPROCESSING 31 mix (external
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Page 63 and 64: 3.8. EXTRACTING FINGERPRINTS 57 Fig
Page 65 and 66: 3.8. EXTRACTING FINGERPRINTS 59 FID
Page 67 and 68: 3.8. EXTRACTING FINGERPRINTS 61 Dim
Page 69 and 70: 3.9. COMPLEXITY ANALYSIS 63 3.9 Com
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Page 73 and 74: 4.1. DATA USED 67 4.1.2 Serum Data
Page 75 and 76: 4.2. STATISTICAL REMARKS 69 1. Vali
Page 77 and 78: 4.2. STATISTICAL REMARKS 71 Molar v
Page 79 and 80: 4.2. STATISTICAL REMARKS 73 � Fir
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Page 87 and 88: 4.3. STUDY RESULTS 81 Figure 4.3.4:
Page 89 and 90: 4.3. STUDY RESULTS 83 � kNN (gen.
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5.4. QAD GRID WORKER 129 field. A w
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5.4. QAD GRID WORKER 131 2. This re
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5.4. QAD GRID WORKER 133 Figure 5.4
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5.4. QAD GRID WORKER 135 Checkpoint
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5.4. QAD GRID WORKER 137 database b
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5.5. QAD GRID PLATFORM SERVICES 139
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5.6. QAD GRID WORKFLOWS 141 � Dat
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5.6. QAD GRID WORKFLOWS 143 Service
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5.6. QAD GRID WORKFLOWS 145 Figure
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5.7. RELATED WORK 147 to set-up sys
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5.7. RELATED WORK 149 Table 5.7.1 -
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Chapter 6 proteomics.net - Product-
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6.2. CASE STUDIES 153 6.2 Case Stud
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6.2. CASE STUDIES 155 Figure 6.2.2:
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6.2. CASE STUDIES 157 MASCOT and SE
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6.2. CASE STUDIES 159 The peak pick
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6.2. CASE STUDIES 161 first entry i
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6.2. CASE STUDIES 163 Approach Base
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6.2. CASE STUDIES 165 Figure 6.2.5:
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Chapter 7 Related Work In this chap
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Chapter 8 Conclusion and Future Dir
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8.3. FROM BIOMARKERS TO BIOPRINTS 1
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Appendix A Implementation Details T
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Appendix B Curriculum Vitae Name Ti
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References Aebersold, R. and Mann,
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REFERENCES 179 Breiman, L. (2001).
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REFERENCES 181 Downard, K. M. and M
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REFERENCES 183 Gillette, M. A., Man
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REFERENCES 185 Huyghe, E., Muller,
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REFERENCES 187 Kuijpens, J. L. P.,
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REFERENCES 189 McLachlan, S. M. and
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REFERENCES 191 Platt, J. C. (1999).
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REFERENCES 193 Stone, M. (1974). Cr
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REFERENCES 195 Washburn, M. P., Wol
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