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## Gene Expression Profiling

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**Good Microarray Studies Have Clear Objectives**• Class Comparison (gene finding) • Find genes whose expression differs among predetermined classes • Class Prediction • Prediction of predetermined class using information from gene expression profile • Response vs no response • Class Discovery • Discover clusters of specimens having similar expression profiles • Discover clusters of genes having similar expression profiles**Class Comparison and Class Prediction**• Not clustering problems • Supervised methods**Levels of Replication**• Technical replicates • RNA sample divided into multiple aliquots • Biological replicates • Multiple subjects • Multiple animals • Replication of the tissue culture experiment**Comparing classes or developing classifiers requires**independent biological replicates. The power of statistical methods for microarray data depends on the number of biological replicates**Microarray Platforms**• Single label arrays • Affymetrix GeneChips • Dual label arrays • Common reference design • Other designs**Common Reference Design**A1 A2 B1 B2 RED R R R R GREEN Array 1 Array 2 Array 3 Array 4 Ai = ith specimen from class A Bi = ith specimen from class B R = aliquot from reference pool**The reference generally serves to control variation in the**size of corresponding spots on different arrays and variation in sample distribution over the slide. • The reference provides a relative measure of expression for a given gene in a given sample that is less variable than an absolute measure. • The reference is not the object of comparison.**Dye swap technical replicates of the same two rna samples**are not necessary with the common reference design • For two-label direct comparison designs for comparing two classes, dye bias is of concern and dye swaps may be needed.**Controlling for Multiple Comparisons**• Bonferroni type procedures control the probability of making any false positive errors • Overly conservative for the context of DNA microarray studies**Simple Procedures**• Control expected the number of false discoveries by testing each gene for differential expression between classes using a stringent significance level • expected number of false discoveries in testing G genes with significance threshold p* is G p* • e.g. To limit of 10 false discoveries in 10,000 comparisons, conduct each test at p<0.001 level • Control FDR • Expected proportion of false discoveries among the genes declared differentially expressed • Benjamini-Hochberg procedure • FDR = G p* / #(p p*)**Additional Procedures**• Multivariate permutation tests • Korn et al. Stat Med 26:4428,2007 • SAM - Significance Analysis of Microarrays • Advantages • Distribution-free • even if they use t statistics • Preserve/exploit correlation among tests by permuting each profile as a unit • More effective than univariate permutation tests especially with limited number of samples**Randomized Variance t-testWright G.W. and Simon R.**Bioinformatics19:2448-2455,2003 • Pr(-2=x) = xa-1exp(-x/b)/(a)ba**Components of Class Prediction**• Feature (gene) selection • Which genes will be included in the model • Select model type • E.g. Diagonal linear discriminant analysis, Nearest-Neighbor, … • Fitting parameters (regression coefficients) for model • Selecting value of tuning parameters**Feature Selection**• Genes that are differentially expressed among the classes at a significance level (e.g. 0.01) • The level is selected only to control the number of genes in the model • For class comparison false discovery rate is important • For class prediction, predictive accuracy is important**Complex Gene Selection**• Small subset of genes which together give most accurate predictions • Genetic algorithms • Little evidence that complex feature selection is useful in microarray problems**Linear Classifiers for Two Classes**• Fisher linear discriminant analysis • Requires estimating correlations among all genes selected for model • Diagonal linear discriminant analysis (DLDA) assumes features are uncorrelated • Compound covariate predictor (Radmacher) and Golub’s method are similar to DLDA in that they can be viewed as weighted voting of univariate classifiers**Linear Classifiers for Two Classes**• Compound covariate predictor Instead of for DLDA**Linear Classifiers for Two Classes**• Support vector machines with inner product kernel are linear classifiers with weights determined to separate the classes with a hyperplane that minimizes the length of the weight vector**Other Linear Methods**• Perceptrons • Principal component regression • Supervised principal component regression • Partial least squares • Stepwise logistic regression**Other Simple Methods**• Nearest neighbor classification • Nearest k-neighbors • Nearest centroid classification • Shrunken centroid classification**Nearest Neighbor Classifier**• To classify a sample in the validation set, determine it’s nearest neighbor in the training set; i.e. which sample in the training set is its gene expression profile is most similar to. • Similarity measure used is based on genes selected as being univariately differentially expressed between the classes • Correlation similarity or Euclidean distance generally used • Classify the sample as being in the same class as it’s nearest neighbor in the training set**Nearest Centroid Classifier**• For a training set of data, select the genes that are informative for distinguishing the classes • Compute the average expression profile (centroid) of the informative genes in each class • Classify a sample in the validation set based on which centroid in the training set it’s gene expression profile is most similar to.**When p>>n The Linear Model is Too Complex**• It is always possible to find a set of features and a weight vector for which the classification error on the training set is zero. • It may be unrealistic to expect that there is sufficient data available to train more complex non-linear classifiers**Other Methods**• Top-scoring pairs • Claim that it gives accurate prediction with few pairs because pairs of genes are selected to work well together • Random Forest • Very popular in machine learning community • Complex classifier**Comparative studies indicate that linear methods and nearest**neighbor type methods often work as well or better than more complex methods for microarray problems because they avoid over-fitting the data.**Evaluating a Classifier**• Fit of a model to the same data used to develop it is no evidence of prediction accuracy for independent data • Goodness of fit vs prediction accuracy**Class Prediction**• A classifier is not a set of genes • Testing whether analysis of independent data results in selection of the same set of genes is not an appropriate test of predictive accuracy of a classifier • The classification of independent data should be accurate. There are many reasons why the classifier may be unstable. The classification should not be unstable.**Hazard ratios and statistical significance levels are not**appropriate measures of prediction accuracy • A hazard ratio is a measure of association • Large values of HR may correspond to small improvement in prediction accuracy • Kaplan-Meier curves for predicted risk groups within strata defined by standard prognostic variables provide more information about improvement in prediction accuracy • Time dependent ROC curves within strata defined by standard prognostic factors can also be useful**Time-Dependent ROC Curve**• M(b) = binary marker based on threshold b • PPV = prob{ST|M(b)=1} • NPV = prob{S<T|M(b)=0} • ROC Curve is Sensitivity vs 1-Specificity as a function of b • Sensitivity = prob{M(b)=1|ST} • Specificity = prob{M(b)=0|S<T}**Validation of a Predictor**• Internal validation • Re-substitution estimate • Very biased • Split-sample validation • Cross-validation • Independent data validation**Split-Sample Evaluation**• Split your data into a training set and a test set • Randomly (e.g. 2:1) • By center • Training-set • Used to select features, select model type, determine parameters and cut-off thresholds • Test-set • Withheld until a single model is fully specified using the training-set. • Fully specified model is applied to the expression profiles in the test-set to predict class labels. • Number of errors is counted**Leave-one-out Cross Validation**• Leave-one-out cross-validation simulates the process of separately developing a model on one set of data and predicting for a test set of data not used in developing the model**Leave-one-out Cross Validation**• Omit sample 1 • Develop multivariate classifier from scratch on training set with sample 1 omitted • Predict class for sample 1 and record whether prediction is correct