Changes in cellular functions in response to drug therapy are mediated by specific transcriptional profiles resulting from the induction or repression in the activity of a number of genes, thereby modifying the preexisting gene activity pattern of the drug-targeted cell(s). Recombinant human interferon beta (rIFNβ) is routinely used to control exacerbations in multiple sclerosis patients with only partial success, mainly because of adverse effects and a relatively large proportion of nonresponders. We applied advanced data-mining and predictive modeling tools to a longitudinal 70-gene expression dataset generated by kinetic reverse-transcription PCR from 52 multiple sclerosis patients treated with rIFNβ to discover higher-order predictive patterns associated with treatment outcome and to define the molecular footprint that rIFNβ engraves on peripheral blood mononuclear cells. We identified nine sets of gene triplets whose expression, when tested before the initiation of therapy, can predict the response to interferon beta with up to 86% accuracy. In addition, time-series analysis revealed potential key players involved in a good or poor response to interferon beta. Statistical testing of a random outcome class and tolerance to noise was carried out to establish the robustness of the predictive models. Large-scale kinetic reverse-transcription PCR, coupled with advanced data-mining efforts, can effectively reveal preexisting and drug-induced gene expression signatures associated with therapeutic effects. By studying gene expression in patients with multiple sclerosis before and after therapy with beta interferon, it is possible to identify gene expression signatures that are associated with therapeutic effects Interferons are small, inducible proteins secreted by nucleated cells in response to viral infection and other stimuli. They act in a paracrine fashion on other cells in their immediate vicinity, triggering a state of growth arrest, so that infected cells cannot be forced to produce viral proteins, and activating the process of programmed cell death, so that infected cells can be removed . InterfeWe generated and analyzed longitudinal patterns of gene expression from interferon beta (IFNβ)–treated patients suffering from MS with the aim of identifying preexisting and drug-induced signatures that would predict or explain the clinical response to the drug.Fifty-two patients with relapsing-remitting MS were followed for at least 2 y after initiation of therapy with IFNβ. Clinical follow-up included a neurological examination every 3 mo and at the time of relapse. At each visit, a blood sample was obtained by venipuncture. After the 2-y endpoint, patients were classified as either good or poor responders based on strict criteria, as described in MX1 as the single best discriminating variable between samples obtained at baseline (T = 0) and at 3 mo after initiation of therapy (T = 3) with a classification accuracy of 79% (data not shown). Given that MX1 is a known marker of IFN bioavailability [Using linear discriminant analysis–based integrated Bayesian inference system (IBIS), we were able to detect the gene lability , this reT = 0 correlated with a good or poor outcome of therapy at the 2-y endpoint. This process exhaustively carried out sample classification by searching through all 54,740 possible three-gene combinations of 70 genes. Higher-order combinatorial searches beyond combinations of three genes are possible using IBIS and are currently under investigation. However, higher-order predictive variable combinations do require the support of many more samples to prevent overfitting of the model.To search for expression signatures associated with therapeutic outcome (good or poor responder), we conducted clustering of samples using normalized data for all 70 genes at each time point . DespiteWe implemented a stringent method for examining the statistical validity of our classification results that consisted in testing the obtained classifier in an independent set of samples not previously “seen” by the program. All of the following statistical analyses were thus performed on split datasets, namely, training (75% of the samples) and test (25%), each reflecting the same relative proportion of classes (63% good and 37% poor responders). We started by conducting 3D IBIS searches using expression data from only the training set and selected the top nine scoring triplets . For each gene triplet, and using the training data only, a committee of classifiers was built based on an internal cross-validation scheme. Subsequently, the classifiers were used to predict the outcome of an independent test set of samples. Gene triplets were ranked on the basis of the prediction accuracies of the classifiers on this independent test set. We identified nine gene triplets with a predictive accuracy of at least 80% . We consCaspase 2, Caspase 10, and FLIP, which yielded a predictive accuracy of 86% in the original split. The bell-shaped distribution resulting from 100 tests for this triplet displayed a mean accuracy of 87.8% and a tenth percentile of 78.6%, meaning that if the prediction were performed multiple times, in 90% of these instances an accuracy of almost 79% or better would be obtained. This histogram only reflects the range of accuracies obtained, should the initial data split be different. Notably, the genes in the top-scoring triplet were Caspase 2, Caspase 10, and FLIP—three apoptosis-related molecules. The second-highest-scoring triplet was that of Caspase 2, Caspase 3, and IRF4 (86.8% mean accuracy after 100 splits). Other high-scoring triplets included IL4Ra and MAP3K1, in addition to other apoptotic molecules   .Caspase 2, Caspase 10, and FLIP; 3D model) was compared with those obtained with the single-gene (1D) and gene-pair (2D) models. We observed that the classification accuracy improves as more genes are added to the classifier. We next plotted the samples of a test dataset (25% of samples) on the predictive probability model shown in Caspase 2/Caspase 10 and Caspase 10/FLIP gene pairs show significant predictive capability, but that all three genes are required to provide the highest level of model accuracy and robustness.In To validate the specificity and predictive capability of the top-scoring gene triplet (for the good and poor responding classes) and its associated classifiers, we examined the model exhibiting the best performance on a “default” expression dataset. This null dataset was built keeping the original gene expression data and randomly permuting the class labels of the outcomes 1,000 times . The prediction accuracies for all the gene triplets obtained with this dataset dropped dramatically as the means ranged from 49.2% to 53.6% (data not shown), emphasizing the specificity of the classifiers. In addition, for the top-scoring gene triplet (for good and poor responder classes), we calculated the probability of achieving, under the null hypothesis, an equal or better accuracy than that obtained in the original prediction (86%), as previously described . This acFinally, we tested the robustness of each of these gene sets as predictors of IFNβ response by simulating experimental measurement error. To accomplish this, we first calculated the standard deviation of the expression measurements for all genes as an estimation of the overall experimental error. We then added a fixed amount of Gaussian noise corresponding to one standard deviation (taken from 20 random deviations) to each expression value and repeated the classification/prediction in 30 different splits of the data . Notably, the mean drop in predictive accuracy after the addition of noise was less than 10%, denoting a significant tolerance to reasonable measurement errors .Because all the patients in this study were systematically followed up for a period of 2 y, we were able to perform a longitudinal analysis. Using a repeated-measures analysis of variance (ANOVA), we searched for genes with significantly different expression patterns based on models that tested for responder effect, time effect, and interaction effect (time × response).IRF4 (p = 0.03), IL4Ra (p = 0.01), Caspase 10 (p = 0.0008), Caspase 7 (p = 0.01), IRF2 (p = 0.02), and IRF6 (p = 0.03) are among the 12 genes that best predict response at T = 0  was observed for the poor responders.Significant responder effect for 20 genes  and signAlthough we successfully identified informative, combinatorial relationships, establishing the causality of the association between gene expression and outcome to therapy is beyond of the scope of this work, and these genes are therefore considered surrogate markers. Moreover, although extensive in vivo and in vitro experiments have been conducted, the full mechanism of action of IFNβ in MS remains unknown.Transcription profiling experiments have involved IFNβ in the regulation of apoptosis in both cancer and MS ,16,17,18IRF4, a gene essential for mature T and B lymphocyte function and homeostasis, and a transcription factor with dual function (activator/repressor) that regulates transcription of IL4 through physical interaction with NFATc2 [IRF4 is a repressor of other IFN-induced genes [IRF4 observed in the poor responders before initiation of therapy.Other differentially expressed transcripts included h NFATc2 . Remarkaed genes , an obseMX1 showed a significant time effect independent of clinical response (p = 0.01). This result is in agreement with previous findings indicating substantial MX1 upregulation in response to type I IFNs [MX1, which occurs minutes after IFN stimulation [MX1 as the best single classifier for samples from patients before (T = 0) and after (T = 3) initiation of therapy. In fact, as MX1 comes from the difference between T = 0 and T = 3.As expected, the gene e I IFNs . Interesmulation , is sustIFNAR1 and STAT2 , their upregulation on administration of rIFNβ is likely related to mechanistic aspects of IFN signaling. Our results suggest that poor response is associated with downstream signaling events rather than deficient recognition or metabolism of the drug. Our previous finding that IFN receptor polymorphisms do not affect therapeutic response in this same set of patients partially supports this hypothesis [Caspase 10 (p = 0.01) and MAP3K1 (p = 0.01) were part of any predictor set . These results highlight the involvement of these genes in the response to IFN both at T = 0 and once therapy has started.Also of interest, a significant time effect (but not responder effect) was observed for nd STAT2 B. Becauspothesis . Only twctor set B. In addHere we combined large-scale, function-oriented gene expression with advanced data mining to identify a set of markers that accurately and robustly predict the response to rIFNβ therapy. Although larger, prospective studies are needed to confirm these findings, our results suggest that the underlying gene activity profile of an individual at the verge of therapy harbors sufficient information to allow investigators to estimate the chances of experiencing satisfactory therapeutic effects. As analytical tools to predict clinical outcomes based on molecular evidence evolve, these types of studies are likely to become a substantial aid to the physician, taking the paradigm of personalized medicine one step further.All studies were approved by the respective Committees of Human Research at Hospital Vall d'Hebron, Barcelona, Spain, and the University of California, San Francisco, United States. Informed consent was obtained for all study participants. All patients were examined by a trained neurologist at the CNI Unit, Vall d'Hebron Hospital. Inclusion criteria for this study were clinically definite MS (Poser's criteria), disease in relapsing-remitting phase, age between 18 and 65 y, recorded history of at least two clearly identified relapses within the preceding 24 mo, and expanded disability status scale between zero and 5.5 (inclusive). Detailed information about clinical aspects of these patients has been recently reported elsewhere [n = 33) if they experienced a total suppression of relapses and no increase in the expanded disability status scale after a 2-y follow-up period. Poor responders (n = 19) were defined as having suffered two or more relapses or having a confirmed increase of one point in the expanded disability status scale score. Patients with intermediate phenotypes were excluded from this study. Blood specimens were taken following institutional guidelines at approximately the same time of the day just before the administration of the first dose of rIFNβ and every 3 mo thereafter during the neurological examination, with the exception of T = 15 and T = 21 mo. Altogether, 336 samples were tested . Immediately after being drawn, all blood samples were spun over Ficoll-Paque  gradients to enrich the sample for mononuclear cells. After three washes with PBS, aliquots of 5 × 106 cells were frozen in RPMI1640 containing 20% DMSO and 20% fetal calf serum.Patients were categorized as good responders . Plates were kept frozen at −70 °C until needed.Peripheral blood mononuclear cells were thawed at 37 °C for 1 min, and RNA lysis buffer was added immediately. RNA was purified with the Strataprep kit  and finally resuspended in nuclease-free water . One-microliter RNA aliquots were subjected to fluorescence-based quantitation (in duplicate) using the Ribogreen reagent  in a Spectra Max Gemini fluorometer . Samples were diluted to 1 ng μlA master mix was prepared essentially as described previously , with thA custom Microsoft Excel  worksheet was prepared for handling reaction data import and performing initial statistics. Normalized data were imported as a .csv file into GeneLinker Platinum  for preprocessing and clustering analysis. Quadratic discriminant analysis–based IBIS implemented for 3D searches was carried out at the School of Computing, Queen's University, Kingston, Ontario, Canada, and at Biosystemix, Sydenham, Ontario, Canada. IBIS is a data-mining algorithm that searches through the gene space for a single gene (or group of genes) that can predict the outcome class . This algorithm incorporates a complete 10-fold cross-validation method with several independently trained classifiers to predict an outcome on the basis of a voting scheme (see below). We used MSE and classification accuracy to assess how well the classification predictions matched the true response of the patients to therapy. The top-performing gene triplets were selected on the basis of a mixed threshold for low MSE levels and high accuracy rates.i,g two Gaussian functions are fitted to the distributions of the observed expression levels in good responding and poor responding patients . Our fitted distribution, Dg(x), denotes the probability of a patient having an expression level of i = x,g given that this patient is a good responder. The fundamental question we are aiming to answer using data-mining methods (here using IBIS particularly) is as follows: what is the probability of a patient being a good responder given the observed expression level of a gene for that patient? Taking advantage of the fitted distributions, a classifier applies Bayes' formula to answer the fundamental question. According to this formula:IBIS identifies genes (or gene pairs or groups of genes) that are highly predictive of the outcome based on probability distributions of those genes in different outcome classes. For example, for a given gene P1= P((i = xg)|Pagood_responder)P(Pagood_responder). In fact, P((i = xg)|Pagood_responder) is the distribution function fitted to the observed gene expression values of ig above (Dg), and P(Pagood_responder), the probability of a patient being a good responder, can be easily calculated using the total and good responding patient counts. The term P2 is strictly analogous to P1 but applies to poor responders. Therefore, according to where To obtain a reliable classifier that is generalizable to all patient samples obtained under similar conditions, the Gaussian distributions and the classifier were only trained on a subsample of the patient data (training set). The results of the classification , however, were tested on patient samples never seen by the classifier before (test set). This ensures limitation of the classifier overfitting. Further, a complete 10-fold cross-validation scheme was built into the training phase. In IBIS, linear and quadratic classifiers correspond to classifiers built using Gaussian distributions with equal or different covariance matrices, respectively. The prediction results of IBIS are visualized graphically within the observed gene expression space by presenting the probabilities of a patient being a good or poor responder as a background color see  and 5. Tiobserved − responseiexpected)2 averaged over all patients. For a given patient, the clinical response determined by the end of the 2-y monitoring period is denoted by responseiobserved and responseiexpected and represents the probability of that patient being a good responder to rIFNβ therapy, using the Bayes' formula above. Classification accuracy simply expresses the percentage of patients that were correctly predicted as being good or poor responders.Several measures were used to assess how well the calculated probabilities matched the true patient responses to therapy. Two of these measures were MSE and classification accuracy. MSE was calculated as the sum of . Only the training set was used for identifying the best predictive gene triplets with the IBIS method, as well as for building the classifier. A committee of classifiers was then generated using a 10-fold cross-validation scheme during training. The training data themselves were divided into ten parts, and each time, a classifier was built using only nine parts of the data. That classifier's predictive capability was determined by its accuracy over the one-tenth of the data withheld. A committee of ten classifiers was assembled from the results of this training stage; this committee was then applied to the test data (which have thus far been hidden from the classifiers). For a patient sample in the test data, each classifier in the committee made a prediction. A majority voting scheme then decided as to which class the sample would be assigned.Given the initial data split into training and test sets, it was important to rule out the role of fortuitous idiosyncrasies in this split and the resulting accuracy rates. To address this point, we created 100 random splits of the data into training and test subgroups. A committee of classifiers was trained on the training set for each data split, and the accuracies were calculated over the blind test set. A histogram of the test set accuracies was then built, representing the expected ranges of accuracies had the initial data split been different. This histogram is not representative of the estimated or idealized distribution of the accuracies for a gene triplet in a machine learning sense. Rather, it is a coarse approximation of the possible range of gene triplet outcome–prediction accuracies that could be expected.p-value, and indicates the number of times in 1,000 trials for which accuracies of 86% or higher can be achieved under the “no predictive capability” null hypothesis.To assess the significance and specificity of the top-scoring gene triplets and their corresponding trained committee of classifiers, a null dataset was created by keeping the same expression levels of genes in the dataset and randomly permuting the class labels of the patients 1,000 times . Classifiers were built using the training null data, and accuracies were calculated on the corresponding test sets. The mean of these accuracies for all the top-performing gene triplets was around 50%. The achieved significance level, which represents the probability of achieving accuracy levels better than or equal to that of the nonpermuted classification, was calculated to be 0.009. This value can be considered a significance level, or Time-series analysis was performed using SAS version 8.0 . Permutation analysis and histogram graphic outputs were produced with Matlab .Dataset S1Gene expression values for all samples at all time points. This is the raw file from which all analyses were performed.(491 KB XLS).Click here for additional data file.Table S1Gene names, symbols, and LocusLink and GenBank accession numbers, as well as primer sequences, are listed for all targets.(160 KB DOC).Click here for additional data file.http://www.ncbi.nlm.nih.gov/projects/LocusLink/) accession numbers for the genes discussed in this paper are BAX (LLID 581), Caspase 10 (LLID 843), Caspase 2 (LLID 835), Caspase 3 (LLID 836), Caspase 7 (LLID 840), FLIP (LLID 8837), IFNAR1 (LLID 3454), IL4 (LLID 3565), IL4Ra (LLID 3566), IRF2 (LLID 3660), IRF4 (LLID 3662), IRF6 (LLID 3664), MAP3K1 (LLID 4214), MX1 (LLID 4599), NFATc2 (LLID 4773), STAT2 (LLID 6773), and TRADD (LLID 8717).The LocusLink (


Precise classification of cancer types is critically important for early cancer diagnosis and treatment. Numerous efforts have been made to use gene expression profiles to improve precision of tumor classification. However, reliable cancer-related signals are generally lacking.Using recent datasets on colon and prostate cancer, a data transformation procedure from single gene expression to pair-wise gene expression ratio is proposed. Making use of the internal consistency of each expression profiling dataset this transformation improves the signal to noise ratio of the dataset and uncovers new relevant cancer-related signals (features). The efficiency in using the transformed dataset to perform normal/tumor classification was investigated using feature partitioning with informative features (gene annotation) as discriminating axes (single gene expression or pair-wise gene expression ratio). Classification results were compared to the original datasets for up to 10-feature model classifiers.82 and 262 genes that have high correlation to tissue phenotype were selected from the colon and prostate datasets respectively. Remarkably, data transformation of the highly noisy expression data successfully led to lower the coefficient of variation (CV) for the within-class samples as well as improved the correlation with tissue phenotypes. The transformed dataset exhibited lower CV when compared to that of single gene expression. In the colon cancer set, the minimum CV decreased from 45.3% to 16.5%. In prostate cancer, comparable CV was achieved with and without transformation. This improvement in CV, coupled with the improved correlation between the pair-wise gene expression ratio and tissue phenotypes, yielded higher classification efficiency, especially with the colon dataset – from 87.1% to 93.5%. Over 90% of the top ten discriminating axes in both datasets showed significant improvement after data transformation. The high classification efficiency achieved suggested that there exist some cancer-related signals in the form of pair-wise gene expression ratio.The results from this study indicated that: 1) in the case when the pair-wise expression ratio transformation achieves lower CV and higher correlation to tissue phenotypes, a better classification of tissue type will follow. 2) the comparable classification accuracy achieved after data transformation suggested that pair-wise gene expression ratio between some pairs of genes can identify reliable markers for cancer. The completion of the Human Genome Project and advances in DNA-array technology have allowed highly parallel genetic analyses to take place on a genome-wide scale. They have revolutionized the way tumors are studied, and promised to provide a better and more thorough understanding of the underlying mechanisms for tumorigenesis. Eventually, they will lead to more comprehensive diagnosis/prognosis of tumor with more effective therapeutic interventions.Tumor development is a process in which gene expression is modified, causing abnormal cell behaviour . Many teDespite its advantages, the DNA-array technology poses three major challenges that render the interpretation of expression data less efficient than expected. Firstly, the gene expression data is inherently variable due to various factors that either depend on biological factors that remain difficult to control , or depend on difficulties in setting up of the experiment (RNA extraction) . These dIn this study, we introduced a novel data transformation meant to investigate relationships between pair-wise gene expression ratios and tissue phenotype within a given experiment. With this procedure, we aimed to discover strong cancer-related signals (features) that exist in the form of pair-wise ratios (or higher order relationship when we extend to N-feature model classifier for N>2) in a given sample, while improving the signal to noise ratio of the dataset by minimizing its coefficient of variation (CV). The underlying concept for adopting pair-wise gene expression ratios as the discriminating axes for tissue type classification is that an experiment is self-consistent . With this approach we could "subtract" correlated variations by considering the sample as a whole, without making inferences such as those needed for normalization. Basically, we avoided studying gene expression in an absolute term because this requires robust normalization method to account for arrays from different experiments, different platforms and different profiling technologies. By resorting to analyze features in the form of ratios, we attempted to minimize the effect of normalization and look for co-varying signals in each experiment..The 62 colon cancer sample dataset is composed of measurements for 1,988 gene probes, of which 40 were labelled as tumor and 22 were labelled as normal. The samples were collected from patients, their RNAs were extracted and hybridised to Affymetrix Hum6000 arrays. Please refer to paper [.The 102 prostate cancer sample dataset is composed of measurements for 12,600 gene probes, of which 52 were labelled as tumor and 50 were labelled as normal. The samples were collected from patients, their RNAs were extracted and hybridised to Affymetrix U95Av2 arrays. Please refer to paper [Both datasets were pre-processed to eliminate those probe pairs that showed significant fluctuation in their hybridisation signals  than their corresponding perfect match probe cells (PM); these probe pairs indicate non-specific hybridisation by background RNAs). Both datasets used average intensity as quantitative measurements of the level of gene expression. Base-10 logarithmic transformations were performed for each dataset.ri (Equation 1) for each gene i using the full dataset, and ranked the genes according to their correlation coefficient ri. For the calculation of r, we assigned a number to each tissue phenotype: 1 for normal tissue and 10 for cancer tissue. After obtaining the correlation coefficients for all genes, we used a simple threshold value (|r|>0.4) to select the set of cancer-related genes. There were two reasons for set the threshold value at 0.4. When lower thresholds were used, we incorporated many genes that were not known to be cancer-related (data not shown). Furthermore, too many genes will later cause computer tractability problem when we calculate their pair-wise gene expression ratio for each tissue sample and later the N-feature model classifier. At |r|>0.4, we were able to account for most of previously known cancer related genes.For downstream classification analysis, we extracted only the genes whose expression pattern correlated strongly to the tissue phenotype. To achieve this, we first calculated the correlation coefficient V1 is a vector representing the gene expression pattern for gene #1; sample Vis the dichotomous representation of tissues; V1Sand sample Sstandard deviation of 1V, sampleV; ,  are the mean of 1V, sampleV.where 1e, 2e...1988e), there are 1988C2 combinations  of pair-wise gene expression ratios , in order to discriminate between the normal/tumor tissues based on specific feature i (single gene expression), the first step is to determine the threshold value, iT, that can optimally splits all the tissue samples into tumor and normal tissue. The FPM algorithm has a recursive version [iTs are derived. Nonetheless, they are very intuitive and non-parametric in nature. Also, they restrict no priori distribution patterns for features used. We adopted the simple FPM for tissue classification where each feature was treated individually. There are two criteria for deriving a valid threshold value i Tfor each feature. First, it has to delineate correctly (discriminating efficiency = 100%) the one-dimensional region (Rfeature_i) for either all the normal/tumor tissues using all tissue samples. Secondly, it has to minimize the percentage of false prediction for the other tissue type. Take gene #1659 for example. To fulfill the two aforementioned criteria, it was determined that the region greater than 63.7 (R#1659) incorporates all the tumor samples  were determined.Regarding the  version , in whics Figure . It clasiTs  were recruited. The outcome of the tissue class will be determined depending on whether one/both the expression values of the unknown sample fall completely in either the normal/cancer region (Rfeature_i). This is to say that if any of the two features from the unknown sample meets the criteria (Rfeature_i) to be either normal/tumor tissue type , the unknown sample will be assigned to be normal/tumor respectively. This is repeated exhaustively for all possible combinations constituting of any two features. The procedure will be repeated for all tissue samples to evaluate the overall classification accuracy for 2-feature model classifier. In total, we evaluated the classification of tissue samples based on different combinations of N genes and investigated the classifiers up to 10-feature model classifier.Now, to classify an unknown sample using 2-feature model classifier, a combination of any two features and their corresponding pre-determined threshold values M. Take the ratio #1537/#1831 for example. To fulfill the two aforementioned criteria, it was determined that the region greater than 0.755 (R#1537/#1831) incorporates all the tumor tissue samples  were recruited. The outcome of the tissue class will be determined depending on whether one/both the expression values of the unknown sample fall completely in either the normal or cancer region (Rfeature_i). This is to say that if any of the two features (pair-wise gene expression ratio) from the unknown sample meets the criteria (Rfeature_i) to be either normal/tumor , the unknown sample will be assigned to be normal/tumor respectively. This is repeated exhaustively for all possible combinations constituting of two features. The procedure will be repeated for all tissue samples to evaluate the overall classification accuracy for 2-feature model classifier. In total, we evaluated the classification of tissue samples based on different combinations of N genes and investigated the classifiers up to 10-feature model classifier.Now, to classify an unknown sample using 2-feature model classifier, a combination of any two features (pair-wise gene expression ratio) and their corresponding pre-determined threshold values r (Equation 1) for all pair combinations of the top 25 genes listed in Table D. Each entry in the pair-wise distance matrix was measured by the value of (1-r). Each row/column corresponds to a specific gene and an entry at the intersection of row X and column Y corresponds to the distance of gene expression between gene #X and gene #Y. Such matrix has a diagonal entry of value 0. Only the lower/upper triangular matrix of D is required to construct the relationship tree. After obtaining lower/upper triangular matrix of D, the neighbor-joining method (NJ) algorithm was used to construct the relationship tree [We calculated the cross correlation coefficient hip tree . with 24 CPUs (each running with a clock speed of 900 MHz) was employed throughout this study. The computation of correlation coefficient and classification procedures were implemented using the Matlab Technical Programming language (Matlab programs can be downloaded at .A Sun Fire 6800 Server r|>0.4) were selected from the colon and prostate dataset for downstream analysis  in a comparable analysis. The heavy chain of non-muscle myosin, denoted as the embryonic smooth muscle myosin heavy chain (SMemb), was found to be down-regulated in cancer. It was also determined experimentally to be a target for the protein encoded by the metastasis-related mts-1 gene [After initial gene selection, respectively 82 and 262 genes , which revealed informative pair-wise gene interaction in relation with their corresponding tissue phenotypes. They reflected how cell adjusts to their pair-wise product in response to physiological changes. Based on these observations, we found that the relative abundance between the numerator and denominator exhibited a strong mutual dependency, and had strong correlation to tissue phenotype. For pair-wise gene expression ratio #119/#54, the elongation factor 1-delta is involved in a sequence of events during the decoding of mRNA on the ribosome [cDNA of mouse that incorporates proteins involved in chromosome partitioning and cell decision [To date, reliable markers with low coefficient of variation (CV) are generally lacking. Discovering robust cancer marker is crucial for the purpose of successful cancer diagnosis. We investigated the CV between samples after data transformation: the lowest CVs decreased to 16.5% in the colon dataset while it increased to 25.8% for the prostate dataset Table . Toppingribosome . For thedecision .Prior to data transformation the lowest coefficients of variations for single gene expression were 45.3% and 24.5% for colon and prostate datasets respectively. When using the data transformation we proposed, significant improvement was achieved in the colon dataset. Interestingly, this was followed by an improved data correlation to the tissue phenotype as well as to the classification efficiency. We did not observe a similar improvement of the CV, data correlation to tissue classes or classification efficiency in the prostate dataset.r| >0.4 from the bulk (Table vs #119 in colon cancer (r = 0.95306) and gene #7775 vs #10749 in prostate cancer (r = 0.92922)). It should be pointed out that the two humps in the probability density function are not zero-centered, but concentrated at non-zero correlation r. For colon dataset, positive correlation was the dominant type. For prostate dataset, a balanced distribution in their gene correlation was observed. We determined that some improvement in tissue classification is achieved when pair-wise gene expression ratio was used as discriminating axes instead of using a single gene expression , others (Human gene for heterogeneous nuclear ribonucleoprotein (hnRNP), P24480 CALGIZZARIN, Human mitochondrial matrix protein P1, Human mRNA for aldose reductase and human adipsin) have not been identified from in-silico studies of tissue DNA-array expression data. The cancer related genes for colon and prostate cancer were ranked according to their discriminating predictive power. The list should provide hints for researchers during selection of molecular target for diagnostic, prognostic or attempts to cure the disease. Overall classification results and accuracies for each N-feature model classifier across two datasets were reported in Table Several previous studies have already endeavored to identify correlations between specific gene expression and cancerous transformation ,13,23. IFor the sake of brevity, we will discuss three single gene expressions and two pair-wise gene expression ratios from colon cancer. For prostate cancer, two single gene expressions and two pair-wise gene expression ratios will be discussed.For colon cancer single gene expression, three axes for discriminating tissue types are: 1) Human monocyte-derived neutrophil-activating protein (MONAP); 2) Human desmin gene and 3) Human cysteine-rich protein (CRP) gene. Their threshold values were determined to be 62.73, 2787.0 and 749.4 respectively.For colon cancer pair-wise gene expression ratio, the two axes for discriminating tissue types are: 1) #1831/#1537 and 2) #753/#768. Their threshold values were reported to be 1.32 and 1.85 respectively.For prostate cancer individual gene expression, the two axes for discriminating tissue types are: 1) Human hepatoma mRNA for serine protease hepsin and 2) Human adipsin. Their threshold values were reported to be 115.0 and 182.0 respectively.For prostate cancer pair-wise gene expression ratio, the two axes for discriminating tissue types are: 1) #6185/#5840 and 2) #6185/#6749. Their threshold values were reported to be 2.69 and 2.55 respectively.To illustrate graphically the result of tissue classification, two examples, each based on three genes or pair-wise gene expression ratios that altogether yielded the optimum classification efficiency for the prostate cancer are shown Figure .B. subtilis and E. coli) and successfully determined the co-regulated operon gene structures (supplementary file #1).The relationship tree for top 25 genes listed in Table As the expression profiling technologies mature, the identification of significant cancer-related signals from noisy datasets (characterized by a high CV) remains a major challenge. In particular, a robust normalization method is critical to ascertain that arrays from two experiments are comparable with minimum noise prior downstream analysis. However, the existing normalization methods pose limitations due to the lack of good models to account for sources of experimental and biological variations . HoffmanHere, instead of resolving to single gene expression, that depends heavily on normalization, for tissue classification, we presented a transformation method that uses pair-wise gene expression ratios within the same experiment as the discriminating axes. By doing so, we aimed to minimize the influence of different normalization methods considering that an experiment is self-consistent with the same factors affecting all genes in the same fashion. The rationale is that even when the normalization methods differ between two array experiments, their pair-wise gene expression ratios within the same experiment will remain relatively stable. If reliable cancer-related signal, exist in the form of pair-wise gene expression ratio, were indeed discovered successfully, they will be relatively independent from the normalization method used on a dataset.100C10= 1.731030945644000 × 1013 different combination of features). As a result, more computation time will be required to search all possibilities. As an example, the discriminating axes that accounted for the optimum accuracy in 1 to 3-feature model classifier are reported in Table The improvement in CV Table  and overiT, in the feature selection procedure. In other word, instead of adopting the more conservative classification accuracy test where only a subset of tissue samples are used to derive a set of classification criteria , we adjusted our methodology to use all tissue samples so that our results are unbiased (when comparing the outcome from single gene and pair-wise gene ratio) and in-line with our objective that is to compare the classification efficiency between single gene and pair-wise gene ratio. Admittedly, we have a noisy dataset whereby selecting a subset of tissue samples that are a representable population for the entire dataset remains a challenge [Regarding the high classification accuracy reported in Table hallenge   Human monocyte-derived neutrophil-activating protein (MONAP); 2) Human desmin gene and 3) Human cysteine-rich protein (CRP) gene. The association of the first two genes and cancer biology had been discussed earlier. We will discuss the Human cysteine-rich protein gene. The expression and induction of this protein has been associated with protection against DNA damage, oxidative stress and apoptosis . In the For colon cancer pair-wise gene expression ratio, the two axes for discriminating tissues are: 1) #1831/#1537 and 2) #753/#768. Using these two axes, 98.4% of the tissue samples can be classified correctly. The expression ratio between #1831 (gelsolin precursor) and #1537  was able to discriminate 93.6% of the total tissue data. The vascular endothelial growth factor was determined recently to be a plausible biomarker for colon cancer . GelsolimRNA for serine protease hepsin, and 2) Human adipsin. The first gene was discussed in the previous paragraph. For the second gene, adipsin had also been suggested by Chow et al. [For prostate cancer single gene expression, the two axes for discriminating tissues are: 1) Human hepatoma w et al.  as a goomRNA for serine protease hepsin) and #5840 (Homo sapiens mRNA for KIAA1109 protein) was able to discriminate 92.2% of total tissues. The human hepatoma mRNA for serine protease hepsin had been determined to be an important marker for cancer cell development [mRNA for serine protease hepsin) and #6749 (Homo sapiens mRNA for KIAA1055 protein) was able to discriminate 90.10% of total tissues. The human hepatoma mRNA for serine protease hepsin was discussed in the previous section. The KIAA1055 protein is an unknown protein in human chromosome 15 [cDNA that had been found to function as a cancer inhibiting protein [For prostate cancer pair-wise gene expression ratio, the two axes for discriminating tissues are: 1) #6185/#5840 and 2) #6185/#6749. Using these two axes, all tissue samples can be classified correctly. The expression ratio between #6185  improved from 87.1% to 93.55% in colon dataset. In prostate dataset, nine out of the top 10 discriminating axes showed significant improvement. The mean accuracy for 1-gene classifier improved from 76.8% to 91.2% and 75.8% to 81.9% in both datasets.4. The comparable classification accuracy achieved after data transformation suggested that there exist some cancer-related signals in the form of pair-wise gene expression ratio, especially prominent in the colon dataset.5. Through the single gene analysis, we identified key biomarkers that agree with the findings by other researchers. In addition, study on gene-to-gene correlation and the classification outcome based on the pair-wise gene expression ratio suggested that genetic network within a cluster of cancer-related genes should be explored further.The authors declare that they have no competing interests.YLY proposed the idea, participated in the design, performed the statistical analysis and wrote the first draft of the manuscript.AD participated in the design and overall coordination of this study as well as in the writing of the manuscript.XWZ participated in the design of the study.YCW, XHW and MTL participated during the revision phase of this study.All authors read and approved the final manuscript.The pre-publication history for this paper can be accessed here:


An increasing number of studies have profiled tumor specimens using distinct microarray platforms and analysis techniques. With the accumulating amount of microarray data, one of the most intriguing yet challenging tasks is to develop robust statistical models to integrate the findings.n = 305 samples) on a common probability scale, we developed a 90-gene meta-signature, which strongly associated with survival in breast cancer patients. Given the set of independent studies using different microarray platforms which included spotted cDNAs, Affymetrix GeneChip, and inkjet oligonucleotides, the individually identified classifiers yielded gene sets predictive of survival in each study cohort. The study-specific gene signatures, however, had minimal overlap with each other, and performed poorly in pairwise cross-validation. The meta-signature, on the other hand, accommodated such heterogeneity and achieved comparable or better prognostic performance when compared with the individual signatures. Further by comparing to a global standardization method, the mixture model based data transformation demonstrated superior properties for data integration and provided solid basis for building classifiers at the second stage. Functional annotation revealed that genes involved in cell cycle and signal transduction activities were over-represented in the meta-signature.By applying a two-stage Bayesian mixture modeling strategy, we were able to assimilate and analyze four independent microarray studies to derive an inter-study validated "meta-signature" associated with breast cancer prognosis. Combining multiple studies (The mixture modeling approach unifies disparate gene expression data on a common probability scale allowing for robust, inter-study validated prognostic signatures to be obtained. With the emerging utility of microarrays for cancer prognosis, it will be important to establish paradigms to meta-analyze disparate gene expression data for prognostic signatures of potential clinical use. DNA microarray analysis has been shown to be a powerful tool in various aspects of cancer research . With thτ2. The effect size was defined to be the difference between the tumor and normal sample means divided by pooled standard deviation. From a Bayesian perspective, Wang et al. [More systematic approaches have been proposed for integration of findings from multiple studies using different array technologies. Rhodes et al.  have prog et al.  used datg et al. . The larpoe  was introduced as a new scale and used in the context of molecular classification [poe in a framework to meta-analyze microarray data. Several desirable features of using poe as a new expression scale include the following: 1. poe provides a scaleless measure and thereby facilitates data integration across microarray platforms; 2. poe is a model-based transformation with direct biological implications in the context of gene expression data, as it is estimated based on a method that adopts an underlying mixture distribution that accommodates over-, under-, and unchanged expression categories; 3. poe unmasks differential expression patterns in microarray data by offsetting the influence of extreme expression values [poe allows merging of samples on the unified scale rather than using gene-specific summaries.A recent study proposed a Bayesian mixture model based transformation of DNA mi-croarray data with potential features applicable to meta-analysis of microarray studies . The basfication . The plan values ; 4. DataIn recent publications of breast cancer microarray studies, several groups have explored the hypothesis that the capacity to metastasize is intrinsic to the tumor and therefore can be revealed by gene expression pattern. Four independent studies have correlated gene expression profiles generated from distinct DNA microarray platforms to breast cancer prognosis -13. Amonpoe. We applied our method to the aforementioned breast cancer DNA microarray data sets. With the strength of the poe transformation and data integration, our goal was to develop an inter-study validated meta-signature that predicts relapse-free survival in breast cancer patients with improved statistical power and reliability.In this proof-of-concept study, we propose a two-stage meta-analysis of microarrays based on poe. The Bayesian hierarchical model employed for estimation borrows strength across genes by assuming further distributions for the gene-specific parameters (see Methods). For data integration purposes, we focused on a common set of 2,555 genes that were profiled in each of the four studies. Although the cost for compiling common genes is a loss of potential predictive features, it is not unreasonable to assume, given the analogous hypothesis explored in each study, that the common set represents the most relevant genes of interest for breast cancer prognosis. The resulting values of poe represent signed probability of differential expression for gene j in sample i, and thus provide a unified measure across studies. Further, the transformation improves contrast in each data set by removing the influence of extreme expression values. In stage 2, the expression profile of tumor samples from multiple studies were combined on the poe scale to generate a meta-cohort. The benefit of data integration using poe is twofold. First, it improves power of statistical analysis by increasing the sample size. Such integration of independent data sets renders sensitivity to those small yet consistent expression changes for certain genes. Second, it reduces the chance of false positive features due to artifacts from a single study, and allows reliable findings across studies. In this paper, we integrated four breast cancer microarray data sets of distinct platforms , not all studies have the time to recurrence information available and instead provide data on recurrence within a certain time interval . To deal with this issue, we utilized a dichotomization where a bad outcome is recurrence during followup and a good outcome is remaining recurrence-free for at least three years. The additional constraint for the good outcome group is to reduce potential bias introduced by short censoring due to insufficient length of follow-up. This is particularly relevant in cross-study analysis, given the heterogeneity in patient recruitment criteria and study designs. Accordingly, of the combined meta-cohort (n = 305) of breast cancer patients, 48.9% were in the poor outcome group, whereas 51.1% in the good outcome group. The sample sizes for each study are shown in Table P ≤ 0.001) in all cross-validation steps, representing a cohort of essential genes strongly associated with breast cancer recurrence. By random chance, there would be on average 2.5 genes to be found significant at P ≤ 0.001 in a set of 2,555. By finding 23 genes with a P ≤ 0.001, it is clear that there are much more predictive features than would be expected by random chance.Each gene was then associated with the recurrence status by a logistic regression within a leave-one-out cross validation scheme, and rank-ordered by the significance level of the coefficient. As a result, 23 genes held up as significant predictor of recurrence  as a linear combination of the P < 0.0001). In spite of the heterogeneity of the combined patient population, the meta-signature predicted the odds of recurrence for a patient showing a high risk signature as four times of the odds of recurrence for a patient showing a low risk signature. Several studies have implicated that the lymph node status is one of the principal clinical factors to classify patients in relation to the risk of relapse of breast cancer [By minimizing the misclassification error, we obtained a 90 gene meta-signature that reliably predicts outcome in the meta-cohort. This meta-signature classified 122 patients into a high risk group, where 84 (69%) of them had a recurrence. On the other hand, the signature classified 183 patients into a low risk group, where 118 (64%) of them did not recur by the end of the followup. By cross-tabulating the risk groups predicted by the meta-signature and the actual recurrence status, we obtained an estimated odds ratio of 4.0 . Similarly for nodal positive patients, a cohort thought to be at high risk of recurrence, the meta-signature identified 79 (51.6%) of the LN+ patients to have, in fact, lower recurrence risk over time . A multivariate logistic regression model suggested that the meta-signature is an independent predictor of the recurrent status with respect to nodal status in the meta-cohort (OR = 3.7(2.3–6.1), P < 0.0001).Kaplan-Meier analysis provides further evidence that the meta-signature was a significant prognostic index of breast cancer recurrence in the meta-cohort Figure . The estTo comprehend the potential gains of such two-stage meta analysis over individual analysis in each single study cohort, we constructed study-wise gene expression signatures using the same method. By minimizing the misclassification errors, we obtained a signature consisting 10, 60, 100, and 130 genes for Sorlie, van't Veer, Sotiriou, and Huang study cohort respectively . The resMeta-analysis accounts for such heterogeneity of the individual signatures in two ways. First its overlap with the study-specific signatures ranged from 3–40%. The excluded genes are likely to be cohort-specific findings that can not be replicated. Second, the meta-signature recruited 41 genes not previously picked by any of the single cohort signature, likely representing predictive features with small but consistent effects previously masked in single studies. When examining the performances of the gene signatures, the meta-signature showed a comparable or better performance compared with the individually optimized signatures both in the odds ratio estimates  terms and then grouped by functional classes. Based on the hypergeometric distribution, we calculated the significance of over-representation of a particular process in the signature. Figure poe scale. In particular, poe provides a unified platform-free scale, and simultaneously enhances the intrinsic contrast in the expression data. Furthermore, combining sample pools on the poe scale mitigates the influence of potential artifacts from a single study. The benefit of such data integration is reflected on two counts. One, integrated sample cohorts improve the reliability of the findings by guarding against false positive results from a single study. Two, it increases the statistical power to detect small consistent effects that can be otherwise masked by inadequacy of the sample size of an individual data set. By implementing this modeling approach, we were able to combine information from four microarray studies to build an inter-study validated meta-signature for predicting survival in breast cancer patients.Several important issues to consider when integrating microarray studies include use of different gene expression measurement scales, varying analytical power and reliability of the results for individual studies. To account for these issues, we proposed a two-stage mixture modeling strategy, the strength of which was built on the mixture model based transformation and the subsequent data integration on the As described earlier, a common set of 2555 genes was used in this meta-analysis, as it is important to provide the same context for data-driven estimation of the posterior probabilities. Although we assume the common set comprises the most biologically relevant genes, the loss of potential predictive genes, however, may offset the statistical power of the analysis. For example, one of our recent studies has established the polycomb protein EZH2 to be an independent predictor of breast cancer survival outcome. This geFunctional annotation of the meta-signature revealed genes such as Cyclin E and BCL2, which were previously shown to be correlated with survival outcome in breast cancer ,24. A stIn conclusion, a distinction of the analysis presented here relative to those by other authors ,6 is thaThe breast cancer microarray data sets were obtained at the author's websites from four recently published studies -13. EachX with elements xij, where i = 1, ..., mk, j = 1, ..., n . The expression measurement xij can be the ratio of the two fluorescent dye hybridization intensities for the spotted cDNA arrays[E be a latent class variable, and eij indicates over-, under- or normal expression for each entry of the R matrices. We have:Each of the four raw data sets was treated as an expression matrix NA arrays,12 and tNA arrays, or averNA arrays. Let E beij are latent and not directly observed from the data. We were interested in estimating the probabilities of eij being 1 or -1 given the observed raw expression xij, which were denoted as  and . Estimates of these latent quantities were obtained under a Bayesian mixture model setting. In particular, we assume the raw expression xij falls into one of the three expression categories. For each gene j, the expression then arises from a mixture of three distributions:The values of xij|eij = 1) ~ fj1,(·), (xij|eij = 0) ~ fj0,(·), and (xij|eij = -1) ~ fj-1,(·). and  = Peij = -1) are the multinomial probabilities for eij. With the specifications of models, we can calculate the latent quantities by Bayes' rule:respectively. Here, U refers to a uniform distribution and N refers to a normal distribution. By noting that the supports for the two uniform distributions are disjoint, the probabilities of differential expression are mutually exclusive with the forms:poe = p+ - p-. As a result, poe ranges from -1 to 1, and can be interpreted as the signed conditional probability of differential expression.A one dimension measure can thus be constructed as To borrow strength across genes, the estimation of the gene-specific parameters was formulated under a Bayesian hierarchical model setting. Given the large amount of parameters, prior distributions were specified to model the variation of the gene-specific parameter estimates, in particular, were obtained for each of the five data sets , we defined outcome groups as recurred during followup and remained relapse-free for at least 3 years. In particular, Let t* can be specified with clinical knowledge. We chose t* = 3 years in this study. We then consider constructing classifiers using y; note that y = 1 corresponds to the poor outcome group and y = 0 to the good outcome group. The sample sizes for each study are shown in Table where j, we fit the following univariate logistic regression model using data from all studies:Logistic regression was used to build a classifier for prognosis. For each gene x* is the rescaled value that allows data integration across multiple studies. The esti-mated values of βj, , are then used to form a risk score using a variation of the compound covariate predictor method [x1, ..., xD, the risk index is given as .where r method ,29; for , where , and  is the effect estimate for gene j in the combined meta-cohort without the ith sample. The risk index for sample i is a weighted linear combination of the expression profiles of the top D genes, where the ranking of the genes is based on their corresponding significance in the univariate logistic model fit. Classification of sample i to the risk groups is then based on the ith leave-one-out risk index, i.e.,  = I{RIi >c} with c being the empirical quantiles (40th - 70th) of the RI's. The number of genes D in a classifier is treated as a parameter and optimized to minimize the prediction error rates.If we want to assess the performance of the classifier, we must deal with the issue of training and testing the model using the same data. An "honest" estimate of the prediction error rate is obtained using leave-one-out cross-validation. Define a risk index The list of the top cumulative genes in the meta-signature was obtained by ranking all 2,555 genes by the number of times in the leave-one-out cross-validation steps that each one had a P-value from the univariate logistic regression less than 0.001.poe pro-files of the meta-signature. Yellow represents high probability of over-expression and blue represents high probability of under-expression. For heat maps of raw data matrices, we preprocessed the data by mean centering and then dividing by the standard deviation for each row. The means and the standard deviations used in the normalization were the relapse-free (RF) sample means and variances for each study data. The values for the recurrence (R) samples after standardizing then represented the number of standard deviations over or under the mean RF sample expression.We used the treeview software  to generRS, DG, and AC designed the study. RS carried out the statistical analysis and prepared the manuscript. DG and AC supervised the analysis and participated in the manuscript preparation. All authors read and approved the final manuscript.Plots of misclassification rates. The PDF file lists plots of misclassification error rates for classifiers identified in each individual study cohort and the meta-cohort.Click here for filePlots of Kaplan-Meier curves. The PDF file lists Kaplan-Meier plots for study-wise cross-validation of the individually identified signatures. A gene signature was trained in one study cohort and used to validate in each of the other study cohorts as testing sets.Click here for fileMeta-signature gene list. The excel file contains a list of Unigene ID, gene symbol, and full name of the 90 genes in the meta-signature.Click here for fileet al. study data .POE imputation of the Sorlie data. The excel file contains a table of imputed signed probability matrix transformed from the Sorlie Click here for fileet al. study data .POE imputation of the van't Veer data. The excel file contains a table of imputed signed probability matrix transformed from the van't Veer Click here for fileet al. study data .POE imputation of the Sotiriou data. The excel file contains a table of imputed signed probability matrix transformed from the Sotiriou Click here for fileet al. study data .POE imputation of the Huang data. The excel file contains a table of imputed signed probability matrix transformed from the Huang Click here for file


Microarray experiments are often performed with a small number of biological replicates, resulting in low statistical power for detecting differentially expressed genes and concomitant high false positive rates. While increasing sample size can increase statistical power and decrease error rates, with too many samples, valuable resources are not used efficiently. The issue of how many replicates are required in a typical experimental system needs to be addressed. Of particular interest is the difference in required sample sizes for similar experiments in inbred vs. outbred populations (e.g. mouse and rat vs. human).We hypothesize that if all other factors  were equal, fewer individuals would be needed for the same statistical power using inbred animals as opposed to unrelated human subjects, as genetic effects on gene expression will be removed in the inbred populations. We apply the same normalization algorithm and estimate the variance of gene expression for a variety of cDNA data sets  comparing two conditions. Using one sample, paired sample or two independent sample t-tests, we calculate the sample sizes required to detect a 1.5-, 2-, and 4-fold changes in expression level as a function of false positive rate, power and percentage of genes that have a standard deviation below a given percentile.Factors that affect power and sample size calculations include variability of the population, the desired detectable differences, the power to detect the differences, and an acceptable error rate. In addition, experimental design, technical variability and data pre-processing play a role in the power of the statistical tests in microarrays. We show that the number of samples required for detecting a 2-fold change with 90% probability and a p-value of 0.01 in humans is much larger than the number of samples commonly used in present day studies, and that far fewer individuals are needed for the same statistical power when using inbred animals rather than unrelated human subjects. Microarray technology has become an important tool for studying gene expression levels on the whole genome scale . One impIn general, the required sample size depends on the magnitude of the variability of the population, the magnitude of the expression change that is biologically meaningful (or desirable to detect), the power to detect the expression change, and the P-value/significance level/false positive rate. However, power and sample size have been viewed as complicated and difficult issues for microarray studies due to the large number of genes being investigated and little knowledge of the degree of natural expression variation within a population. To date, very few studies have assessed power and sample size requirements in microarray experiments. Pan et al.  proposedPair-wise comparisons between conditions/groups/treatments are frequently used in microarray studies. Parametric and nonparametric statistical methods have been proposed to identify differentially expressed genes, among which t-tests are most commonly used. This paper is intended to provide some guidelines for sample size planning for pair-wise comparisons. Normalization is an essential and important pre-processing step in microarray data analysis. To our knowledge, no previous studies using multiple data sets have pre-processed the data sets in a comparable way. In addition, previous studies did not look at the effect of inbred vs outbred populations on the variation of gene expression. In order to make the results more comparable, we make use of 7 cDNA microarray data sets and apply the same normalization method .th, 75th, 50th and 25th percentile of genes ranked by variability at fixed settings for false positive and false negative rates. The sample size calculation provides the approximate but not exact number of replicates required for a given set of criteria.We estimate the variance by one sample t-test, paired t-tests or two sample t-tests on a gene-by-gene basis using several large expression data sets from both human, rats and mice. We then calculate the sample size required to detect a 1.5-, 2-, and 4-fold change in expression levels for the 90. Removing the gene IDs does not affect the analysis in this paper in any way. The same website also provides the links for the published data sets. In addition, all the control genes were removed from the data analysis for the cDNA data sets.We estimate the standard deviation and required sample size from 1 unpublished and 6 published cDNA data sets (Table Data set A comprises data generated from 40 liver RNA samples isolated from paired liver hepatocellular carcinoma (HCC) tumor and adjacent cirrhotic non-tumor tissue from 20 HCV infected Caucasian patients . The objData set B was generated from 41 matched pairs of prostate tumor and non-tumor tissue hybridized to arrays spotted with 38627 cDNAs. All samples were labeled with Cy5 and co-hybridized with a common reference labeled in Cy3 [Data set C was generated from RNA isolated from paired HCC tumor and adjacent non tumor liver from 41 HBV infected patients ,9 hybridData set D was generated from RNA isolated from paired liver and kidney tissue from 6 male C57BL6 mice  hybridizData set E was generated from RNA isolated from 36 breast ductal tumor and 16 lobular tumor tissues  hybridizData set F consists of data generated from 24 liver tissue samples from 12 inbred mice (unpublished data). One third or two thirds of the liver was removed from each mouse and used as the baseline samples. At 12 hours post operation, the mice were sacrificed and the remaining liver tissue was used as the experimental sample. The aim of this study was to screen for genes potentially related to liver regeneration after hepatectomy. RNA samples from the 12 hour post-operation livers were co-hybridized with their own baseline liver samples. A total of four DNA arrays were used for each sample comparison. Two sets of arrays (MOD1 and MOD2), each containing 6528 different cDNAs spotted in duplicate (A and B) on each array were used. In addition, each comparison was done with a dye flip pair of slides. This data set made use of arrays generated at the University of Washington Center for Expression Arrays.The goal of data set G was to identify genes with altered expression in the liver tissues of two mouse models with very low HDL cholesterol levels (treatment groups) as compared to inbred control mice. The mouse model considered in this study is the Apolipoprotein AI (ApoAI) knock-out, where ApoAI is a gene known to play a pivotal roles in HDL metabolism ,12. EachIn summary, three of the data sets  are from inbred mouse and rat strains respectively, and the other four data sets  are from large scale studies of gene expression in humans. If all other factors  were equal, one might anticipate that fewer individuals would be needed for the same statistical power using inbred animals as opposed to unrelated human subjects..Background adjustment and normalization is necessary to remove systematic biases of non-biological origin in microarray studies. A number of methods of background correction and normalization have been proposed ,14. We u2 transformed prior to data analysis. Figure 2 ratio (sample/reference) of two independent groups.The distribution of the standard deviations estimated from these 7 data sets are presented in Figure σ), the desired detectable fold change (δ), the power to detect this change , and a chosen type I error rate (α). For microarrays, a combination of fold-change and test p-value is commonly used for selecting differentially expressed genes between two groups or conditions. In this study, sample sizes were calculated in R using the function of power.t.test. The required input parameters are the log scale fold change of interest δ , significance level, power, and the standard deviation , the type of t-tests , and the type of test (two sided or one sided).The required sample size of an experiment depends on the variance component (δ = 1) in expression level between tumor and non-tumor tissue in the 75% least variable genes (σ <= 0.5884) with a two sided 0.001 significance level test with 90% power, we could use the following R functionFor example, in the case of data set A (one sample t-test), if we wish to find out the approximate sample size to detect a 2 fold change th percentile of the standard deviation of log ratio.Where sd = 0.5584 is the 75δ = 1) in expression level between knock-out and control mice in the 75% least variable genes (σ <= 0.3102) with a two sided 0.001 significance level test with 90% power, we could use the following R functionIn the case of data set G (two sample t-test), if we wish to find the approximate sample size to detect a 2 fold change th percentile of the common standard deviation of log (sample/reference).Where sd = 0.3102 is the 75β to reject for a two sided testing and strict interpretation of tail probability with significance level α for detecting a difference of δ, the minimum number of samples or pairs is obtained by solving the following equation iterativelyIn R, for a one sample t-test or a paired t-test to have power 1-v, ncp < tα/2v, ) + PrPower = Pr, then the sample size (n) for each group is obtained by solving the following equation iterativelyFor a two sample t-test with equal sample sizes, if we wish to have a large enough sample to detect a difference v, ncp < tα/2v, ) + PrPower = Pr of 0.05 is often employed in hypothesis testing. Thousands of genes are usually studied in microarray experiments. When more than 10,000 genes are tested independently, we would expect more than 500 genes to appear as false positives when the 0.05 significance level is applied. Hence, a smaller cut-off p-value should be used in order to reduce the number of false positives. Many multiple testing correction methods have been proposed. The simplest one is the Bonferroni correction (family wise error control) where the nominal significance level is divided by the number of tests. The Bonferroni correction is very stringent. False discovery rate (FDR) , the proFor reference, Table Factors that affect sample size calculation include the magnitude of the variability of the population, the magnitude of the desired detectable expression change, the chosen power to detect the expression change, and the cut-off P-value/significance level/false positive rate. For a given study, the variability of the population being studied is fixed, and once researchers have identified the desired detectable expression change, the required sample size depends on the chosen false positive and false negative rates. The variability of human subject data is typically larger than that seen with laboratory animals and cell lines due to genetic influences on gene expression. Hence, more replicates are needed for studies that involve human subjects (or any other outbred population) than for studies with samples from an inbred population. This is readily apparent in the cDNA data in Multiple levels of replicates are common in two color microarray experiments. Multiple arrays probed with RNA samples isolated from multiple individuals of a population/treatment/group are referred to as biological replicates. Multiple arrays hybridized using the same RNA or multiple replicates of the same gene within an array are referred to as technical replicates. Although technical replicates can improve the precision and the reliability of the measurement and provide information for quality control, biological replicates are most effective in reducing the variance of the estimate of mean difference. Biological replicates therefore increase the power to detect biologically significant gene expression differences. More importantly, when trying to identify differences between a treatment and a control group, accurate estimates of the biological variability within the groups is essential to determine if the between group differences are meaningful  or other method).Careful experimental design is necessary to maximize the statistical power of the test -18 whileThis paper is intended to give some guidance to those planning microarray experiments. The sample size calculations we performed provide an approximate number of replicates for a given set of criteria. Our studies were limited to a small number of published microarray studies for which the following criteria were true:1) A reasonably large number of biological replicates were analyzed.2) Raw data was readily available so that we could reprocess all data with the same algorithms.3) Other potentially large sources of variability such as flow sorting, laser micro-dissection and/or multiple rounds of amplification were not present.We have only analyzed date from a limited number of tissue types – liver, prostate, breast and blood in human, liver and kidney in mouse, and mammary gland in rat. It is entirely possible that different tissue types will have larger or smaller degrees of biological variation and hence will require more or fewer samples to reach a given conclusion. In addition, lab or experiment specific methods of obtaining and processing samples may induce greater degrees of expression variation than seen in our sample data. As more large data sets become available, it will be useful to extend these studies to better define the magnitude of gene expression variation in purebred animals and in outbred humans across a variety of tissues.However, the data shown in Background adjustment and normalization is needed in microarray data analysis in order to remove non-biological variation. Intensity based normalization methods such as locally weighted least square polynomial regression (lowess) is commonly used in cDNA microarray experiments. The background subtracted intensities were normalized by the spatial lowess method using the R add on package MAANOVA written by the Jackson Lab. For the two cDNA experiments with replicate panels within each array, we normalized the two panels separately. All control genes were excluded from data analysis for data sets A-G.Pair-wise comparisons among conditions/groups/treatments of gene expression levels are common goals of microarray studies. Simultaneous comparison of more than two treatments/conditions using one way ANOVA can be advantageous. However, a significant F for a comparison of several treatments does not provide information about which particular groups differ from each other. In addition, one way ANOVA is not sensitive to treatment effects when only one or two samples out of many are quite different. T-tests are commonly used to compare individual treatments in pairs.2 ratio of tumor/non-tumor as the response variable. Data sets B-D were generated from paired samples using a reference design on cDNA arrays; Paired t-tests are appropriate for these three data sets. We performed two tailed, two sample (or independent) t-tests on data sets E-G with normalized log ratio as the response variable. The two sample t-tests are based on unequal variances for the two groups of samples.In order to calculate power and plan sample size, one must first estimate the variance. We applied paired or two sample t-tests in this study based on the correlation between the two groups. For data set A, as the pairs of tumor and adjacent non-tumor tissue are highly correlated, we used two tailed one sample t-tests with the normalized logThe variances of the data sets with paired samples are the variance of the difference. The common variance of the datasets with independent samples was estimated by the following formula:1, n2 are the number of observations for group 1, and group 2, respectively; and S1 and S2 are the standard deviation for group 1, and group 2, respectively.Where nbiological variance, the log ratios of the 4 technical replicates of data sets A, E, and G were averaged for each RNA pair (data set A) or sample (data sets E and G). The standard deviations across biological replicates were estimated on a gene-by-gene basis. Sample sizes were calculated using R for detecting a 1.5-, 2- or 4-fold change for the 90%, 75%, 50%, and 25% least variable genes with a range of power  and confidence level , assuming equal sample size for the two groups. The numbers for sample size are rounded to integers.To simplify power and sample size calculation, and to focus our calculation on JL provided the mouse liver microarray data set F prior to publication. CW performed all the analysis in this paper. RB supervised JL and CW and contributed to the design, coordination and writing. All authors read and approved of the final manuscript.α) and power (1-β). This additional file shows the estimated sample size to a 1.5-, 2, and 4-fold changes of expression level for the 90%, 75%, 50%, and 25% least variable genes for a given settings of false positive rates (α) and power (1-β) for all of the data sets referred in Table 1.Sample size required to detect a 1.5-, 2-, and 4-fold changes of expression level for the 90%, 75%, 50%, and 25% least variable genes for a given settings of false positive rates (Click here for file