Breast cancer is the most common malignancy in women, and because it has a high mortality rate, it is urgent to develop computational methods to increase the accuracy of breast cancer survival predictive models. Although multi-omics data such as gene expression have been extensively used in recent studies, the accurate prognosis of breast cancer remains a challenge. Somatic mutations are another important and promising data source for studying cancer development, and its effect on the prognosis of breast cancer remains to be further explored. Meanwhile, these omics datasets are high-dimensional and redundant. Therefore, we adopted multiple kernel learning (MKL) to efficiently integrate somatic mutation to currently molecular data including gene expression, copy number variation (CNV), methylation, and protein expression data for the prediction of breast cancer survival. Before integration, the maximum relevance minimum redundancy (mRMR) feature selection method was utilized to select features that present high relevance to survival and low redundancy among themselves for each type of data. The experimental results demonstrated that the proposed method achieved the most optimal performance and there was a remarkable improvement in the prediction performance when somatic mutations were included, indicating that somatic mutations are critical for improving breast cancer survival predictions. Moreover, mRMR was superior to other feature selection methods used in previous studies. Furthermore, MKL outperformed the other traditional classifiers in multi-omics data integration. Our analysis indicated that through employing promising omics data such as somatic mutations and harnessing the power of proper feature selection methods and effective integration frameworks, the breast cancer survival predictive accuracy can be further increased, thereby providing a more optimal clinical diagnosis and more effective treatment for breast cancer patients. Breast cancer is the most common malignant tumor in women. Although there are millions of breast cancer survivors in the United States, breast cancer is the main cause of cancer-related deaths worldwide because of its high mortality rate . Thus, iRecently, the Cox regression model  and tradOne of the biggest challenges in breast cancer research involves the effective combination of heterogeneous data sources into survival prediction models, making the selection of a proper integration method essential. In previous studies , multiplA previous study  showed tCurrently, somatic mutations are strongly correlated with the clinical symptoms of breast cancer , and theIn the present study, we applied the state-of-the-art MKL method in the integration of somatic mutation datasets with previously used omics data, including Exp, CNV, Methy, and Protein, to train and test an integrated breast cancer survival prediction model. The maximum relevance minimum redundancy (mRMR) algorithm  was usedIn order to gauge the performance of our method, first, the newly introduced method was compared with different single data types and integrated datasets to verify the effectiveness of somatic mutations, and the results indicated that there was a remarkable improvement in the prediction performance when somatic mutations were included. Different feature selection algorithms were then studied, and the experimental results demonstrated that mRMR was the most optional among them. Furthermore, the MKL classification method was compared with other traditional classifiers, and the experimental results proved the superiority of MKL in data integration. Finally, the newly introduced model was validated in an independent validation dataset and achieved a promising high accuracy in survival prediction. According to the results, the most optimal performance was achieved by our method, which demonstrated the feasibility of integrating somatic mutations in the prognostic models and the usefulness of mRMR and MKL in breast cancer prognosis.The reminder of this article is organized as follows. A workflow of our proposed method and related methods are described. Next, comparative studies were carried out to evaluate the performance of the proposed methods and their comparison methods, as well as to analyze the most informative features discovered by our model. Then, we applied our model on the validation dataset. Finally, the proposed method is discussed, and it is expected to undergo the improvement in future studies.The workflow chart of the proposed method is shown in The three main steps include: (1) The most N-informative features were separately selected using the mRMR method for each type of data in the learning dataset; (2) SimpleMKL with 10-fold cross-validation was deployed on the learning dataset for breast cancer prognosis to train an optimal model; and (3) the prediction model on learning dataset and the validation dataset were evaluated for their ability to learn data. A detailed description of each of the steps is listed below.1  cancer browser website1 . The dow1 . We fina1 .We followed the protocol from our previously published studies , 2019, aIn the present study, the survival prediction for breast cancer was defined as a binary classification problem with a threshold of 5 years as conducted in previous studies . Of the Five different types of genomic data were used in the present study, as described above, and the number of variables for most types of genomic data exceeded 10,000 after feature preprocessing. However, this large number of features may cause poor performance due to dimensionality and high redundancy . Therefoith variable with N individuals is denoted as vi ∈ MR,i = 1,…,M, and the survival prediction labels with N individuals as l ∈ R. For label l, mRMR aims to search a feature subset S with k features{vi}, which collectively have the maximal relevance (Max-Relevance) Relon the target label l and the minimal redundancy (Min-Redundancy) Red(S).The mRMR is a feature selection method that aims to select a subset of features that are highly related to the output classes and have low redundancy between them . In the S,l) is calculated using the mean value of all F-statistic values F of the individual variables vi with the label l. In parallel, the Min-RedundancyRed(S) constraint was adopted to select irrelevant features, and is shown as Eq. 2.The F-statistic (F) was used to calculate the relevance between feature variables with binary survival terms and the Pearson correlation coefficient (PCC) was used to measure the redundancy for the continuous feature variables of the gene expression, CNV, gene methylation, and protein datasets. Max-Relevance is defined in Eq. 1, where relevance Rel is obtained by the mean value of all MI values of individual variable vi with label l. The Min-Redundancy constraint Red(S) is used to select irrelevant features, and is shown as Eq. 4.For binary discrete feature variables of somatic mutation data, the mutual information (MI) was used to calculate both the relevance between feature variables and survival terms, and the redundancy between mutations. Max-Relevance is used to select features satisfying Eq. 3, where relevance Rel was deployed to simultaneously optimize the two constraints “Max-Relevance” and “Min-Redundancy” based on the MI quotient (MIQ) criterion  to obtaik for each data type was determined by comparing the AUC valued for the models. After the mRMR features were selected for each type of genomic data, the most informative features were combined and used as the input feature set for the classification problems.The area under the curve (AUC) value is used as a metric to evaluate the performance and the most optimal number of the most relevant and non-redundant features M kernels. The optimal combination of kernels is given as Eqs 6 and 7:In our study, we aimed to integrate multiple types of genomics data, with a focus on somatic mutations. Although the fusion of multiple types of data into one model is one of the most widely used methods for classification, this is not feasible due to the fact that different types of molecular data present different feature representations . MKL hasdm denotes the weight of the mth different kernel Km.where dm of the kernels were 0 and thus non-contributory to the MKL model . The “Poly” (Eq. 11) polynomial base kernel with a search range of degrees of freedom d{1 2 3}  and the d{1 2 3}  were useIn summary, the SimpleMKL directly addressed a multiple kernel SVM optimization problem and greatly reduced computation costs when compared to the use of learning kernel combinations from individual kernels.The dataset used in our study was randomly divided into learning and validating sets in order to assess the performance of the proposed method. For the learning set, we used mRMR to select the most optimal features and to determine the model through 10-fold cross-validation experiments. Then, the pre-trained MKL model and its optimal parameters were used to predict the validation set. Because the validation dataset was not used in the cross-validation process, the model derived from the learning dataset was tested on an independent validation dataset.To assess the performance of our model, AUC, the most widespread evaluation metric for classification problems, was used to assess the performance of the proposed model. AUC is defined as the area under the receiver operating characteristic (ROC) curve, and it is used to quantify the overall performance of a classification model. Specifically, AUC = 1 denotes perfect performance, and 0.5 denotes random guessing. Pre , Sn , Sp , and Acc  were also employed in addition to AUC as classification performance metrics for breast cancer prognosis. The definitions of those metrics are provided below:where TP, FP, TN, and FN denote true positive, false positive, true negative, and false negative, respectively.The proposed method was compared with other methods in three different applications: (1) comparison of the results of the models with different datasets based on the same method; (2) comparison of the results of different feature selection methods under the same datasets; and (3) comparison of the integration results of classification methods, under the same integrated datasets. AUC was used as an evaluation metric when comparing different methods and 10-fold cross-validation was applied for all methods.Seven different MKL-based models were built using five single types of molecular data  and two integrated datasets with and without somatic mutation data in order to evaluate the role of somatic mutations in breast cancer survival prediction. The dataset integrating gene expression, CNV, gene methylation, and protein expression is abbreviated as “ECMP,” and the dataset integrating all five molecular datasets including somatic mutations is denoted as “ECMPS.”The corresponding mean of the AUC value of 10-fold cross-validation (CVmean_AUC) for each of the seven models, using the mRMR feature selection and the MKL classification method, was calculated to compare the predictive performance of breast cancer survival models. The results are displayed in In The Pre, Sn, Sp, and Acc values for each dataset model were calculated in addition to the AUC based on the proposed method, and the results are presented in k for each molecular data type was determined by comparing the AUC values in the prediction results. According to the number of features reported in the previous study , respectively, for further integration analysis, and the total 290 features were obtained for our integrated ECMPS model.The classification outcomes of the five data types under different parameters are presented in The F-statistic (F) and PCC were used for the mRMR feature selection method to calculate the relevance and redundancy , respectThe proposed mRMR method outperformed both k-best feature selection methods F-statistics and IGR for four continuous molecular data types and their integration ECMP model according to the results shown in As the red line shows in The proposed method achieves a stronger performance by integrating somatic mutations compared with those methods incorporating single data types and integrated datasets without somatic mutations. The MKL classification method was compared with two widely used classifiers, SVM and RF, to further verify its ability to combine different types of data. Experiments were conducted in two integrated datasets: ECMP and ECMPS, which were selected by mRMR. The AUC value  was used to assess the performance of different methods and the results are provided in In addition, the performances of all the classifiers were improved when employing ECMPS compared with ECMP, which further suggested that somatic mutations can provide adequate supplementary information for survival prediction of breast cancer. Finally, our method achieves the most optimal performance due to its ability to integrate multiple molecular data types, including somatic mutations, and MKL was quite efficient in integrating the data from distinct sources in breast cancer survival prediction.The top 10 features ranked by mRMR for each molecular data type were further analyzed by conducting a simple analysis on their association with breast cancer. Only features from somatic mutations and gene expression datasets were explored to further assess the effectiveness of our method. The results of this analysis showed that it was previously reported that some of the genes are associated with breast cancer survival. These genes and their references are listed in Optimization techniques have been previously applied  to selecWe integrated somatic mutations and previously used data types, including Exp, CNV, Methy, and protein, using MKL to predict breast cancer patient survival. Applying mRMR-selected features and MKL classification, we found that the integration of somatic mutations enriched the diversity of features and was conducive to the improvement of the prediction model. In all, integrating promising data sources such as somatic mutations and harnessing the powerful feature selection method mRMR and the effective data fusion method MKL can increase the prediction accuracy of breast cancer patient survival.Although our method is effective and can accurately predict the survival of breast cancer patients, some limitations remain in the prognosis of breast cancer. For instance, there may be more effective methods that can be used to construct kernels for an improved multi-kernel learning method in the future that will further improve the performance in multi-omics data fusing. In addition, our available sample size was limited by the intersection of multiple types of molecular data samples. Thus, the performance of our method could be promoted when a larger population of samples becomes available in the future. Furthermore, somatic mutations are highly heterogeneous among patients, and therefore, further understanding of the mechanism of somatic mutation in cancer may lead to a more accurate prognostic model for breast cancer.The original contributions presented in the study are included in the article/ZH and JZ participated in the design of algorithms and experiments and participated in the design of the whole framework of prediction of breast cancer survival. JZ directed the whole work. YZ participated in the analysis of the performance of the proposed method. JZ and XY conceived of the study and helped edit the manuscript. All authors read the final manuscript and approved the submission.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Determining the etiologic basis of the mutations that are responsible for cancer is one of the fundamental challenges in modern cancer research. Different mutational processes induce different types of DNA mutations, providing ‘mutational signatures’ that have led to key insights into cancer etiology. The most widely used signatures for assessing genomic data are based on unsupervised patterns that are then retrospectively correlated with certain features of cancer. We show here that supervised machine-learning techniques can identify signatures, called SuperSigs, that are more predictive than those currently available. Surprisingly, we found that aging yields different SuperSigs in different tissues, and the same is true for environmental exposures. We were able to discover SuperSigs associated with obesity, the most important lifestyle factor contributing to cancer in Western populations. Cancer is the end result of a process of accumulation of genetic and epigenetic alterations. A small fraction of these alterations is inherited and the remainder is due to either random errors made during DNA replication or to environmental factors . DelineaMutational signatures can provide unique insights into etiology because different mutational processes result in different types of mutations. For example, it has long been known that ultraviolet light often results in C to T transitions at dipyrimidine motifs , while aBased on these classical studies, systematic analyses of genome-wide sequencing data have been performed in an effort to discover new mutational signatures associated with various exposures. The classic and most commonly used approach  employs supervised learning methods are expected to identify stronger associations and make more accurate predictions than unsupervised ones  database . Four key features distinguish our approach for identifying signatures.Our primary methodological step is to use supervised machine learning, that is we learn the signatures from the data, by using the available annotation on clinical variables such as age, smoking status, and body mass index. By using this information explicitly, we expect to identify stronger associations and make better predictions.We do not specify a pre-determined base length, such as 3-base pairs , as the We employ a probabilistic approach to signature discovery. An important characteristic of any mutational process is its randomness. The mutational distribution caused by the same etiological factor varies greatly among exposed patients: a mutation type very frequent in some patients may not be common in others. From a biological point of view, it seems natural that each patient – and in fact each cell - may have her/his individualized signature characterizing a specific etiological factor. Our signatures are therefore built only on a subset of selected features that are robust across the exposed population, that is features with relatively low variance, thereby increasing their predictive power.We do not force the assumption that a given mutational process must have the same mutational signature across tissues, contrary to the approach developed by Alexandrov et al. where a given signature (e.g. signature 1) is the same across all tissues.Our method for deriving mutational signatures is based on several steps. First, we construct a nested tree containing all potential features, with all mutations as the root, and all six single-base substitutions  as the first level, followed by single-base substitutions with one flanking base as the second level, and by single-base substitutions with two flanking bases as the third level, and where the edges are placed between features which share mutations . In prinAfter ‘pruning’ the tree in order to keep only the features that have counts significantly different from their expected values , these remaining features are ranked based on their ability to classify a given exposure, that is to discriminate exposed patients from unexposed ones, as measured by the area under the receiver operating characteristic (ROC) curve (AUC). The set of n top features that provide the highest prediction performance in terms of AUC form our signature for a given exposure and are used for prediction . A detaiThe value of a mutational signature can be assessed by its prediction accuracy (AUC) in classifying patients as exposed or not to the associated etiological factor, or by its correlation with exposure to that factor. In the next sections, we provide statistical evaluations for both, relying on the availability of clinical annotation for the etiological factor associated to that signature.In addition to simple performance, it is also important to evaluate the degree to which a given mutational signature improves upon prior knowledge about the mutational effects of an exposure to an etiological factor . For exaTo statistically evaluate the added value of the information provided by the signatures of Alexandrov and colleagues, hereafter termed ‘unsupervised’, as well as of our SuperSigs, we compared both of their performances against random alternatives carrying no additional knowledge beyond the known peak, for both aging and smoking . We termed these prior knowledge signatures ‘random’ because they were purposely created to just reflect random noise around the already known peak . Such rahttps://portal.gdc.cancer.gov). After splitting each dataset randomly into training and test partitions, we applied the method above to derive signatures of aging and smoking in the training data, evaluating performance in the test data. Our SuperSigs aging signatures, applied to classify patients in a binary fashion (i.e. young versus old) yielded a median AUC of 0.73, calculated over 30 tumor types, outperforming our random aging signature , which was built on the well-supported observation that over time, cytosines will consistently deaminate to thymine in the CpG context , cervical (CESC), esophageal (ESCAD and ESCSQ), head and neck (HNSCC), kidney (KIRP), lung (LUAD), and pancreatic (PAAD) cancers. The SuperSigs added value to prior knowledge while the unsupervised signatures did not, as the AUCs obtained by the SuperSigs were higher than the ones achieved by the random single peak but not so for the unsupervised ones  . The corThese data do not indicate that unsupervised signatures for aging and smoking are meaningless. However, the data indicate that the unsupervised signatures do not add any information to prior knowledge of a peak at [C>T]G for aging and at C>A for smoking. Optimally, an algorithm based on genome-wide cancer genomic sequencing data should add information that was not available from prior studies, and SuperSigs indeed added such information that goes beyond the previously known mutational peaks .Do supervised signatures perform better than unsupervised ones when no prior knowledge about an etiologic factor is available  as smokers versus never-smokers. Similarly, the cross-validated AUC was 0.96 when classifying bladder urothelial carcinomas (BLCA) patients who were exposed or not to aristolochic acid . At the When clinical annotation is not available for an etiologic factor , the unsIt has long been known that certain types of mutations, such as C>T transitions resulting from cytosine deamination, accumulate with age. We wondered whether other mutational signatures of aging were present in cancers and whether they varied among tissue types. To avoid confounding factors as much as possible, the analysis was confined to patients without known cancer-associated environmental exposures and without known germline predispositions to cancer.We thereby obtained SuperSigs associated with aging for each cancer type analyzed, examples of which are shown in We also sought to identify tissue-specific SuperSigs associated with specific environmental carcinogens. The analysis was performed after controlling for age and for other relevant covariates . We obtained tissue-specific SuperSigs for smoking, alcohol, hepatitis B and C virus infection , aristolochic acid (AA), asbestos, and ultraviolet (UV) light  where each entry is given by the average count of that mutation type, in the cohort of the samples with that exposure, divided by the average age in that cohort. The mutational landscape of aging is obtained in the same way using the cohort of samples without any known exposure (‘unexposed’). Consider now the distance between any two mutational landscapes as given by the Pearson’s correlation between the two mutational landscapes. The heatmap in We define the Moreover, in several cases, the tissue-specific mutational landscape associated with an environmental factor was similar to the aging mutational landscape of the same tissue –35. For These analyses then suggest that a major effect of some environmental factors may simply be to increase the rate of cell division. This increase would induce a linearly proportional increase in mutation rate, but with a mutation pattern that remains similar to the one caused by normal aging, that is it would not be associated with new signatures such as those caused by direct interaction of carcinogens with DNA. Increases in the rate of cell division are known to occur when tissues are damaged or inflamed . These oObesity  has emerged as the major lifestyle factor contributing to cancer in general . How obeWe applied the supervised approach to estimate the proportion of the overall mutational load that can be attributable to normal aging rather than to other mutational processes. This proportion is directly provided by the contribution of the age SuperSigs in each patient . When considering all 30 tissues, we estimate that on average 69% of the mutations can be attributable to the normal endogenous mutational processes associated with aging, that is normal DNA replication . This esTo validate our results, we tested the performance of the SuperSigs via four different analyses: cross-validation, random label shuffling, partial label switching, and validation on external data. First, we performed five iterations of 5-fold cross-validation of our SuperSigs . Only ICGC datasets that were not present in the TCGA database were used. All signatures that had previously achieved a cross-validated AUC of at least 0.6 on TCGA data were tested, as the others should not be considered reliable. Using, for each exposure, the associated logistic regression model trained on TCGA data only, and containing its SuperSig, we predicted the unexposed versus exposed status for all available factors and tissues in the ICGC data. The AUC for every of those signatures is reported in Finally, we externally validated our results on an independent whole-genome sequencing (WGS) dataset from the International Cancer Genome Consortium (ICGC) database  and filtered out the mutations which have less than 5% Variant Allele Frequency (VAF). Out of the total thirty-three datasets available, large B-cell lymphoma (DLBC) was not included in the analysis because of the small number of samples available, while lung squamous cell carcinoma (LUSC) and mesothelioma (MESO) were excluded because of the extremely small number of patients unexposed to smoking and asbestos, respectively. For ovarian cancer (OV) and acute myeloid leukemia (LAML) whole genome sequencing data were used. The human genome reference build hg38 was used to determine the context (flanking bases) for each mutation. The clinical information was downloaded from the website Cbioportal . For calculating the background frequency of each trinucleotide on both the exome and the genome, we used the R package, deconstructSigs. For the Unsupervised Signature method (http://cancer.sanger.ac.uk/cosmic/signatures) and used the table http://cancer.sanger.ac.uk/signatures/matrix.png in order to determine which signatures were present in which tissue.We downloaded somatic exomic mutational data from the TCGA Bioportal  was performed using the function nmf with method ‘Lee’ from the package NMF.All analyses were performed using To reduce the effect of confounding factors, we applied several filtering criteria. In each tissue type, we divided samples into two categories: (1) ‘unexposed’, meaning that no exposure to a known environmental factor was recorded, according to the available clinical annotation, and (2) ‘exposed’. To mitigate the effects of other unknown factors in the unexposed group, we removed any sample with a mutational load more than 3 times higher than the median number of mutations found among the unexposed samples. We also excluded samples if the total number of mutations was equal to zero on the exome, a probable indication of low neoplastic cell content. We removed samples with microsatellite instability (MSI) or with a mutation in POLE/POLE2/POLE3/POLE4 or POLD1/POLD2/POLD3/POLD4 genes - except for when the signature for the specific effects of those mutations was the objective of the analysis - because of the known large increase in the number of mutations they induce. A tissue type was divided into subtypes whenever possible. Acute Myeloid Leukemia (AML) patients younger than 40 years old were not considered because we were interested in adult rather than childhood AML. Among the ‘exposed’ samples we excluded samples with known multi-factor exposures to minimize confounding factors and only evaluated samples with a single known exposure. Samples with unknown exposure were treated as unexposed.Mutation counts are used to characterize mutational burden when considering predictors of aging. For all other exposures, mutation rates (i.e. counts/age) are used. In a patient exposed only to time, that is unexposed to any known environmental or inherited factor, the rate of a mutation type is expected to remain constant irrespective of age – as dictated by the aging signature – while the absolute count is expected to increase with age. In contrast, in a patient exposed to an environmental or inherited factor, the rate of a mutation type as well as the count may change with respect to the age signature.We provide here the details for the method we developed to obtain the supervised mutational signatures .At its simplest, a mutational signature of exposure is nothing more than a set of substitutions that characteristically occur at different rates in exposed tissue than in unexposed tissue. In practice, though, a few considerations suggested by prior biological knowledge quickly turn a simple calculation into a complex engineering problem. Specifically, a key principle of the SuperSig approach is that signatures may not be optimally described by the same base length units. Accordingly, we consider all single-base substitutions, with or without the flanking context bases, as potential, signature features. In addition to six single base substitutions: C>A, C>G, C>T, T>A, T>C, and T>G, named according to the pyrimidine of the mutated Watson–Crick base pair, there are 48 dinucleotides, in which the substitution is paired with a specific base as a prefix or as a suffix but not both (e.g. A[C>T] or [C>T]G), as well as 96 trinucleotides (e.g. A[C>T]G), which include both flanking bases as context. Hence, we have a list of 151 children, such as A[C>T], and trinucleotide grandchildren like A[C>T]G. Frequent, exposure-driven A[C>T] substitutions would increase the observed rates of both the C>T parent and the trinucleotide children, making it difficult to assign ownership to the correct generation. The next section, ContextMatters, describes our approach to solving this problem, while the sequel, FeaturesSelection, describes how candidate signature features are combined to create a final signature.The resulting flexibility carries a price, however, as features are no longer independent. The simple substitution C>T spawns dinucleotide Total Mutations, parent to all six simple substitutions, describing the overall mutation rate . Such a tree can represent the mutations found in a single sample, or summarize results observed across a set of samples. In practice, we build two trees for each combination of exposure and tissue, to capture mutation rates separately in exposed and unexposed individuals, and combine them later.The set of features described above thus form a family tree, in which the observed mutational rate  for each substitution is propagated down the tree to children and grandchildren . For comAll criteria for splitting samples in young vs old, smoker vs never-smoker, etc, were selected prior to any application of our algorithm or cross-validation. For the age analysis, we divided the unexposed samples into three groups  based on the tertiles of the age distribution and discarded the middle group before training the algorithm . For allFeatures of interest are selected in each tree by a two-phase process, first working down the tree from the root and then back up again. The very simple principle behind the first phase is that the mutation rate for each feature is to be compared to that expected by chance alone, to distinguish features that may be associated with exposure. As an unfortunate consequence of the family structure, however, the simplest implementation of this principle is biased toward the selection of late-generation features, where the propagation of individually insignificant deviations across 2 or 3 generations may add up to a significant cumulative difference. Thus, in practice each feature must pass a series of tests against a hierarchy of conditional null distributions defined by accounting for the observed mutation rates of each ancestor in turn. In consequence, unless proven otherwise, the mutational wealth of a given feature is explained by inheritance from its ancestors. This leads to the second phase of the process, where we work back up the tree, reevaluating all parent-child pairs selected in the first phase to make sure that we have not over-corrected, and erroneously attributed later generation wealth to earlier generations. Mathematical details are provided below.Total Mutation_Count * Normal_Frequency_of_C * 1/3, the last factor accounting for three, equally likely substitutions for C. The C>T substitution would be selected as a candidate feature if the observed number of C>T mutations were significantly greater than the expected value, according to a one-sided binomial test. Moving down a generation, [C>T]A, as the child of the C>T substitution, and the grandchild of the total number of mutations , would be tested twice to see if it significantly exceeded its expected number based on the total number of mutations as well as the number of C>T. The expected value of [C>T]A mutations would be given by Total Mutation_Count * Normal_Frequency_of_C * 1/3 *X, where X is the expected frequency of CA (i.e. C followed by an A) out of all C nucleotides in the exome, as estimated by deconstructSigs  for the sum of the pseudo count of that feature, of which we then took the median. The start for the pseudo count of the Total Mutations is not tested against. If the null hypothesis was rejected, we selected that potential feature as a ‘first-phase’ candidate feature for the next supervised selection step. First-phase candidate features are colored in grey in All results were considered significant at a p-value of 0.05, subject to Bonferroni correction for 150 tests, as second-phase candidate features  step separately to samples from patients that were respectively unexposed or exposed to the factor under consideration. We then combined these two lists of second-phase candidate features, which are both partitions, by considering all intersections and relative complements of the elements in the two original partitions, to form the minimal refinement of the two, and define this final list as the list of For aging signatures, we applied the feature engineering steps described above only to samples from patients who were unexposed to any known environmental or inherited factor. Therefore, we skip this step of combining partitions, because we only have one partition, that is its second-phase candidate features, which automatically provided its ‘candidate features’ list.We performed the supervised feature engineering step described in the previous section in an inner loop of 5 iterations of 3-fold cross-validation. Each feature in each fold was ranked according to its ability to discriminate exposed samples from unexposed, based on the rates for that feature . Discriminatory performance was measured by the area under the receiver operating characteristic (ROC) curve (AUC).The fifteen lists of ‘candidate features’ obtained across the 3 folds of each of the five iterations was then combined by considering all intersections and relative complements of the features in the original lists. The minimal refinement thus obtained constitutes the final list of candidate features. These candidate features were then ranked by their median AUC across the 15 folds.n corresponding to the top n ranked features that provided the highest AUC - using a multivariate, logistic regression classifier (LR) - was selected. The median of those 15 n values, defined as n*, was then used to select the first n* candidate features according to their median AUC ranking. Out of these n* features, the ones for which the median AUC ≤ 0.6 were discarded, and the remaining features are what we defined as the predictive features for a given exposure.Also, for each fold, the number The set of predictive features selected above form the supervised signature (SuperSig). Two values are associated to each one of these predictive features: (1) the difference in mean counts (age) or rates  between the exposed and unexposed cohorts, and (2) the beta (β) coefficient for that feature as estimated by logistic regression. Both vectors yield critical information.The difference in means for each feature, which is the only constraint used by logistic regression in maximizing entropy over the dataset, provide a natural measure of the difference in counts or rates for that feature induced by a given exposure. We report these values in the figures of the main text and in C versus the unexposed one, given the mutational data (counts or rates), is given byThe beta coefficients of the features in a logistic regression have also an intuitive interpretation, since the logarithm of the odds of being in the exposed class β of a feature is the factor by which the odds of being in the exposed class increase for every extra unit increase in that feature, when all other features are kept constant. The β coefficients of the mutational signatures for each factor (aging or exposure) can be found in Therefore, eWe used Logistic Regression (LR) to test the predictive accuracy of each set of features representing a mutational signature as measured by AUC. We also report the performance of Linear Discriminant Analysis (LDA), and Random Forest (RF), when applied to both feature selection and prediction . In bothapparent results, or via five iterations of fivefold cross-validation for the cross-validated results, where we reported the mean AUC across the five iterations.Training was performed via five iterations of threefold cross-validation as described above. Once the predictive features had been selected, the algorithm was then trained using LR over the whole dataset for the To assess the feasibility of implementation of the SuperSigs methodology, we provide as a performance metric the runtimes for both whole exome and whole genome sequencing datasets in peak feature. Specifically, we would like to assess the value of the aging (Signature #1) and smoking unsupervised signatures in When prior literature has established a strong relationship between an exposure and a particular mutational feature, that is [C>T]G for aging and C>A for smoking, we would like to know that any new candidate signatures actually improve on these central, single peak signatures’ for brevity.To do this, we generate a signature for smoking, whose property is a higher proportion of C>A mutations than the other mutation types and where, beside this ‘peak’ at C>A, the proportion of all the other mutation types is assigned randomly. Similarly we generate a signature for aging, whose property is a higher proportion of [C>T]G mutations than the other mutation types and where, beside this ‘peak’ at [C>T]G, the proportion of all the other mutation types is assigned randomly. We do this by building ‘randomly generated single peak signatures’, or ‘smoking single peak signature’ is then the distribution among them with the highest proportion of C>A substitutions. In step two, we randomly break down the obtained proportion of each of the six main mutation types into the 16 fundamental trinucleotide mutations .More precisely, for the smoking signature, we create this randomly generated smoking peak signature in a two-step process. In step one, we generate 30 (since in Cosmic v.2 there are about 30 signatures) probability distributions over the six main mutation types (which lack suffix and prefix base). Each distribution is created by sampling six numbers from a uniform distribution and by dividing them by their sum. The ‘aging single peak signature’ is then the distribution with the maximum proportion of [C>T]G substitutions.We apply a similar process to the derivation of the randomly generated peak age signatures. The difference is that we assume the main types of mutations are now seven: [C>T]G, [C>T]H, C>A, C>G, T>A, T>C, and T>G, due to the fact that we need to have [C>T]G as one of the features, since that is the peak obtained from prior-knowledge. Among the 30 signature candidates, the ‘In order to compare the prediction accuracy (AUC) of all three sets of signatures , we first apply the same prediction methodology that was previously used in Alexandrov et al. to determine the contribution of each signature in each patient: non-negative least squares (NNLS).iX of each mutational signature i = 1,…, k, where a total of k signatures are present in that tissue, NNLS is applied toY = AX in matrix form, where iY is the total number of mutations of type i, and ijA is the relative frequency  or the difference in mean count (SuperSigs for age) or rate  of mutation type i in the mutational signature j, across each one of the k signatures present in that tissue.More specifically, to determine in a given patient the respective proportional contributions (used as a score) The performance of the various methodologies is presented in For Alexandrov et al. their Signature one was used for predicting age in one comparison , and theAll mutational signatures were clustered using unsupervised agglomerative hierarchical clustering and a threshold was selected to identify the set of consensus mutational signatures. Mis-clustering was avoided by manual examination (and whenever necessary re-assignment) of all signatures in all clusters. 27 consensus mutational signatures were identified across the 30 cancer types." Thus, we chose to use the core methodology used in Alexandrov et al., which is non-negative matrix factorization (NMF)  , and appr, of the NMF algorithm equal to what shown in Cosmic signature v2 (https://cancer.sanger.ac.uk/cosmic/signatures_v2) for the tissue of interest. We hardwired this parameter to help the unsupervised method to limit model misspecification .For both approaches, we applied NMF (Lee-Sung NMF_0.21.0) to the profile of the count mutations of the training samples, that is a matrix whose 96 rows represent mutation types and columns represent training samples. We set the rank parameter, r signatures from NMF, we used two alternative methods to select among them the signature of a specific age or environmental factor: (1) for BestNMF, we chose the signature whose contributions had the highest AUC in classifying exposure to the environmental factor on the training set; (2) for MatchedNMF, we paired each of the identified signatures from the training set to exactly one of those listed in Cosmic v2 for this specific tissue. This pairing process was obtained by maximizing the sum of the cosine similarity for each pair.After obtaining the Then, on the test set, we used an NNLS algorithm to estimate the contribution of each signature on the test set.The performance of the various methodologies is presented in We would like to note that we are being conservative against our own supervised results when using the alternative method called ‘BestNMF’ to cross-validate the unsupervised approach. In fact, BestNMF is more of a weakly supervised method rather than a purely unsupervised method, and therefore having an expected better performance. This can also be verified by comparing the apparent performances of Alexandrov and BestNMF in We explain here how the supervised learning of a mutational signature  can be used to improve the performance of an unsupervised approach by discounting the effects of that supervised signature on the test data. We refer hereafter to this methodology as ‘partially supervised’.To simplify matters, we do not engineer features; rather, we use the 96 fundamental mutations as in We apply NMF (Lee-Sung ref) with rank equal to three to decompose the test set, Y, thus obtaining two matrices, A and X: one containing the unsupervised signatures (A) and a second one with the corresponding contributions of each of those signatures in each patient (X). These contributions have not been discounted for age yet. This is the standard unsupervised approach. However, in order to estimate the discounted contributions of a signature in each test sample, we now discount the effect of age of a patient on each unsupervised signature, by multiplying the learned supervised age signature by the age of the patient, times the estimated mutation rate, and then projecting this vector onto the directions identified by NMF using NNLS, and then subtracting these projected contributions of age from the contributions of the three unsupervised signatures obtained by NMF. To conform to the premises of NMF, we set the negative discounted contributions to zero.We then choose the direction whose contribution, divided by the total number of mutations, is the most associated (in terms of the highest AUC) to the exposure status using the known ground-truth, for both the unsupervised and the partially supervised methods, by using the not discounted and discounted contributions, respectively. To obtain the ‘partially supervised signatures’ we now use again non-negative linear regression but this time where the contributions (X) are known and the signatures (A) are unknown. In other words, we still have the decomposition Y=AX, but now, Y and X are known and we want to estimate A.We used the AUC to evaluate the association of the signature with the exposure status, for both the unsupervised and partially supervised approach, where the contribution of each signature has been divided by the number of total mutations. We repeated 50 times this whole process  and take the average AUC over them to account for the effect of randomness. This is what is depicted in In this partially supervised extension, we have used NMF to easily compare with the unsupervised approach by Alexandrov et al. However, other methodologies (e.g. a classifier based on EM) may provide even better performance.Pretend we had no annotation for the presence of defects in the gene POL-ε among patients with endometrial cancer in the UCEC-TCGA dataset and that we did not know the POL-ε signature. The normalized results for an NMF decomposition are depicted in rate’ of feature i, ia,r is defined as the mean of the ratio:iar of each feature i present in our SuperSig age signature by the patient’s age of that specific sample. The number obtained by summing the above counts for each feature in the age SuperSig is then divided by the total number of mutations observed in that sample. This resulting ratio, being forced to be not greater than 1, is our estimate for the proportion of somatic mutations attributable to age in that sample  where each entry is given by the average count of that mutation type in the cohort of the samples with that exposure divided by the average age in that cohort. The mutational landscape of aging is obtained in the same way using the cohort of samples without any known exposure (‘unexposed’). Then, the distance between any two mutational landscapes is given by the Pearson’s correlation between the two mutational landscapes  for 5, 10, 20, and 25% of the samples in the training set. For example, non-smokers would be mislabeled as smokers and vice versa. Then we rerun our supervised method, including feature engineering and selection, on the training set to obtain new signatures. These new signatures are then used for prediction in the test set, where we used the original labels as the ground truth. The performance is reported in distance between any two mutational landscapes is given by 1- the Pearson’s correlation between the two mutational landscapes. See Materials and method section for details.Heatmap of the distance, in terms of correlation, between any two etiological factors’ mutational landscapes in the corresponding tissues. Distance not discounted for age. The distance between any two mutational landscapes is given by 1- the Pearson’s correlation between the two mutational landscapes. See Materials and method section for details.Heatmap of the distance, in terms of correlation, between any two etiological factors’ mutational landscapes in the corresponding tissues. Distance not discounted for age. The ctomasetti@jhu.edu. A repository for the R package containing the SuperSigs algorithm can be found at https://github.com/TomasettiLab/superSigs (swh:1:rev:7d6aac85a1b3930cb93e0810039db4d65a242cca).Correspondence and requests for materials should be addressed to C.T.:  In the interests of transparency, eLife publishes the most substantive revision requests and the accompanying author responses.Acceptance summary:The approach described in this manuscript provides a new method to analyze sequencing data, which will be of general use to the scientific community. In addition, this work identifies hypotheses concerning the etiology of certain cancers.Decision letter after peer review:eLife. Your article has been reviewed by four peer reviewers, one of whom is a member of our Board of Reviewing Editors, and the evaluation has been overseen by a Senior Editor. The following individuals involved in review of your submission have agreed to reveal their identity: Peter J Campbell (Reviewer #2); Elaine Mardis (Reviewer #4).Thank you for submitting your article "Supervised mutational signatures for obesity and other tissue-specific etiological factors in cancer" for consideration by The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission.eLife". Please let us know if you would like to pursue this option. As the editors have judged that your manuscript is of interest, but as described below that additional experiments are required before it is published, we would like to draw your attention to changes in our revision policy that we have made in response to COVID-19 (https://elifesciences.org/articles/57162). First, because many researchers have temporarily lost access to the labs, we will give authors as much time as they need to submit revised manuscripts. We are also offering, if you choose, to post the manuscript to bioRxiv  along with this decision letter and a formal designation that the manuscript is "in revision at Summary:This manuscript by Tomasetti and colleagues describes a conceptually novel approach to derive somatic mutational signatures (SuperSigs) from whole exome tumor sequencing data using supervised machine-learning techniques. A large and growing number of mutational signatures have been described using non-negative matrix factorization (NMF), an unsupervised method. These signatures are widely used to describe the mutational processes operant in individual tumors and have spawned many studies examining environmental exposures and intrinsic genetic mechanisms that underlie these patterns. However, when accompanying clinical data are available, supervised learning may produce more informative signatures that correlate more strongly with environmental exposures, as well as enable the discovery of signatures associated with previously unappreciated factors. This work describes one such effort and using these methods, identify differences in penetrance of such signatures in a tissue restricted manner.Essential revisions:1) One weakness is the reliance on one dataset, and a highly curated, highly polished one at that. The authors used the TCGA data with random splits to training and test sets via a cross-validation design. The vast majority of the data studied was exome data, with only AML and ovarian cancers using whole genome data. A specific challenge of supervised machine learning techniques is that any hidden confounding factor in the dataset  can be extracted as apparent signal for the variable of interest  – a random test / training split on one dataset will still be subject to this confounding, since it operates at the level of the combined patients. The best way to avoid this  is to validate signal on external datasets.We therefore recommend testing predictors trained on TCGA data but tested on external data. There is plenty of non-TCGA exome data available and accessible, and even reasonable amounts of whole genome data, with basic clinical variables  – this would give much greater confidence in the signals extracted.2) The authors make reference to "partially-supervised signatures" in Figure 2A and in the text, claiming that they are "superior to" unsupervised signatures when clinically annotations are not available. This is confusing because SuperSigs is motivated by the advantage of supervised methods specifically for when clinical data are available. Moreover, I don't see any data presented in the Results to support the claim that partially-supervised signatures are better. While there is a detailed description in Materials and methods, more description and evidence should be included in the text, or else the paper should focus only on the scenario when clinical data are used.3) The figures are generally unclear and need to be improved. For instance, Figure 2B attempts to show examples of randomly generated single peak signatures, but I am confused why there are multiple colored dots for each trinucleotide if there is only one signature per color. I believe the trinucleotide sequences are also incorrect, as the right half of the plots in 2B should have a T at the center of each trinucleotide, not C. Additionally, it is unclear in Figure 3 (panel B) which tumor types were chosen for the characterization of smoking signatures, and why. I also can't understand why smoking is shown again in panel c or why age is shown in panel d when the legend describes it as "all etiologic factors other than age".4) The Introduction mentions a critique of unsupervised NMF signatures that they don't incorporate knowledge of exposures or their intensity . But it is not clear that SuperSigs explicitly models the intensity either. Samples are divided into two categories: "unexposed" and "exposed". Is the intensity of smoking exposure reflected in the smoking signatures from different tissues?5) How many tumor types have a detectable smoking signature? How many tumor types were examined for a smoking signature? Figure 4 displays smoking signatures for pancreatic adenocarcinoma and bladder urothelial carcinoma, which are surprising given that these tissues do not have nearly as much direct exposure to the carcinogens in cigarette smoke as lung cancer, head and neck cancer, and esophageal cancer.6) The authors fail to address the potential for overfitting. A strong test against overfitting would be to shuffle the labels and then re-run their entire framework from feature selection to test prediction. A clear sign the model is overfitting would be obtaining similar AUCs on the shuffled dataset to that of their unshuffled dataset.7) AUCs as a metric for model performance can be deceiving; an H-measure would be more informative here see David J. Hands paper 2009 Machine Learning for more details.8) The addition of performance metrics such as speed benchmarks for exome and WGS data sets is needed to assess the feasibility of implementation for end users. This is especially true considering the large number of bootstraps needs for feature engineering.9) How does the novel feature engineering technique compare to state-of-the-art methods like sigLASSO? Does it take into account the transcript strand bias of genes?10) Supervised learning depends on the quality of the data annotations, which as noted above are quite variable for different TCGA projects. In most instances, there are not quantitative information available to establish what age ranges were considered “young” vs. “old”, nor were there specifics around environmental exposures such as pack-years for smoking, ranges of BMI for obesity, etc. Could these please be specified and also some reference as to how these were selected, and were they selected prior to or after cross-validation was performed for the different categories?11) The conclusions about SuperSigs algorithm performance compared to NMF seem to be based on core NMF rather than the improved versions from Alexandrov. The authors claim that it is not possible to use Alexandrov's implementation, however, offer no reason as to why. Please specify the NMF approach used in the Materials and methods so it is clear to readers.12) The authors provide a strong rationale for the greater flexibility for mutational signatures beyond a three nucleotide fixed size improves their models' performance, but don't provide statistical analysis to support this.13) Context of this publication with previous work. The aging signature is based on mutation counts, rather than rates. Does this not vary according to the tissue, based on the prior work published by this group? Is this another basic principle that could be addressed by comparing to SuperSigs analysis of pediatric cancer data?14) The conclusions around obesity and tissue variance are overstated with respect to causality. Since these studies are observational, the authors cannot conclude evidence of causality.eLife. Your revised article has been re-reviewed by two peer reviewers, and the evaluation has been overseen by a Reviewing Editor and a Senior Editor. The following individual involved in review of your revised submission has agreed to reveal their identity: Elaine Mardis (Reviewer #4).Thank you for resubmitting your revised article "Supervised mutational signatures for obesity and other tissue-specific etiological factors in cancer" for consideration by As for the original submission, the reviewers have discussed their reviews with one another, and the Reviewing Editor has drafted this to help you prepare a revised submission.Summary:In this manuscript, the authors describe a new approach to identify patterns of genetic alterations in tumors that reflect biological processes that affect DNA. This approach does not use prior information and uses more sequence information to look for evidence of mutational processes. Among many interesting observations is the finding that certain mutational processes occasionally have different signatures across tissue types.Essential Revisions:1) The authors should revise the description of the methods to provide greater detail. One example of this is the last paragraph in subsection “Do mutational signatures add to prior knowledge about etiologic factors?”, where "information" is used extensively throughout, without ever really defining what type of information is being provided by SuperSigs.2) Please provide a weblink for the TCGA Genomics Data Commons.3) In subsection “Do mutational signatures add to prior knowledge about etiologic factors?” (and throughout), resist using "significantly" unless you have a p value that substantiates the term, and the test used to derive the p value.4) In the Discussion, it is mentioned that SuperSigs associated with BRCA2 vary with tissue type (ostensibly meaning breast and ovarian) but only SuperSigs for breast cancer associated with BRCA2 is shown in Figure 4.5) Discussion paragraph two is the first mention of inflammation, which is known to be linked to obesity yet is not specifically called out here.6) In the same paragraph, both signature 4 and signature 6 are mentioned in terms of liver cancer but only signature 6 is explained as being “rare in liver cancers”. is it also the case that smoking is not associated with liver cancer, or…? Please edit this sentence so the reader understands why you are also mentioning the smoking signature result.Reviewer #3:This manuscript describes a conceptually novel approach to derive somatic mutational signatures (SuperSigs) from whole exome tumor sequencing data using supervised machine-learning techniques. A large and growing number of mutational signatures have been described  using non-negative matrix factorization (NMF), an unsupervised method. These signatures are widely used to describe the mutational processes operant in individual tumors and have spawned many studies examining environmental exposures and intrinsic genetic mechanisms that underlie these patterns. However, when accompanying clinical data are available, supervised learning may produce more informative signatures that correlate more strongly with environmental exposures, as well as enable the discovery of signatures associated with previously unappreciated factors.This study is innovative, clearly written, and logically presents the benefits of supervised learning methods to identify signatures more strongly associated with meaningful clinical factors. The conceptual advantages of SuperSigs as an alternative to NMF-based signatures are compelling. Among many interesting observations is the finding that certain mutational processes occasionally have different signatures across tissue types. Given the ubiquity of mutational signatures in cancer genomics research and the challenge in connecting many signatures to their underlying cause, I think this study and the associated algorithm will be of broad interest.Recommendations for the authors:I am satisfied that the authors have sufficiently addressed the concerns raised in my original review.Reviewer #4:This manuscript describes an approach to uncovering mutational signatures and their associated causative factors, using a new approach that does not rely on NMF/unsupervised methods, which are in widespread use yet often yield complex or indeterminate underlying causes. The work takes advantage of publicly available TCGA genomic data and associated clinical data for 30 different cancer types, and utilizes the ICGC data to test their supervised approach to mutational signatures, or SuperSigs. Important results obtained by this approach include the observation that signatures of aging differ between different tissue types, perhaps linked to the underlying cell division rate differences that are well known to exist. Another important result is the derivation of two signatures related to obesity, which is emerging as the key contributor to cancer susceptibility in first world economies. Another major strength of this approach is that by first removing known etiological signatures such as smoking with SuperSigs, more refined signatures of underlying or associated etiologic factors may be revealed by a secondary NMF-based approach. This partially supervised method achieves higher concordance than by NMF only for all known etiologies  recorded in TCGA clinical data. Of necessity, this approach was tested with a large data set that left out the nuances of different tumor types. For example, breast cancers are well characterized into different subtypes, especially with respect to underlying factors such as BRCA1/2 mutation status (germline) that associate with the different subtypes (e.g. triple negative disease). As such, it remains to be seen whether this method may be more specifically applied to large genomic data sets across different subtypes and in the context of underlying genetic predispositions to further understand the susceptibility-based etiology of a specific tissue type. However, as a general method, SuperSigs provides a new and well-tested method for deriving mutational signatures from cancer genomic data that likely will have a significant impact on the field of cancer research and, ultimately in areas of cancer prevention as well as revealing new cancer etiologies.Recommendations for the authors:In general, the authors responded well to the critiques raised, including the ones I contributed. I was pleased they were able to utilize the ICGC data and to show the method transferred well to the analysis of these data. It would be a good idea for the figure they produced in the response to reviewers to be included as a supplementary figure in the revised manuscript, if possible.The figures are all quite improved, although the use of colors to help differentiate different tumor types and different etiologies sometimes is challenging to decode. This will likely be helped by preparation for publication. My only remaining critique is the language used to quantify the SuperSigs improvements over NMF are sometimes poorly quantitative. One great example of this is the last paragraph in subsection “Do mutational signatures add to prior knowledge about etiologic factors?”, where "information" is used extensively throughout, without ever really defining what type of information is being provided by SuperSigs. This needs to be edited accordingly. Please provide a weblink for the TCGA Genomics Data Commons. In subsection “Do mutational signatures add to prior knowledge about etiologic factors?” (and throughout), resist using "significantly" unless you have a p value that substantiates the term, and the test used to derive the p value. This is standard. In the Discussion section, there are two areas of confusion for me. In the Discussion, it is mentioned that SuperSigs associated with BRCA2 vary with tissue type (ostensibly meaning breast and ovarian) but I only found a SuperSigs for breast cancer associated with BRCA2 in Figure 4. This is a very important observation, so please be certain it is presented for both tissues in an accessible way in the main text. Discussion paragraph two is the first mention of inflammation, which is known to be linked to obesity yet is not specifically called out here. If this is indeed the inference being made, please be more explicit so the reader understands the importance of this conclusion! In the same paragraph, both signature 4 and signature 6 are mentioned in terms of liver cancer but only signature 6 is explained as being “rare in liver cancers”. is it also the case that smoking is not associated with liver cancer, or…? Please edit this sentence so the reader understands why you are also mentioning the smoking signature result. Essential revisions:1) One weakness is the reliance on one dataset, and a highly curated, highly polished one at that. The authors used the TCGA data with random splits to training and test sets via a cross-validation design. The vast majority of the data studied was exome data, with only AML and ovarian cancers using whole genome data. A specific challenge of supervised machine learning techniques is that any hidden confounding factor in the dataset  can be extracted as apparent signal for the variable of interest  – a random test / training split on one dataset will still be subject to this confounding, since it operates at the level of the combined patients. The best way to avoid this  is to validate signal on external datasets.We therefore recommend testing predictors trained on TCGA data but tested on external data. There is plenty of non-TCGA exome data available and accessible, and even reasonable amounts of whole genome data, with basic clinical variables  – this would give much greater confidence in the signals extracted.We are grateful for this critical recommendation by the reviewers. We have added a whole new section in the main text entirely dedicated to validation, describing the results of four different validations: cross-validation, random shuffling, partial random shuffling, and testing on external data. They all provide positive support for our supervised signatures.https://dcc.icgc.org/releases/PCAWG/). As some TCGA datasets are also present in ICGC, only ICGC datasets that were not present in TCGA were used for testing. All signatures that had achieved a cross-validated AUC of at least 0.6 on TCGA data were tested, as those not satisfying this minimum requirement should not be considered reliable. The way we tested on ICGC data our predictors was as follows: using the logistic regression models trained exclusively on TCGA data, with their associated signatures, we predicted the unexposed versus exposed status for all available factors and tissues in the ICGC database. The AUC for every of those signatures is reported in Table 1 of the main text. We found that the predictive power of the signatures that was observed in the TCGA data was retained in the ICGC data. In fact, several of them achieved AUCs that were much higher than those obtained in cross-validation using TCGA data. The only exception was the age signature in melanoma (SKCM). This signature, however, had a borderline performance already in the original analysis (AUC=0.61), probably due to the inability of the methodology to properly remove sun exposure as a confounding.With respect to testing on external data, and as requested by the reviewers, we externally validated our results on an independent WGS dataset from the ICGC database (downloaded from 2) The authors make reference to "partially-supervised signatures" in Figure 2A and in the text, claiming that they are "superior to" unsupervised signatures when clinically annotations are not available. This is confusing because SuperSigs is motivated by the advantage of supervised methods specifically for when clinical data are available. Moreover, I don't see any data presented in the Results to support the claim that partially-supervised signatures are better. While there is a detailed description in Materials and methods, more description and evidence should be included in the text, or else the paper should focus only on the scenario when clinical data are used.It is true that our supervised methodology requires clinical annotation. At the same time there are many cases where we may have annotation available for some factors – e.g. age is typically available – but not for others. And it may be desirable to attempt to identify and detect those other non-annotated factors. Are we then forced to exclusively use an unsupervised methodology? The answer is no. The rationale for extending the method to a partially-supervised approach is that any time some annotated factors are present it is better to take care of them first, by identifying them using a supervised approach and removing their effects, and then applying an unsupervised methodology on the mutational “leftover”, rather than using the unsupervised methodology on the whole. We show this in our analysis, which we have now brought to the main text with a figure  and a more detailed description. We consider it an important finding as it indicates that even when using an unsupervised approach with the intent to discover new, not annotated signatures, it is still best to first take care of the annotated component present in the mutational load of a sample.3) The figures are generally unclear and need to be improved. For instance, Figure 2B attempts to show examples of randomly generated single peak signatures, but I am confused why there are multiple colored dots for each trinucleotide if there is only one signature per color. I believe the trinucleotide sequences are also incorrect, as the right half of the plots in 2b should have a T at the center of each trinucleotide, not C. Additionally, it is unclear in Figure 3 (panel b) which tumor types were chosen for the characterization of smoking signatures, and why. I also can't understand why smoking is shown again in panel c or why age is shown in panel d when the legend describes it as "all etiologic factors other than age".We thank the reviewers for pointing out that some figures were unclear and needed improvements. We have redone almost all figures. Part of the confusion in Figure 2 was generated by the fact that 3 distinct random single peak signatures were represented in the lower part of Figure 2B. We have now reduced that number to only one, to make the interpretation of the figure clearer. We also changed the colors accordingly (color now corresponds to mutation type), and fix the typo in the trinucleotide sequence. In Figure 3 we have eliminated some confusion created by the fact that some factors were reported in multiple plots. In particular smoking was reported on its own as well as in other plots including all factors. We have reduced the figure to two plots, one comparing the performance of the supervised and unsupervised methods over age and one for all other factors. As indicated in the text, all TCGA datasets (tumor types) containing smoking status information  had been analyzed, and their performance reported in Supplementary file 1. We have now added the names of those 8 types in the main text for added clarity. However, only the 5 tumor types for which Alexandrov et al. found the presence of a smoking signature are reported in Figure 3B, as only for them we can present a comparison. We have clarified this further in the caption of Figure 3.4) The Introduction mentions a critique of unsupervised NMF signatures that they don't incorporate knowledge of exposures or their intensity . But it is not clear that SuperSigs explicitly models the intensity either. Samples are divided into two categories: "unexposed" and "exposed". Is the intensity of smoking exposure reflected in the smoking signatures from different tissues?Our reference to NMF not requiring knowledge of the intensity of an exposure was meant as a potential advantage of NMF and not as a criticism. We have removed the indicated sentence on intensity to avoid any confusion. In principle SuperSigs can be used to model different intensities of exposure by creating multiple groups of exposed patients clustered by intensity. We have not done that in this manuscript. However, we are reporting in the main text correlations between exposure intensities in smoking and the score obtained using both SuperSigs and NMF signatures.5) How many tumor types have a detectable smoking signature? How many tumor types were examined for a smoking signature? Figure 4 displays smoking signatures for pancreatic adenocarcinoma and bladder urothelial carcinoma, which are surprising given that these tissues do not have nearly as much direct exposure to the carcinogens in cigarette smoke as lung cancer, head and neck cancer, and esophageal cancer.We thank the reviewers for these questions and comment. We analyzed all tumor types for which smoking status information was available in the TCGA database, for a total of 8 tumor types, and their performance reported in Supplementary file 1. Specifically, bladder (BLCA), cervical (CESC), two esophageal (ESCAD and ESCSQ), head and neck (HNSCC), kidney (KIRP), lung (LUAD), and pancreatic (PAAD) cancers. While all these tumor types were examined for a smoking signature, only for three of them  the signature satisfied a minimum requirement in cross-validation (CV AUC>0.60). For added clarity we have now made this explicit in the main text, indicating that in general any signature with a CV AUC<0.60 should not be considered reliable, and only reported those 3 smoking signatures in Figure 4C, moving the full list of smoking signatures to the supplementary materials, as they may still carry valuable information.With respect to the two specific tissues mentioned by the reviewer, the smoking signature in pancreatic adenocarcinoma does not pass this minimum requirement, but smoking in bladder cancer does, with a CV AUC=0.68, suggesting a smaller direct exposure than in head and neck (CV AUC=0.81) or lung (CV AUC=0.90), yet still a relevant one.6) The authors fail to address the potential for overfitting. A strong test against overfitting would be to shuffle the labels and then re-run their entire framework from feature selection to test prediction. A clear sign the model is overfitting would be obtaining similar AUCs on the shuffled dataset to that of their unshuffled dataset.We thank the reviewers for this recommendation. As mentioned above, we have added a whole new section in the main text entirely dedicated to validation, describing the results of four different validations: cross-validation, random shuffling (i.e. the one asked here by the reviewer), partial random shuffling, and testing on external data. They all provide positive support for the robustness of our supervised signatures. Also, to minimize further the risk of overfitting, we have now slightly simplified the methodology requiring that each individual feature selected satisfies an AUC>0.60 . This has the desirable effect to increase the robustness of the signatures, reducing the drop in performance when going from apparent to cross-validated AUC, and resulting in SuperSigs with a smaller and more robust number of predictive features.7) AUCs as a metric for model performance can be deceiving; an H-measure would be more informative here see David J. Hands paper 2009 Machine Learning for more details.We thank the reviewer for this interesting recommendation, as we agree that AUC as a measure of performance has important limitations. At the same time, we would like to leave the reviewer suggestion to future work as the AUC is a very familiar and typical measure used in the literature and switching to an H-measure may obscure a bit the main points of this manuscripts. Also, using an H-measure would require us to make some arbitrary choices (β distribution parameters) and force us to completely modify our approach in several parts (e.g. we use AUC in feature engineering/selection) and revisit all of our results. Of course, we will be happy to implement it if required by the reviewer.8) The addition of performance metrics such as speed benchmarks for exome and WGS data sets is needed to assess the feasibility of implementation for end users. This is especially true considering the large number of bootstraps needs for feature engineering.We now include this information in a section of the Materials and methods with a Figure 3—figure supplement 38 depicting the runtimes for both whole exome and whole genome datasets The runtime naturally depends on the number of samples analyzed but it is relatively fast at an average of 27 minutes per dataset.9) How does the novel feature engineering technique compare to state-of-the-art methods like sigLASSO? Does it take into account the transcript strand bias of genes?The main message of this paper is that using clinical information – i.e. with supervision – can help us improve mutational signatures. While the sigLasso contribution is certainly an improvement over the standard methodology, it still has the flavor of an unsupervised feature engineering. It will be interesting to work on combining ideas from the sigLasso methodology with a supervised method like superSig, but we feel it is beyond the scope of this first paper. We cited this as a future direction in our Discussion section of the main text: “And more sophisticated extensions to SuperSigs obtained by borrowing advanced sparse techniques used in, e.g., the sigLassso method [1], may provide further significant improvements.” In terms of strand bias of genes, we did not use it but it is easy to see how to control for it in the future extensions (e.g. counting mutations separately by strand).10) Supervised learning depends on the quality of the data annotations, which as noted above are quite variable for different TCGA projects. In most instances, there are not quantitative information available to establish what age ranges were considered “young” vs. “old”, nor were there specifics around environmental exposures such as pack-years for smoking, ranges of BMI for obesity, etc. Could these please be specified and also some reference as to how these were selected, and were they selected prior to or after cross-validation was performed for the different categories?We thank the reviewer for the request. All criteria for young/old, smoker vs never-smoker, etc., were selected prior to cross-validation. To clarify, we have now included the following paragraph in “The mutational family tree” section in the Materials and methods:“All criteria for splitting samples in young vs old, smoker vs never-smoker, etc., were selected prior to cross-validation or any application of our algorithm. For the age analysis, we divided the unexposed samples into three groups  based on the tertiles of the age distribution and discarded the middle group before training the algorithm. For all other exposures, unexposed and exposed – as indicated by the available annotation – formed the two groups except for: (1) obesity, where a BMI = 30 was used as the splitting value between obese and non-obese, and (2) ultraviolet light (UV) and asbestos, for which samples with respectively the lowest 10% and 33% of the Total Mutations count were used as a proxy for the unexposed group, and all the other samples for the exposed one.”We are also attaching in 11) The conclusions about SuperSigs algorithm performance compared to NMF seem to be based on core NMF rather than the improved versions from Alexandrov. The authors claim that it is not possible to use Alexandrov's implementation, however, offer no reason as to why. Please specify the NMF approach used in the Materials and methods so it is clear to readers.We appreciate the request. We have now clarified it in both the main text and in the Materials and methods section. The cross-validation of Alexandrov’s implementation was not possible mainly due to the multiple manual or only semi-automated steps in their signature creation, validation and association to the risk factors. For example, in their 2013 paper, in the section “Samples and curation of freely available cancer data” it is stated that: “All mutational signatures were clustered using unsupervised agglomerative hierarchical clustering and a threshold was selected to identify the set of consensus mutational signatures. Mis-clustering was avoided by manual examination (and whenever necessary re-assignment) of all signatures in all clusters. 27 consensus mutational signatures were identified across the 30 cancer types.” Thus, we chose to use the core methodology used in Alexandrov et al., which is non-negative matrix factorization (NMF) , and approximate their method in two alternative ways in order to perform cross-validation: (1) “BestNMF” and (2) “MatchedNMF”.We would also like to note that we are being conservative against our own supervised results when using the alternative method called “BestNMF” to cross-validate the unsupervised approach. In fact, BestNMF is more of a weakly-supervised method rather than a purely unsupervised method. This can also be verified by comparing the apparent performances of Alexandrov and BestNMF in Supplementary file 3. Also, BestNMF provides us with signatures for cases that Alexandrov et al. did not study like BMI, alcohol, etc. and it is not clear how we can generate those signatures in Alexandrov as the Cosmic signatures are pre-fixed for tissues.The closest we can get to the Alexandrov implementation is with what we termed “MatchedNMF”. It is still in favor of the Alexandrov implementation because the process for matching the signature uses the Cosmic signatures and those signatures indirectly used the exposure labels of test labels to identify the associated risk factor as well.12) The authors provide a strong rationale for the greater flexibility for mutational signatures beyond a three nucleotide fixed size improves their models' performance, but don't provide statistical analysis to support this.We apologize for any possible confusion. We could not find claims of improved performance, rather only of greater flexibility. Our current approach is indeed offering higher flexibility as the fundamental unit of analysis is not forced to be the trinucleotide, but it is found to be of length 1, 2 or 3 nucleotides depending on our statistically guided approach of feature engineering/selection . Thus, the SuperSigs already contain features of variable length in the current manuscript. The only thing we have not explored in the current work is lengths > 3. While one of the potential strengths of our methodology is that it naturally allows for its extension to greater lengths, we feel that the most important aspects of our approach is the flexibility obtained in the choice of a given feature length within a given maximum length. We have now clarified further in the main text that “We will restrict our present analysis to only 1, 2, and 3 base pairs lengths to simplify the presentation, as this is already sufficiently different from current methods using only trinucleotides, and leave the further extension to future work.”13) Context of this publication with previous work. The aging signature is based on mutation counts, rather than rates. Does this not vary according to the tissue, based on the prior work published by this group? Is this another basic principle that could be addressed by comparing to SuperSigs analysis of pediatric cancer data?The reviewer makes an important point: counts vary with tissue. We plan to address this in a follow-up manuscript, as in this one we have focused and addressed a somewhat related point: the relative contribution of the normal aging process to the overall mutational load.14) The conclusions around obesity and tissue variance are overstated with respect to causality. Since these studies are observational, the authors cannot conclude evidence of causality.We have toned down our description of the findings. For example, we have now eliminated two of the four obesity signatures on the base of a poor performance in terms of cross-validated AUC. We also have now used the word “suggest” rather than “provide” in several places to lessen the strength of the statements. In some other cases, the statements are referring specifically to the SuperSigs .Essential Revisions:1) The authors should revise the description of the methods to provide greater detail. One example of this is the last paragraph in subsection “Do mutational signatures add to prior knowledge about etiologic factors?”, where "information" is used extensively throughout, without ever really defining what type of information is being provided by SuperSigs.We have now provided greater detail on the method, specifically on the way we defined “information”. We have done so by including the following new paragraph defining “information” the first time we use it in the main text:“In addition to simple performance, it is also important to evaluate the degree to which a given mutational signature improves upon prior knowledge about the mutational effects of an exposure to an etiological factor . For example, consider the case when clinical annotation is available and the main “peak” of a mutational signature, i.e. its most common mutation, is already known before the mutational signature is obtained. The peak may be a nucleotide, a dinucleotide, or a trinucleotide, depending on the specific mutational process. For example, prior validated knowledge indicated that aging induces [C>T]G mutations, and smoking induces C>A mutations. The added value of a mutational signature then depends on the additional “information” that signature provides beyond this already-known peak. If a mutational signature yields additional mutations that, under the effects of a given exposure, the genome is enriched for –– but was previously unknown to be –– then that signature adds valuable information to prior knowledge. Mathematically, a mutational signature is represented by the set of “weights” that signature attributes to all mutations included in the analysis, with the larger weights associated to mutations the signature is more enriched for. If these weights enable a mutational signature to have a higher prediction accuracy, or correlation, than random weights do, then we say that mutational signature provides “information”.”2) Please provide a weblink for the TCGA Genomics Data Commons.Thank you, we have now added the link .3) In subsection “Do mutational signatures add to prior knowledge about etiologic factors?” (and throughout), resist using "significantly" unless you have a p value that substantiates the term, and the test used to derive the p value.We thank the reviewer for spotting that mistake. We have also specified the test and its significance level. All other times a “significant” appears is either when citing results claimed to be significant by other papers , or just descriptions of a statistical test – and associated significance thresholds required – used when describing our methodology.4) In the Discussion, it is mentioned that SuperSigs associated with BRCA2 vary with tissue type (ostensibly meaning breast and ovarian) but only SuperSigs for breast cancer associated with BRCA2 is shown in Figure 4.We fully agree with the reviewer that this is an important observation. We have updated Figure 4, which now includes the BRCA2 signatures for both breast and ovarian cancers, to make this observation more easily accessible in the main text.5) Discussion paragraph two is the first mention of inflammation, which is known to be linked to obesity yet is not specifically called out here.We thank the reviewer for this important comment. We have now specifically called out obesity, in that sentence. We have also explained further the connection between our findings and the literature on inflammation  which was already cited. The text now reads:“These analyses then suggest that a major effect of some environmental factors may simply be to increase the rate of cell division. This increase would induce a linearly proportional increase in mutation rate, but with a mutation pattern that remains similar to the one caused by normal aging, i.e. it would not be associated with new signatures such as those caused by direct interaction of carcinogens with DNA. Increases in the rate of cell division are known to occur when tissues are damaged or inflamed . These observed similarities between the environmental and aging signatures then support the idea that, in certain tissues, the environmental factor’s main effect is to induce inflammation in that tissue, thus increasing its cells’ division rate.”6) In the same paragraph, both signature 4 and signature 6 are mentioned in terms of liver cancer but only signature 6 is explained as being “rare in liver cancers”. is it also the case that smoking is not associated with liver cancer, or…? Please edit this sentence so the reader understands why you are also mentioning the smoking signature result.Thank you for the comment. We have now edited the sentence to include also smoking, as follows:“Similarly, Signature 4, a signature for tobacco smoking, and Signature 6, a signature associated with defective mismatch repair mechanisms (MMR), was found in virtually every liver cancer patient ), though it is unlikely that all kidney cancer patients included in the TCGA database were smokers and MMR-deficiency is rare in liver cancers.”References1) Li, Shantao, Forrest W. Crawford, and Mark B. Gerstein. "Using sigLASSO to optimize cancer mutation signatures jointly with sampling likelihood." Nature communications 11.1 (2020): 1-12.