A study of the suitability of autoencoders for preprocessing data in breast cancer experimentation

A study of the suitability of autoencoders for preprocessing data in breast cancer experimentation Laura Macías-García a , José María Luna-Romera b, ⇑ , Jorge García-Gutiérrez b , María Martínez-Ballesteros b , José C. Riquelme-Santos b , Ricardo González-Cámpora c a Department of Anatomic Pathology. Hospital Infanta Elena, Huelva, Spain b Department of Computer Languages and Systems, ETSII, University of Seville, Spain c Department of Anatomic Pathology, Hospital Universitario Virgen Macarena, Seville, Spain article info Article history: Received 21 November 2016 Revised 19 May 2017 Accepted 25 June 2017 Available online 27 June 2017 Keywords: Autoencoder Biomedical data Breast cancer Deep learning Preprocessing abstract Breast cancer is the most common cause of cancer death in women. Today, post-transcriptional protein products of the genes involved in breast cancer can be identified by immunohistochemistry. However, this method has problems arising from the intra-observer and inter-observer variability in the assessment of pathologic variables, which may result in misleading conclusions. Using an optimal selection of preprocessing techniques may help to reduce observer variability. Deep learning has emerged as a powerful technique for any tasks related to machine learning such as classification and regression. The aim of this work is to use autoencoders (neural networks commonly used to feed deep learning architectures) to improve the quality of the data for developing immunohistochemistry signatures with prognostic value in breast cancer. Our testing on data from 222 patients with invasive non-special type breast carcinoma shows that an automatic binarization of experimental data after autoencoding could outperform other classical preprocessing techniques (such as human-dependent or automatic binarization only) when applied to the prognosis of breast cancer by immunohistochemical signatures. 1. Introduction Breast cancer is currently the most common cause of cancer death in women and the most usual non-cutaneous malignancy in European women [1]. Breast cancer is the leading lifethreatening cancer among women aged 20–59 years worldwide [2]. On average, one out of every nine women will suffer from breast cancer during their lifetime and 130,000 die each year because of metastatic disease [3]. The high morbidity associated with metastatic breast cancer requires the identification of biomarkers to classify patients based on the risk of metastasis. In the last decade, genetic alterations related to breast cancer have been identified and analysed by different techniques obtaining a genomic signature with prognostic value [4]. However, genomic signature is usually obtained by techniques that make it limited in daily clinical care [5]. More precisely, genomic signature requires the use of DNA sequencing technologies that, although are undergoing rapid development and thus lowering costs, still present some issues [6]. Namely, tiny or heterogeneous tissue fragments may limit the sensitivity of some genetic tests and sequencing requires extraction of DNA which destroys in situ information. Moreover, DNA sequencing data is typically complex and therefore requires special expertise for interpretation with higher risk of misinterpretation. At the present time, there exists other options such as immunohistochemistry which can be used to study the post-transcriptional protein products of many of the genes involved in tumour development and progression of breast cancer. Thus, we can define an ‘‘immunohistochemistry signature” with prognostic value [7]. Although immunohistochemistry is an affordable, robust and widely available technology used for decades [6], it could be affected by issues related to observer variation [8–10]. Although observer variation is normally related to diagnosis or prognosis, it could also affect the level of activation provided by experts for biomarkers included in biomedical databases leading to possible over- or under-estimation of the biomarkers activity. Moreover, biomedical databases are usually submitted to procedures to modify the original data before a statistical study (e.g., a binarization procedure to carry out a survival analysis [11]) which could also increase the effects of noise in databases. The influence of all the previous factors could be mitigated by the selection of a proper preprocessing technique. Otherwise, there exists risk of reaching misleading conclusions and therefore producing discrepancies in signature composition and outcome concordance [12]. The selection of a proper preprocessing technique for human studies has long been a concern [13]. In this context, automatic preprocessing by machine learning [14] could overcome problems related with human interaction (e.g., observer variation) which, as stated before, could be prone to error. Recently, a new approach related to machine learning, called deep learning, has been developed [15,16]. Deep learning has already been applied to biomedicine with success in areas related to biomarker development (including genomics, transcriptomics, proteomics, structural biology and chemistry) and drug discovery [17]. Denoising autoencoders (a specific technique often used to feed deep learning networks [18]) provided evidence of being able to effectively extract key biological principles from gene expression data and summarise them into constructed features with convenient properties for identification of patient survival in breast cancer [19]. Although autoencoders can be seen as a mechanism to construct new features, they might also be used as a preprocessing technique. This statement could be supported by the fact that autoencoders’ objective is to approximate the identity function. Thus, an autoencoded output is mainly one of the original inputs (features) with slight differences by the influence of the rest of inputs (rest of features). The purpose of this work is therefore to explore the use of autoencoders as preprocessing technique to improve the quality of the experimental data used to develop immunohistochemistry signatures with prognostic value in breast cancer. To this end, we tested autoencoders using data from patients with invasive breast carcinoma of no special type (NST). We carried out survival analysis regarding mortality and recidive and then compared the p-values obtained for a set of key biomarkers in breast cancer with those obtained after preprocessing by other techniques (manual [11,20] and automatic binarization [21]) used as baseline for the comparison. Finally, we established a statistical framework to validate our results and provide some insights into how autoencoders could improve experimental data. The remainder of this paper is organised as follows. Section 2 describes the experimental data used in this work and the methodology applied. Section 3shows the results achieved and their statistical validation. Section 4discusses the main findings from the results. Finally, Section 5is devoted to a summary of the conclusions and to discuss future lines of work. 2. Materials and method 2.1. Biomedical database The data used in this study were obtained from 222 patients (size large enough to fulfill the requirements of a survival analysis [22]) with diagnosed NST invasive breast carcinoma who received no neo-adjuvant treatment and were followed up for a minimum of 5 years. Histological preparations were examined and corresponding case histories were also reviewed to determine subsequent disease progression (local recidive and/or metastasis and disease-related mortality), resulting in two target binary variables, recidive (REC) and mortality (MORT), and two continuous variables which measured the time to recidive (TREC) or exitus (TMORT). The study design was approved by the appropriate institutional review board and it included informed consent from all patients. Tumour tissue was obtained from formol-fixed, paraffinembedded surgical specimens. Tissue microarrays (2.5-mm cores) for immunohistochemical examination were obtained and the expression of 21 antibodies related to breast cancer (Table 1) were independently evaluated by 2 pathologists blinded to the patient data. The extent and intensity of staining was scored semi quantitatively using up to 4 categories for each antibody. The final score was obtained by multiplying staining score by intensity score. When discrepancies in results between pathologists occurred, the highest of the 2 scores was used. The final database had 25 attributes (score levels for 21 antibodies in Table 1, REC, MORT, TREC and TMORT) for 222 instances (patients). A detailed explanation about the procedure to build the database can be found in [11,20]. 2.2. Compared techniques The Cox proportional hazard regression model is the most widely used semiparametric survival model in the health sciences [43]. Binarization is usually applied to the covariates before the development of Cox regression models, mainly because the effect of a covariate on the hazard is assumed to have a log-linear functional form. For continuous covariates, this assumption is often violated as the effect is highly non-linear [44]. In addition, understanding the risks associated with every continuous covariate is also more complicated since the risks are the ratio of the hazards between 2 individuals whose values for a covariate differ by one unit (although the concept of a unit is not easy to define for nonbinary covariates) when the rest are held constant. In this work, we compared three different preprocessing methods applied to the original data: manual binarization and automatic binarization (baseline techniques for our comparison) and automatic binarization after an autoencoding transformation. 2.2.1. Manual binarization This type of binarization consisted of the selection by pathologists of specific thresholds according to the literature for every predictor. Thus, the responsibility of defining when a predictor is activated (positivity) or not (negativity) is exclusively human. A deeper explanation is provided in the articles which originally built the study dataset [11,20]. 2.2.2. Automatic binarization Automatic binarization is a well-known technique in machine learning. In this study, it was a simple processing of the data which consisted of 2 steps: a normalisation phase which translated original values into the interval [0,1] taking maximum and minimum values for each feature and a posterior step which discretized the Table 1 Antibodies and corresponding features used in this study, plus a reference in the last 5 years regarding its importance for breast cancer oncogenesis. Antibody Feature Reference E-cadherin E-cadherin [23] Twist Twist [24] Survivin Survivin [25] c-Kit CD117 [26] CD44 CD44 [27] CDK2 CDK2 [28] RKIP RKIP [29] Topoisomerase II aTOP2A [30] Fascin Fascin [31] ABCG2 ABCG2 [32] CK5-6 CK56 [33] FOXA 1 (HFN 3a) FOXA1 [34] P53 P53 [35] CD10 CD10 [36] Estrogens Receptor ER [37] Progesterone Receptor PR [38] Ki67 Ki67 [39] HER2 HER2 [40] CXCR4 (nuclear location) CXCR4n [41] CXCR4 (cytoplasm location) CXCR4c [41] Caveolin Caveolin [42] 34 values into 0 or 1. The discretization applied was equal-width [45] which involved that values under 0.5 were discretized to 0 and equal or over into 1. 2.2.3. Autoencoded binarization The last option tested was the use of an automatic binarization with a previous application of autoencoders to the original data. Thus, although it was essentially the same procedure, the data binarized differed from the original by the action of the autoencoding phase so that the binarized dataset was different. An autoencoder is a neural network trained to reproduce its input at the output layer. Thus, an autoencoder takes a set of inputs and tries to build an identity function through a neural network model. As a result of this, the network must decide the data features that are the most important, essentially acting as a feature extraction engine [15]. As Fig. 1 shows, autoencoders are comprised of an input layer, an output layer that has the same size as the input layer, and (in its simplest form) a single hidden layer [16]. In our case, we actually tried to preprocess the original dataset without generating new features and the same number of neurons in the input and output assured this requirement. An autoencoder has 2 steps: encoding and decoding. In our study, encoding was the step whereby the initial values of the predictors were transformed as a result of applying a sigmoid function to the input vector. Decoding is the procedure used to convert the values in the hidden layer into the ones shown as output vector in the output layer. This last transformation was also carried out by a sigmoid function. An autoencoder can be seen as a double transformation which tries to provide an approximation of the identity function. By placing constraints on the network, such as by limiting or increasing the number of hidden units, interesting structure about the data can be discovered [46]. For our experiments we used an implementation of autoencoder from Weka [47] based on a multilayer perceptron [48]. Concretely, we applied a contractive autoencoder [49] which only allowed a single hidden layer. This type of autoencoder was mainly controlled by two parameters: k(penalty applied in the training phase of the model) and the number of hidden neurons. 2.3. Statistical framework In this article, we compared the results obtained after a survival analysis applied to 3 different datasets: the original dataset from biomedical data with a human-dependent binarization, an automatic binarization and automatic binarization after autoencoding. With a survival analysis, we tried to identify independent prognostic factors from the immunohistochemical markers for outcomes other than disease-free survival (i.e., recidive and exitus). To this end, we applied Cox regression models following univariate analysis with a confidence interval of 95%. In addition, for every model, we evaluated the slopes in generalised linear regressions of the scaled Schoenfeld residuals on functions of time (TREC and TMORT). A non-zero slope regarding a predictor is an indication of a violation of the proportional hazard assumption which is needed to assure the validity of the conclusions reached by a Cox regression [50]. Cox regression using R [51] returned p-values associated with each predictor. Each p-value showed the significance for a particular covariate regarding a dependent variable (REC, MORT). It is well-known to pathologists that ER, PR, Ki67 and HER2 are important indicators for breast cancer [52]; hence, we mainly focused on them to test the validity of the 3 compared options. In the case of the autoencoding preprocessing, default values were used except for the number of neurons in the hidden layer, that was set up as the number of items from input layer plus one. That value was found optimal after a trial-and-error procedure on the complete dataset. We selected this option to parameterize and validate results instead of a more classical option in machine learning such as hold-out or cross-validation due to the fact that those methodologies are based on splitting the original data in training and testing sets. Unfortunately, survival analysis has constraints regarding the size of the database under study if p-values are intended to be meaningful [22]. Since we were working with only 222 cases and wanted to compare the competitors in terms of the real significance of a set of key biomarkers in breast cancer, it was not possible to apply a split-based strategy. However, regardless the real significance of the studied biomarkers, it is important to take into account the fact that using a machine learning approach such as autoencoders could involve risk of overfitting. Especially, when parameterization was carried out with all the dataset of patients. To assess the validity of the conclusions of the previous analysis (i.e., if there was risk of overfitting), we repeated the previous study but following a hold-out procedure (see Fig. 2). Thus, we randomly split the dataset into two subsets, training and test sets, and we used training to automatically build the preprocessing techniques (training an autoencoder, learning bounds for automatic binarization or doing nothing in the case of manual binarization since binarization rules, regardless the data, were taken from the literature). For the parameterization of the autoencoder, we applied a grid search with: lambda from 0.001 to 0.03 and an increasing step of 0.03; a number of hidden neurons from 2 to the number of biomarkers plus 1 (22 in our case) and an increasing step of 2. Then, we applied each preprocessing technique to transform the test set. Finally, we applied a survival analysis to the transformed test set and accumulated the corresponding p-values. We repeated the complete procedure ten times for each compared preprocessing technique to avoid bias due to initial random selection and took the mean of the pvalues. The source code and the data (including the training and test partitions) used in this part of our analysis can be found published on the web [53]. Fig. 1. Autoencoder schema with a hidden layer composed of a number of neurons equal to the number of items in the input layer plus one. 35 According to the p-values obtained for ER, PR, Ki67 and HER2 regarding MORT and REC in Cox regression, we could state that a transformation based on the use of an automatic binarization after autoencoding would be better qualitatively than the other options, but not quantitatively. To this end, we used a non-parametric procedure from the p-values obtained in Cox regression on the 3 transformations of the original dataset (for ER, PR, Ki67 and HER2 regarding REC and MORT) that obtained the averaged rankings of each transformation, then provided a best technique and finally demonstrated the significant difference between the best transformation and the others. We selected the p-values obtained after analysis of the complete database because those results fitted the requirements of survival analysis [22] in a better way than the hold-out procedure previously described. The chosen nonparametric procedure used the Friedman test and the Holm posthoc procedure to statistically validate the differences in the mean ranks of the corresponding p-values reached. This statistical analysis was carried out using the open-source platform StatService [54]. The Friedman test is a non-parametric statistical test for evaluating the differences between more than 2 related sample means [55] where the related samples were the p-values of 3 different transformation options across 8 target values (p-values obtained by Cox regression for ER, PR, Ki67 and HER2 when REC and MORT were the dependent variables). The null hypothesis being tested was that all the preprocessing options performed in the same way and any observed differences were merely random. This was equivalent to testing whether the measured average ranks r j were significantly different from the expected mean rank. In our case, the lower the p-value, the higher was the certainty that a preprocessing technique worked effectively, and therefore, it obtained better ranking (possible values were from 1 to 3, with 1 as the best possible) for the Friedman test. Average ranks for each technique provide a fair comparison of the compared techniques. Given the measured average ranks, the Friedman test could check whether the average ranks were significantly different from the mean rank expected under the null hypothesis. When we found that the measured average ranks were significantly different (at a ¼0:05) and provided that the Friedman test rejected the null hypothesis, we could proceed with a post-hoc test that would evaluate the relative performance of the studied algorithms against a control algorithm (usually the one with the best average rank) avoiding family-wise error. The Holm stepdown procedure can carry out this task by testing hypotheses sequentially ordered by their significance. The zstatistic comparing the i-th classifier against the control can be seen in Eq. (1) where nstands for the number of values used to build the rankings, kfor the number of compared techniques, r 0 for the ranking of the control method and r i for the mean ranking for every other method compared in the i-th step. z¼ðr i r 0 Þ ffiffiffiffiffiffiffiffiffiffi kðkþ1Þ 6n qð1Þ With the Holm post-hoc test, we could decide whether the control method was significantly different from its rivals. Thus, if p i was below a =ðkiÞwhere a is the level of significance (usually 0.05), the corresponding hypothesis would be rejected and we proceeded to compare p iþ1 with a =ðki1Þ. As soon as a certain null hypothesis could not be rejected, all the remaining hypotheses would be retained as well. Otherwise, the control method could be stated as significantly different from the rest of the competitors and then better since it obtained a better mean ranking. 2.4. Sensitivity analysis This work aimed to show autoencoders could lead to benefits regarding the issue of the observer variability and preprocessing adequation in the assessment of pathologic variables. To this end, we established a comparison with other preprocessing techniques and an additional study regarding autoencoders exclusively. We were also interested in obtaining some insights about how autoencoders worked in the way they did. Therefore, we designed a procedure where a predictor was selected, then we developed an autoencoder removing the selected predictor from the inputs and outputs and recorded the values for the rest of the outputs (the rest of the autoencoded predictors). In this way, we could obtain the influence of every selected predictor on the rest of the autoencoded ones. For this, we developed the dmeasurement which follows the equation: dðx;yÞ¼1j q ðaðX;xÞ;aðXy;xÞÞj ð2Þ where Xstands for the set of inputs (original predictors), xand y stand for two concrete predictors, aðI;iÞis a function which provides the output corresponding to the input iin an autoencoder built with a set of inputs I¼i 0 ;i 1 ;...;i n ;Iiand qis the correlation function. With the results of dfor every predictor combination, we built a matrix where each cell represented the value of d(influence) of a predictor (column) on the rest (rows). Fig. 2. Hold-out scheme for the validation of the results of every preprocessing technique. 36 Fig. 3. Parallel coordinates describing the distribution of immunohistochemical signatures for every patient free of disease during the studied period in the original (top), the original with a 10% noise addition for visual purposes (middle), and autoencoded (bottom) datasets. 37 3. Results Fig. 3 shows the parallel coordinates (a common way of visualising and analysing high-dimensional multivariate data) formed by the values of each covariate obtained for each patient free of disease in the original and the autoencoded dataset. An additional image is provided which shows the same distribution as the original but with a 10% of noise for visual purposes (original data was discretized and most patients provided overlapping signatures). Parallel coordinates for other groups (all the patients, patients who presented recidive and patients who did not survive) are provided as supplementary data. Table 2 provides a summary of the differences provided by the compared techniques. It shows the percentage of positivity and Table 2 Summary of the percentage of positivity or negativity for the main four predictors (ER, PR, Ki67 and HER2) according to the procedure applied (manual binarization, automatic binarization, automatic binarization on autoencoded data) and the type of group of patients beside the differential between percentage of each group regarding free-of-disease patients. In bold, the highest absolute difference regarding the three procedures (manual, automatic and autoencoded). Preprocessing Patients ER PR Ki67 HER2 "#"#"#"# Manual ALL 79.91 20.09 76.07 23.93 64.10 35.90 22.22 77.78 FREE 84.44 15.56 79.44 20.56 61.67 38.33 23.33 76.67 RECIDIVE 66.67 33.33 64.29 35.71 78.57 21.43 21.43 78.57 EXITUS 59.26 40.74 70.37 29.63 66.67 33.33 18.52 81.48 r FREE vs. RECIDIVE 17.77 15.15 16.9 1.9 r FREE vs. EXITUS 25.18 9.07 5 4.81 Automatic ALL 71.37 28.63 66.24 33.76 13.68 86.32 21.79 78.21 FREE 80.1 19.9 74.35 25.65 17.28 82.72 28.27 71.73 RECIDIVE 61.9 38.1 59.52 40.48 26.19 73.81 21.43 78.57 EXITUS 56.25 43.75 56.25 43.75 18.75 81.25 25 75 r FREE vs. RECIDIVE 18.2 14.83 8.91 6.84 r FREE vs. EXITUS 23.85 18.1 1.47 3.27 Autoencoded ALL 82.48 17.52 72.22 27.78 20.94 79.06 27.78 72.22 FREE 88.89 11.11 76.11 23.89 17.22 82.78 25.00 75.00 RECIDIVE 64.29 35.71 57.14 42.86 30.95 69.05 42.86 57.14 EXITUS 51.85 48.15 59.26 40.74 33.33 66.67 37.04 62.96 r FREE vs. RECIDIVE 24.6 18.97 13.73 17.86 r FREE vs. EXITUS 37.04 16.85 16.11 12.04 Table 3 P-values obtained after survival analysis and Schoenfeld residuals testing of proportionality of the original pathologist-dependent binarized, automatic binarized and afterautoencoding binarized datasets. Boxed values are those related to the gold standard in the literature [52]. In bold, p-values under a¼0:05. 38 negativity of the main predictors under study for the different preprocessed datasets along with the differences between the distributions of the different patient types (ALL, all the patients; FREE, patients free of disease; RECIDIVE, patients who presented recidive; EXITUS, patients who did not survive). Table 3 shows the obtained p-values after survival analysis and the Schoenfeld residuals test of proportionality (carried out by R software [51]) applied to the manually-binarized original, automatically-binarized original and automatically-binarized autoencoded datasets. Key predictors for breast cancer [52] are in boxed cells and p-values below a ¼0:05 are in bold. For recidive cases, boxed key predictors (a gold standard according to the literature) should have been significant (p-values under a ¼0:05 for the survival analysis). In the case of the original dataset, ER, PR and Ki67 were 0.01, 0.04 and 0.04 respectively. For the binarized dataset only ER and Ki67 had values below 0.05 (0.02 for ER and 0.01 for Ki67). The autoencoded dataset showed better results with p-values near 0 for ER, 0.01 for PR, 0.04 for Ki67 and 0.01 for HER2. Table 4 shows the results obtained after following the procedure described in Fig. 2 to assure overfitting did not affect the previous results. Although, as stated before, the p-values obtained by this procedure were not meaningful from the point of view of the importance of each biomarker, the survival analysis on the autoencoded dataset obtained the best result for 6 out of the 8 cases. The Friedman test rankings are shown in Table 5 and the mean for every technique regading the key biomarkers in Table 6. The highest result for a ranking was 1 and the worst was 3. As the ranking shows, the autoencoded dataset was in the first position with 1.25, the original was in the second with a ranking of 2.25 and the binarized dataset was the last one with 2.50. The statistic for Friedman was 7.0, distributed according to a chi-square distribution with 2 degrees of freedom. The p-value for Friedman was 0.0302 and lower than 0.05. Therefore, the null hypothesis was rejected (that they all behaved in a similar way) with a level of significance of a ¼0:05. Table 7 shows the p-values,z-value and Holm ’ s a , using automatically-binarized autoencoded data as the control algorithm since it obtained the best ranking. As can be seen, the null hypothesis was rejected for both competitor preprocessing methods. Thus, we concluded that the autoencoder generated the best results (since it obtained the best average ranking) and they were statistically different from those of the other options. Fig. 4 shows the influence of every single descriptor (column) regarding the rest (rows). Namely, each cell corresponds with the degree of variation (d) of a biomarker (row) after autoencoding the original dataset if another biomarker (column) is included or not in the training. The relationships between predictors were stronger when dwas near 1. The most influential results appear in lighter-coloured cells in the matrix. 4. Discussion Our results suggest that autoencoders could statistically be a valuable tool to reduce noise in data (related to breast cancer but potentially to any other biomedical research area) using hidden relationships between biomarkers. This statement was supported by statistical significance which depends on relatively clear patterns and differential behaviours in the compared groups that let a statistical test validate the differences among them. The first part of that idea can be seen in Fig. 3 where a clear pattern appears for autoencoded data whilst it does not in the original data. Similar patterns were not so clear in the rest of subgroups but Table 4 Mean p-values obtained for main biomarkers after following procedure described in Fig. 2 for the original pathologist-dependent binarized, automatic binarized and afterautoencoding binarized datasets. In bold, the best p-values. RECIDIVE MORTALITY ER PR Ki67 HER2 ER PR Ki67 HER2 Manual 0.14 0.41 0.14 0.59 0.16 0.58 0.42 0.47 Automatic 0.10 0.25 0.22 0.65 0.19 0.47 0.59 0.55 Autoencoded 0.27 0.01 0.01 0.17 0.30 0.23 0.27 0.39 Table 5 Rankings obtained by each technique according to the p-value found in Table 3. Dependent Variable Predictor Original Binarized Autoencoded REC ER 2 3 1 PR 2 3 1 Ki67 2 1 2 HER2 2.5 2.5 1 MORT ER 2 3 1 PR 3 2 1 Ki67 1 3 2 HER2 2.5 2.5 1 Mean ranking 2.25 2.50 1.25 Table 6 Sorted mean ranking for Friedman’s test. Dataset Ranking Autoencoded 1.25 Original 2.25 Binarized 2.50 Table 7 Post-hoc analysis using Holm procedure and the autoencoder option as the control algorithm. Dataset pzHolm a Binarized 0.012 2.500 0.025 Original 0.046 2.000 0.050 39 E-cadherin Twist Survivin CD117 CD44 CDK2 RKIP TOPO2A Fascin ABCG2 CK56 FOXA1 P53 CD10 ER PR Ki67 HER2 CXCR4n CXCR4c Caveolin E-cadherin Twist Survivin CD117 CD44 CDK2 RKIP TOPO2A Fascin ABCG2 CK56 FOXA1 P53 CD10 ER PR Ki67 HER2 CXCR4n CXCR4c Caveolin 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Fig. 4. Influence (d) of every single descriptor (columns) on the output of the autoencoder for each other descriptor (rows). 40 this fact could be due to a limited number of cases with recidive or mortality (30 and 15, respectively) in comparison with the group free of disease (180). Table 2 seems to confirm the second part of our initial statement. If we focus on the differences between the percentage of positivity/negativity in the groups free of disease and recidive/exitus, we see that differences are maximised mainly for the autoencoded data. This fact is important because differences between groups are the key to validate the significance of a biomarker in a statistical analysis. Our results therefore seem to show that autoencoders might preprocess the input variables as PCA does in other areas [46] but with the difference that the former is not limited to a linear transformation [56]. In other words, autoencoders reduce the level of noise in the inputs trying to build real patterns from data to slightly modify the original feature set. The potential benefits of autoencoders for preprocessing (not only for developing new features) were validated in our experiments, although a more complicated parameterization compared with PCA could be a limitation that should be considered. The better results obtained by preprocessing with autoencoders compared to the use of the rest of options could have been due to the risks of overfitting by non-parametric techniques such as neural networks. However, if we compare the results in Tables 3 and 4 we can see that the relative results are similar. Therefore, the use of autoencoders improved the p-values (associated with the importance of the main indicators in breast cancer) in the survival analysis regardless the experimental framework selected. Table 6 shows that autoencoded binarization obtained better results than manual or automatic binarization on average. A key point is that HER2 resulted in a significant finding for the recidive data after preprocessing by an autoencoder. This predictor was not found to be significant in the original studies [11], although it is well-known that HER2 positivity is a factor for a poor prognosis for this type of tumour [52]. Table 8 shows the most influential relationships found in Fig. 4 according to dvalue between descriptors, beside a reference in the literature that reports such relationships. For visual purposes, we focused on relationships with a dequal to or higher than a fixed threshold, d¼0:65, and equal or over the 95th percentile by predictor (using the values of every single predictor row to calculate the percentiles). Moreover, we used a text mining component to find relationships between the predictors in the literature [71]. Regarding number 1 in Table 8 we found that Twist is a wellknown transcriptional repressor of E-cadherin gene expression in breast cancer [57]; thus, the autoencoder could take advantage of this situation to recalculate E-cadherin values. We also found that Twist represses ER-alpha expression by recruiting the nurd protein complex in breast cancer cells [58] (2). In the latter case, the autoencoder seemed to suggest a reverse relationship since each cell quantified the influence of the column predictor on the row predictor. This effect was reported in other cases and will be discussed later in this section. If we focus on the relationship between CD117(3) and ER, we found that 17b-estradiol (E2), which induces the non-genomic activities of its receptors (ER alpha and ER beta) in different cell cancer lines [72] also down-regulated the expression of the SCF/ c-KIT system in prostate cells [59]. However, we could not find any reference that reported the same findings for breast cancer. Regarding 4, CD44 isoforms can be associated with different breast cancer subtypes and clinical markers such as HER2, ER and PR, which suggested involvement of CD44 splice variants in specific oncogenic signalling pathways [60]. Some degree of morphological interrelation in squamous cell carcinoma (6) was reported between ABCG2 and CK5/6 [61],although this relationship in breast cancer has not been verified yet. CD10 and RKIP were found to be downregulated in prostate cancer cases [62] and this could denote some degree of relationship (7) but has also not been reported for breast cancer. With regard to 8, CD10 expression has proved to be strongly correlated with well-established negative prognostic markers such as HER2 positivity [63]. The influence of HER2 on PR (9) has already been reported in women with breast cancer, aged more than 45 years [64]. Since most patients in our dataset were women born in the 1950s or before (see Fig. 5) and the first reported case was in 2004, this fact seems to have also been confirmed by the autoencoder indirectly. Higher Ki67 tumours have been recently reported as usually showing HER2/neu overexpression [65]. Our experiments seem to confirm this relationship (10). In addition, a strong dependence of HER2 on FOXA1 (11) was also reported and may correspond to a strong association between the overexpression of FOXA1 and HER2 demonstrated in ER-negative breast tumours [66]. CXCR4 was related to RKIP [67] in carcinogenesis and breast cancer metastasis (12). CXCR4 was also related to Fascin (13) and found to have a certain role in the infiltration and metastasis of colorectal carcinoma [68] but a similar study for breast cancer could not be found. Finally, mechanistic investigation revealed that caveolin-1 silencing could downregulate the b-catenin/ABCG2 pathway [69]. In addition, caveolin-1 down-regulation was also reported as an activator of ER signalling in breast cancer samples [70]. Both examples were inversed regarding the information in Table 8 (14 and 16). In conclusion, the analysis of the literature provided enough evidence of the fact that autoencoded datasets may rely on the relationships among biomarkers to reduce noise impact in the original set of covariates without the need to build new features such as clusters of the original set [19]. Some of the examples given from the literature showed inversed relationships to those reported by our sensitivity analysis. This fact needs to be further studied but it is important to emphasise that our experimental analysis only showed direct relationships. The possibility that there exists other hidden relationships that modified the behaviours of the predictors cannot be ruled out. There could be indirect interactions that we could not represent in our experimental framework. Some other covariates could be acting on an intermediary which appeared as the strongest influencer of a concrete predictor, although a relationship between them could not exist. In most cases ER, which depends on many other biomarkers according to the literature, was the influencer which seems to confirm our hypothesis. Table 8 Examples of evidence in the literature regarding the most influential column descriptors on row descriptors according to dmeasure in Fig. 4. # Affecting predictor Affected predictor Related research 1 Twist E-cadhering [57] 2 ER Twist [58] 3 ER CD117 [59] 4 ER CD44 [60] 5 CDK2 RKIP Not found 6 CK5/6 ABCG2 [61] 7 RKIP CD10 [62] 8 HER2 CD10 [63] 9 HER2 PR [64] 10 Ki67 HER2 [65] 11 FOXA1 CXCR4n [66] 12 RKIP CXCR4c [67] 13 Fascin CXCR4c [68] 14 ABCG2 Caveolin [69] 15 FOXA1 Caveolin Not found 16 ER Caveolin [70] 41