The main information sources were the population-based cancer registry of the health region of the province of Lleida, the eCAP (a computerized medical history program used by doctors, pediatricians, and nurses in primary care centers when they see their patients [14]) software, and the Central Register of Insured Persons (a register that allows the unique identification of those covered by the Catalan Health Service through the personal identification code, the management and consultation of their data, and their updates [15]). Before applying the statistical technique, the information was validated by experienced professionals (doctors, nurses, and documentalists) in the Lleida population-based cancer registry who reviewed the clinical history of each patient. After that, the International Agency for Research on Cancer tool was applied to detect unlikely or impossible codes or combinations of codes [16]. Then, an accurate description of the data and basic concepts of the MCA and k-means used in this work are explained in this section. See the system flow chart of the whole process in Figure 1; it shows the different registers used to extract the data, its process and transformation, and its applied analysis. The patients with empty fields were removed.

The colorectal cancer data were extracted from the new cases registered between 2012 and 2015 in the Lleida population-based cancer registry [5,17,18] for patients with cancer in the main hospitals in the health care region of the Lleida province. Specifically, the data set consisted of 1083 new colorectal cancer cases. These hospitals were the Arnau de Vilanova University Hospital and the Santa Maria University Hospital, and the primary information sources were hospital records (International Classification of Diseases, ninth revision codes-140.0 to 208.9) and reports from pathological anatomy. Additionally, these reports confirmed >92% of cases included in the sample. Risk factors such as BMI and smoking were extracted from eCAP software and the SES was extracted from the Central Register of Insured Persons. The study is compliant with the General Data Protection Regulation (European Union), thereby maintaining the anonymity of the patients. Cancer episodes were recorded according to international criteria. In addition, the data analysis (done with R) can be freely downloaded from this GitHub repository [19]. It also included a mock data set randomly generated to test the models. The original data set could not be uploaded due to General Data Protection Regulation, which does not permit sharing patients’ information.

The BMI was used to calculate the obesity of each patient by standard weight status categories [20]. We categorized the BMI as the established table: <24.9 as normal weight, 25-29.9 as overweight, and >30 as obesity. Regarding SES, we categorized the variable according to the annual income available from the Central Register of Insured Persons. According to the legislation [21], we created 2 groups: annual income <€18,000 (low income) and >€18,000 (high income) (€1=US $1.04). The population was categorized as rural, semiurban, and urban. In accordance with [22], people living in cities with a population of more than 10,000 were classified as urban, population between 10,000 and 2000 in towns as semiurban, and the rest as rural. The Spanish National Statistics Institute has defined rural areas as those with a population of less than 2000, semiurban areas as those with a population between 2001 and 10,000, and urban areas as those with a population with more than 10,000 people. All the cancer cases that did not conform to one of these fields were discarded automatically. To sum up, each register contains the following fields: age group (50-64 years, 65-74 years, ≥75 years); gender (male, female); population (rural, semiurban, urban); exitus (death, alive); BMI (normal, overweight, obesity); smoking (ex-smoker/smoker, nonsmoker); income (high income, low income); and stage (0, I, II, III, undefined). Table 1 shows the number of cases for each category.

MCA is an unsupervised learning algorithm for visualizing the patterns in large and multidimensional categorical data [23]. This method can be used to analyze, explore, summarize, and visualize information contained of individuals described by categorical variables [24]. Unlike correspondence analysis (CA), MCA can deal with more than one categorical variable. This is the main advantage of the MCA technique. In our case, MCA was first used to evaluate the relationships between all the features. MCA was then used to evaluate the relationships among population, age, gender, exitus, BMI, smoking, and tumor stage. Associations between features are represented graphically [25]. The graphs aim to visualize the similarities or differences in the profiles simultaneously, identifying those dimensions that contain most of the data variability. Features or their categories close to each other are significantly related statistically.

The factors were interpreted with the help of various statistical coefficients, which complemented each other to provide a better interpretation. The most common and important are inertia, eigenvalue, contribution, and factorial coordinates. Inertia is a measurement of the dispersion of the set of computed distances between points. Analogously, in principal CA, inertia corresponds to the explained variance of dimensions. The eigenvalue allows the inertia that a specific category produces to be quantified determining a certain percentage relative to the entire set of the active category. The percentage coordinates (x- and y-axis) of the graph enable the category points in a graph to be represented and established. In MCA, the distance between 2 or more categories of different variables can be interpreted in terms of the associations and correlations between these. If 2 categories present high coordinates and are close in space, this means that they tend to be directly associated [26,27]. If 2 categories present high coordinates but are distant from each other (eg, they have opposite signs), this means that they tend to be inversely associated [28,29]. A heatmap was created to help the interpretation of the MCA. This plot used the intensity of the colors to show the level of association between the variables. Our graphs showed the association by the distance between the categories in the MCA plot.

K-means [30] is a nonsupervised learning algorithm used in data mining and pattern recognition. The algorithm partitions the data set in k predefined distinct nonoverlapping subgroups (clusters) where each data point belongs to only one group. It tries to make the intracluster data points as similar as possible while also keeping the clusters as different (far) as possible. It assigns data points to a cluster such that the sum of the squared distance between the data points and the cluster’s centroid is at the minimum. The less variation we have within clusters, the more homogeneity (similarity) there is between the data points within the same cluster. The k-means algorithm is composed of the following steps: (1) it places k points in the space represented by the patients who are being clustered, (2) it assigns each patient to the group that has the closest centroid, and (3) when all patients have been assigned, it recalculates the positions of the k centroids. Steps 2 and 3 are repeated until the centroids no longer move. This produces a separation of the patients into homogenous groups while maximizing heterogeneity across groups. The optimal number of clusters was obtained by the elbow method [31]. This consists of plotting the explained variation as a function of the number of clusters and picking the elbow of the curve as the number of groups to use. To assess internal cluster quality, cluster stability of the optimal solution was computed using Jaccard bootstrap values with 10,000 runs [32].

All the information presented was analyzed using MCA, an extension of CA, and the k-means algorithm. The combination of MCA and k-means benefits the effectiveness of the calculation process and, in consequence, the k-means results. MCA helps to reduce the noise, which allows the k-means algorithm to obtain more accurate distances. The MCA dimension reduction automatically performs data clustering according to the k-means objective function [33]. In addition, the potential confounding factors in this study were assessed by calculating the distances between the variables (inertia) that take into account their relative weight in the database as a whole. However, these variables were related to each other depending on the similarity of each register. Previously, the patients with empty fields were removed.

The MCA method was implemented in scripts performed with R [34], an open-source programming language and environment for statistical computing and graphics. Specifically, the main library used to implement the methods and obtain the results was FactoMineR [35]. K-means was written in Python [36], and the main library used scikit-learn [37]. These methods were launched by their default configuration and using a personal computer.

The analysis of the MCA and k-means without the stage variable included 1083 registers. Figure 2 shows the different categories and their possible associations. The variance for dimension 1 was 15% (eigenvalue 0.21) and that for dimension 2 was 12% (eigenvalue 0.17). Figure 2 also shows the position of each category in the plot and its contribution on the dimensions. Note the contribution of mortality (15% on the negative x-axis and 10.2% on the positive y-axis), the ≥75 years age group (18.8% on the negative x-axis and 4.5% on the positive y-axis), and the ex-smoker/smoker (16.5% and 12.3% on positive x-y axis). Figure 3 shows the relation between the categories. The associations between the points were significant when they were closer and the distance was minimum. For example, females and obesity were represented in the same dimension in the MCA plot. Therefore, the heatmap also demonstrated this association with a distance of 0.4 between the points in the MCA plot.

Graphically, the points closer to each other or the points represented in the same direction of the axis suggest associations. As can be seen, mortality and older age are very close in the plot. This suggests a possible association. Another possible relation observed could be between females and obesity. Then, a cloud on the positive x-axis and the negative y-axis was made up of the 65-74 years age group, high income, and survival. Finally, additional associations could be made up of the 50-64 years age group, males, smokers or ex-smokers, and normal weight.

Table 2 shows the centroids of the main clusters obtained after applying the k-means algorithm. The recommended number of optimal clusters was 5 [31] (see the GitHub [19] repository to evaluate the plot). The first cluster grouped 242 registers among which the main register was males aged ≥75 years from urban populations, with low income, nonsmokers who were overweight, and with a low risk of dying. The next cluster (259 registers) represented females aged between 50 and 64 years with high income. It grouped the cases from rural populations with normal weight and survival. Cluster number 3 was made up of 180 registers. These were mostly males aged ≥75 years with low income and from semiurban populations. They were nonsmokers but were obese and unfortunately included exitus. It was the only cluster that included mortality. The fourth cluster represented urban males aged between 65 and 74 years and with low income. In this case, they were smokers or ex-smokers with normal weight and no mortality. It contained 194 registers. Finally, the last cluster was made up of 208 cases, which included semiurban females aged between 65 and 74 years with low income. They were not smokers but they were overweight. Fortunately, surviving patients predominated in this cluster and the risk of dying was low. See these clusters represented graphically in the GitHub [19].

This subsection presents the outcomes, including the stage of the tumor. The data set used for this analysis discarded the registers, which did not contain the stage (647 registers). Therefore, the number of cases analyzed was 438 (Table 1). Figure 4 shows the outcomes obtained after applying MCA. The variance of dimension 1 was 11.4% (eigenvalue 0.18) and that of dimension 2 was 10.2% (eigenvalue 0.16). Mortality was also one of those with the highest contribution (26.4% on the positive x-axis and 10.5% on the positive y-axis). Near this was stage III with a high contribution (16.3% on the positive x-axis and 13.7% on the positive y-axis). Ex-smoker/smoker contributed significantly compared with the rest of categories (9.1% on the negative x-axis and 1.3% on the positive y-axis). The relations between these and other categories are shown in Figure 5. See the death and its correlation between stage III. The heatmap differentiated this association clearly, as the MCA plot also showed. The location of the categories in the plot and their contributions suggested possible associations. The main association was between stage III and mortality and with females with stage II, the ≥75 years age group, and nonsmokers. Another relation could be males with high income, aged between 50 and 64 years, stage 0, and ex-smokers or smokers. However, these results could be affected by the decrease in cases.

Table 3 shows the clusters obtained from the data set with the tumor stage. All the clusters obtained were male nonsmokers owing to the decrease in the number of registers in the data set. The first cluster with 135 cases represented obese urban patients aged between 65 and 74 years with stage II reached and a low risk of death. The second cluster had 120 registers of patients with stage II and age ≥75 years from semiurban populations. Their risk of death was also low. The next cluster included 76 registers and they were from the urban population but overweight. They included the younger patients (50-64 years age group), with a low risk of death and the lowest stage (stage 0). The fourth cluster (n=72) represented rural inhabitants, aged between 65 and 74 years. They were obese with stage III cancer but low risk of death. However, the fifth cluster was patients from the semiurban population, aged ≥75 years, overweight, in an advanced stage (III), and with a high risk of death. See these clusters represented graphically in the k-means folder of GitHub [19].