An improved survivability prognosis of breast cancer by using sampling and feature selection technique to solve imbalanced patient classification data
- Kung-Jeng Wang†^{1}Email author,
- Bunjira Makond†^{1, 2} and
- Kung-Min Wang^{3}
https://doi.org/10.1186/1472-6947-13-124
© Wang et al.; licensee BioMed Central Ltd. 2013
Received: 1 June 2013
Accepted: 28 October 2013
Published: 9 November 2013
Abstract
Background
Breast cancer is one of the most critical cancers and is a major cause of cancer death among women. It is essential to know the survivability of the patients in order to ease the decision making process regarding medical treatment and financial preparation. Recently, the breast cancer data sets have been imbalanced (i.e., the number of survival patients outnumbers the number of non-survival patients) whereas the standard classifiers are not applicable for the imbalanced data sets. The methods to improve survivability prognosis of breast cancer need for study.
Methods
Two well-known five-year prognosis models/classifiers [i.e., logistic regression (LR) and decision tree (DT)] are constructed by combining synthetic minority over-sampling technique (SMOTE) ,cost-sensitive classifier technique (CSC), under-sampling, bagging, and boosting. The feature selection method is used to select relevant variables, while the pruning technique is applied to obtain low information-burden models. These methods are applied on data obtained from the Surveillance, Epidemiology, and End Results database. The improvements of survivability prognosis of breast cancer are investigated based on the experimental results.
Results
Experimental results confirm that the DT and LR models combined with SMOTE, CSC, and under-sampling generate higher predictive performance consecutively than the original ones. Most of the time, DT and LR models combined with SMOTE and CSC use less informative burden/features when a feature selection method and a pruning technique are applied.
Conclusions
LR is found to have better statistical power than DT in predicting five-year survivability. CSC is superior to SMOTE, under-sampling, bagging, and boosting to improve the prognostic performance of DT and LR.
Keywords
Breast cancer Decision tree Logistic regression Imbalanced data Synthetic minority over-sampling Cost-sensitive classifier techniqueBackground
The need to monitor the survivability of breast cancer patients is threefold. First, breast cancer is one of the most critical cancers [1] and is a major cause of cancer death among women. DeSantis et al. [2] reported that in 2011, around 230,480 American women were diagnosed with invasive breast cancer and 39,520 breast cancer patients died. Second, the survivability of breast cancer patients has a significant impact on healthcare expenses and planning for both the government and private sectors. Third, the survivability of most common cancers (e.g., breast, prostate, lung, and colorectal) has changed over time, increasing continuously over the long term [3] because of the recent advances in cancer diagnosis and treatments, which reduce mortalities and increase survival time. Although many previous studies have been conducted, constant monitoring is still necessary. Thus, the survivability of breast cancer patients without bias is a critical task for the healthcare system.
Recently, artificial-intelligence-based data-mining techniques have been comprehensively used to predict the survivability of breast cancer patients. Lundin et al. [4] used the artificial neural network (ANN) to predict breast cancer survival in Turku, Finland, from 1945 to 1984. Soria et al. [5] compared three classifiers-naive Bayes algorithm, C4.5 DT, and multilayer perceptron function-to evaluate the most suitable technique for predicting the survivability of breast cancer patients from the Nottingham Tenovus Primary Breast Carcinoma Series. Khan et al. [6] used fuzzy DTs to predict breast cancer survivability. Chang and Liou [7] investigated the application of ANN, DT, logistic regression (LR), and genetic algorithm in the prognosis models of breast cancer acquired from patients at the University of Wisconsin.
Breast cancer survival prognosis researches using SEER data
Sources | Class distribution | Classifier methods | Accuracy performances |
---|---|---|---|
Delen et al. [8] | Survival: 46% | C5 DT | 93.62% |
Non-survival: 54% | ANN | 91.21% | |
LR | 89.20% | ||
Bellaachia and Guven [9] | Survival: 76.80% | C4.5 DT | 86.70% |
Non-survival: 23.20% | ANN | 86.50% | |
Naïve BN | 84.50% | ||
Endo et al. [10] | Survival: 81.50% | LR | 85.80% |
Non-survival: 18.50% | J48 DT | 85.60% | |
DT (with naïve Bayes) | 84.20% | ||
ANN | 84.50% | ||
Naïve BN | 83.90% | ||
BN | 83.90% | ||
ID3 DT | 82.30% | ||
Liu et al. [11] | Survival: 86.52% | C5 DT | 88.05% (AUC = 0.607) |
Non-survival: 13.48% | Under-sampling + C5 DT | 74.22% (AUC = 0.748) | |
Bagging algorithm + C5 DT | 76.59% (AUC = 0.768) |
The studies using SEER data reveal two interesting points. First, the results proposed by previous studies that used DTs and LR to predict five-year survivability for breast cancer patients are controversial. Delen et al. [8] concluded that DT is more accurate than LR for breast cancer survivability, whereas Endo et al. [10] stated that the performance of LR is better than DT. Second, data mining methods were applied to a balanced data set in Delen et al. [8], whereas other studies, except Liu et al. [11], did not deal with imbalanced data which affected the performance of those methods. Owing to the conflicting results for predicting breast cancer survivability using LR and DT, and the imbalanced data situation, further investigation is required.
Several researchers argued that the imbalanced data problem will harm the performance of standard data mining methods [12–17]. Although researchers have devoted efforts to study imbalanced data sets, the subject remains unsolved: the number of survival and non-survival patients is obviously unequal, such as in the studies of Bellaachai and Guven [9], Endo et al. [10], and Khan et al. [6]. Liu et al. [11] employed the under-sampling technique and bagging algorithm to deal with imbalanced data and showed that the predictive performance is improved. However, under-sampling could lose information of the majority class, thereby reducing the predictive performance [18, 19].
In recent years, a number of approaches are available to deal with imbalanced data problem. Re-sampling approaches which can be categorized into three groups: under-sampling method, over-sampling method, and hybrids method are useful approaches to balance the data set. Moreover, they are independent of the underlying classifier [20]. Random under-sampling and over-sampling are the simplest pre-processing approaches. Several empirical studies proved that random under-sampling is better than random over-sampling [21]. Synthetic minority over-sampling technique (SMOTE) proposed by Chawla et al. [22], is a well-known over-sampling method employed in data pre-processing, for example, by Zhao et al. [23], Pelayo and Dick [24], Kamei et al. [25], and Gu et al. [14]. Cost-sensitive learning (CSL) is a learning approach in data mining that considers the misclassification costs. The CSL minimizes the misclassification costs. Mostly, standard classification methods implicitly assume that all misclassification errors cost equally but it is not true in many applications. For example, in the medical problem, the classification of the presence of cancer in patients as the absence is more serious than the opposite misclassification because cancer patients will not be able to undergo appropriate treatments and will likely die [26]. Furthermore, bagging and boosting are ensemble learning methods and often adopt to the imbalanced data set problem. They improve the performance of single classifier by building several classifiers from the training data set and aggregating their predictions when unknown instances exist [20].
The present study predicts the five-year survivability of breast cancer patients by conducting a comparative study of DT and LR models. These models are constructed by combining SMOTE, cost-sensitive classifier technique (CSC), under-sampling, bagging, and boosting. Feature selection method is used to select relevant variables, and pruning technique is applied to obtain low information-burden models. Analysis of variance is used to detect the differences of these models and Tukey’s HSD test specifies which models are distinctive.
Methods
Data and pre-processing
This study uses data from the SEER_1973_2007_TEXTDATA [27] stored in four sub-directories, each of which consists of nine ASCII text files. The original data set has 973,125 records and 118 variables. The data of patients diagnosed from 1988 to 2002 are used to predict the five-year survivability for breast cancer patients because the follow-up cut-off date for this SEER data is December 31, 2007, and several variables (i.e., “Extent of Disease” and “AJCC stage of cancer” which are important to survivability prognosis modeling, as stated by Delen et al. [8]; Bellaachia & Guven [9], Khan et al. [6], and Liu et al. [11]) have only been recorded since 1988. Agrawal et al. [28] also selects the same period of data from the SEER database for lung cancer study.
Data pre-processing is crucial for data mining. It follows four principles: data cleaning, data integration, data transformation, and data reduction. The data are needed to resolve incompleteness and they undergo cleaning before application. In the current study, the following records are removed: (i) outliers, which are unusual data values that can seriously affect the models produced; for instance, the values of "Tumor size" greater than 200 mm are unusual because of obviously misrecorded data (also refer to Han & Kamber [29]); (ii) males, because this study focuses on breast cancer in females; and (iii) the instances that did not survive five years from the diagnosis date and have a recorded cause of death other than breast cancer. The remaining instances are indicated as survival if they survived five years after the diagnosis date; otherwise they are indicated as non-survival.
Cancer survivability class distribution
Class | Number of records | Percentage |
---|---|---|
Survival (denote as 0) | 195,172 | 90.68% |
Non-survival (denote as 1) | 20,049 | 9.32% |
Total | 215,221 | 100% |
Feature selection
Resulting predictor variables selected in this study
Categorical variables | Number of distinct values | ||||
---|---|---|---|---|---|
Variable ID in the study | Label | ||||
re_v4 | Race | 27 | |||
re_v20 | Grade | 4 | |||
re_v24 | Extension of disease | 32 | |||
re_sss | Site-specific surgery code | 9 | |||
re_v26 | Lymph node involvement | 9 | |||
re_v102 | Stage of cancer | 4 | |||
re_v104 | SEER modified AJCC stage 3rd | 9 | |||
Numerical variables | Mean | S.D. | Min. | Max. | |
v23 | Tumor size | 20.70 | 16.24 | 0 | 200 |
v27 | Number of positive nodes | 1.44 | 3.69 | 0 | 79 |
Synthetic minority over-sampling technique
SMOTE operates in feature space rather than data space. Using this approach, the number of instances for the minority class in the original data set is increased by creating new synthetic instances, which results in broader decision regions for the minority class as compared to over-sampling with replacement. Consequently, the over-fitting problem in the learning algorithm can be avoided [14, 15, 22]. The new synthetic samples are created depending on the amount of over-sampling required (%) and the number of nearest neighbors (k). The procedures to create new synthetic instances for continuous features and nominal features are different.
The new synthetic samples for continuous features are generated through the following steps [12]:
Step 1: For each instance in the minority class, compute the distance between a feature vector of the instance and one of its k nearest neighbors.
Step 2: Multiply the distance obtained in Step 1 by a random number between 0 and 1.
where x _{ new } represents a new synthetic sample, x is denoted by a feature vector of each instance in the minority class, x _{ i } is the ith selected nearest neighbor of x, and δ is a random number between 0 and 1. For example, given β% = 300% and k = 5, we have to generate three new synthetic instances for an original instance. The aforementioned three steps are repeated three times. Each time a new synthetic instance is created, one of the five nearest neighbors of x is randomly chosen.
For nominal features, synthetic instance generation is carried out through the following steps [12]:
Step 1: Obtain the majority vote between the features under consideration and its k nearest neighbors for the nominal feature value. In the case of a tie, choose at random.
Step 2: Assign the obtained value to the new synthetic minority class sample. For example, a set of features of a sample is {a, b, c, d, e} and the two nearest neighbors have the sets of features are {a, f, c, g, n} and {h, b, c, d, n}. Thus, the new synthetic sample has a set of the features, which is {a, b, c, d, n} [33].
Cost-sensitive learning
CSL is an algorithm used to deal with the imbalanced data problem by considering misclassification costs. It can be categorized into two methods: direct and meta-learning [26]. The present study focuses on the wrapper method that converts any cost-insensitive algorithm into a cost-sensitive one without actually modifying the algorithm. The costs are not limited to finance, but also to time loss, the severity of an illness, and so on. The purpose of the learning is to build a model with minimum misclassification total costs.
Cost matrix
Predicted class | |||
---|---|---|---|
Positive | Negative | ||
Actual class | Positive | C(1,1), or TP | C(1,0), or FN |
Negative | C(0,1), or FP | C(0,0), or TN |
where P(j|x) is the probability estimation of classifying an instance into class j.
We use CSC [34], a meta-learning method, because it is superior to MetaCost as shown in [35]. In addition, Afzal et al. [17] stated that MetaCost results in a large pre-processing time. CSC has two implementations [36]. The first is reweighting of training instances according to the total cost assigned to each class in the cost matrix, and the second is predicting the class with the minimum expected misclassification cost by using the values in the cost matrix [37]. The former is implemented for this study.
Logistic regression
Logistic regression [38] is a statistical method used to describe the relation between predictor variables denoted by x ^{'} = (x _{1}, x _{2}, …, x _{ p }) and a response variable, which is a categorical variable with two values (here, “survival” or “non-survival”).
where 0 ≤ π(x) ≤ 1
To find the maximum likelihood estimators, L(β) is differentiated with respect to each parameter, and then the resulting terms are set as equal to zero. Other methods such as Newton's method can be utilized.
The odds ratio (OR) is widely used to interpret the model. It associates with one unit change in x _{ j } represented with $\phantom{\rule{0.25em}{0ex}}{e}^{\left({\beta}_{j}\right)}$.
where β _{ mle } is the maximum likelihood estimator of β, V is the diagonal matrix of the maximum likelihood estimators of success probabilities, I is the identity matrix, and k is the ridge constant.
Decision tree
This study also adopts the J48 DT algorithm to predict the survivability of breast cancer patients. J48 is a release of C4.5, which has high accuracy, comprehensibility, and stability. In addition, C4.5, which was developed from the ID3 algorithm, deals with problems of missing data, continuous data, pruning rules, and splitting criterion [40]. Throughout the current paper, we use the DT notation instead of J48 DT.
Model evaluation
To evaluate the performance of the proposed prognosis models, a full data set is divided into two sets: training and testing sets. In this study, a 10-fold cross-validation is employed so that the bias caused by random sampling for training and testing sets can be reduced [34]. In this way, a full data set is divided into 10 independent folds (subsets); each fold is approximately one-tenth of the full data set (with approximately one-tenth of survival and one-tenth of non-survival). Nine of the ten subsets are combined and used as the training set, and the remaining subset is used as the testing set. Each of the 10 subsets is used once as the testing set to evaluate the performance of the model, which is built from the combination of the other remaining subsets.
The sensitivity, specificity, accuracy, area under the receiver operating characteristic curve (AUC), and g-mean are used to evaluate the prognosis performance of the models.
Confusion matrix
Predicted class | |||
---|---|---|---|
Non-survival | Survival | ||
Actual class | Non-survival | TP | FN |
Survival | FP | TN |
Experiment framework
SMOTE is implemented to the training data set to increase the number of instances in the minority class by creating new synthetic instances. The number of new synthetic instances increases depending on the amount of over-sampling required. For this study, the amount of over-sampling is set at 900% because the numbers of instances in majority and minority classes will be approximately balanced. Moreover, because of the wide use of five nearest neighbors in various studies, we use five nearest neighbors in this study as well.
CSC is implemented to the training data set so that each training instance is reweighted according to the costs assigned to each class. We identify the misclassification cost of a model by following Lopez et al. [42]; that is, the cost of misclassifying a non-survival patient as survival equals the imbalance ratio, which is the ratio of the number of instances of the majority class and the minority class. Therefore, the cost of misclassifying a non-survival patient as a survival patient is 10 [i.e., C(1,0) = 10], whereas the cost of misclassifying a survival patient as a non-survival patient is 1 [C(0,1) = 1]. The cost of correct classification in each class is 0 [C(1,1) = C(0,0) = 0].
Under-sampling, bagging, and boosting are also used for comparison. Under-sampling is implemented to the training data set to balance class distribution through the random elimination of majority class instances. In this experiment, we define the class distribution is uniform distribution. Bagging and boosting are ensemble methods. Bagging sample subsets from the training set to form different classifiers and aggregate their predictions to make final prediction. Boosting uses all data set to train each classifier serially. After each round, it gives more focus to difficult instances and assigns the weight to each individual classifier depending on its overall accuracy. Finally, each classifier gives a weight vote to the new instance and the class label is selected by majority. The implementation of both bagging and boosting follows the default setting. AdaboostM1 is used for boosting method. These methods are implemented on Weka.
All studied models in form of acronyms along with the descriptions
Acronym | Description |
---|---|
DT_9 | Decision tree algorithm with 9 predictor variables |
LR_9 | Logistic regression algorithm with 9 predictor variables |
S_DT_9 | Decision tree algorithm with 9 predictor variables, pre-processed by using the SMOTE |
S_LR_9 | Logistic regression algorithm with 9 predictor variables, pre-processed by using the SMOTE |
S_DT_10 | Decision tree algorithm with 10 predictor variables proposed by Endo et al. [10], pre-processed by using the SMOTE |
S_LR_10 | Logistic regression algorithm with 10 predictor variables proposed by Endo et al. [10], pre-processed by using the SMOTE |
S_DT_16 | Decision tree algorithm with 16 predictor variables proposed by Delen et al. [8], pre-processed by using the SMOTE |
S_LR_16 | Logistic regression algorithm with 16 predictor variables proposed by Delen et al. [8], pre-processed by using the SMOTE |
S_DT_20 | Decision tree algorithm with 20 predictor variables, pre-processed by using the SMOTE |
S_LR_20 | Logistic regression algorithm with 20 predictor variables, pre-processed by using the SMOTE |
S_pDT | Pruning decision tree algorithm pre-processed by using the SMOTE |
S_rLR | Logistic regression algorithm pre-processed by using the SMOTE (This model is constructed by the same predictor variables as in S_pDT) |
C_DT_9 | Decision tree algorithm with 9 predictor variables, wrapped with CSC |
C_LR_9 | Logistic regression algorithm with 9 predictor variables, wrapped with CSC |
C_DT_10 | Decision tree algorithm with 10 predictor variables proposed by Endo et al. [10], wrapped with CSC |
C_LR_10 | Logistic regression algorithm with 10 predictor variables proposed by Endo et al. [10], wrapped with CSC |
C_DT_16 | Decision tree algorithm with 16 predictor variables proposed by Delen et al. [8], wrapped with CSC |
C_LR_16 | Logistic regression algorithm with 16 predictor variables proposed by Delen et al. [8], wrapped with CSC |
C_DT_20 | Decision tree algorithm with 20 predictor variables, wrapped with CSC |
C_LR_20 | Logistic regression algorithm with 20 predictor variables, wrapped with CSC |
C_pDT | Pruning decision tree algorithm wrapped with CSC |
C_rLR | Logistic regression algorithm wrapped with CSC (This model is constructed by the same predictor variables as in C_pDT) |
U_DT_9 | Decision tree algorithm with 9 predictor variables, pre-processed by using the under-sampling approach |
U_LR_9 | Logistic regression algorithm with 9 predictor variables, pre-processed by using the under-sampling approach |
U_DT_10 | Decision tree algorithm with 10 predictor variables proposed by Endo et al. [10], pre-processed by using the under-sampling approach |
U_LR_10 | Logistic regression algorithm with 10 predictor variables proposed by Endo et al. [10], pre-processed by using the under-sampling approach |
U_DT_16 | Decision tree algorithm with 16 predictor variables proposed by Delen et al. [8], pre-processed by using the under-sampling approach |
U_LR_16 | Logistic regression algorithm with 16 predictor variables proposed by Delen et al. [8], pre-processed by using the under-sampling approach |
U_DT_20 | Decision tree algorithm with 20 predictor variables, pre-processed by using the under-sampling approach |
U_LR_20 | Logistic regression algorithm with 20 predictor variables, pre-processed by using the under-sampling approach |
U_pDT | Pruning decision tree algorithm pre-processed by using the under-sampling approach |
U_rLR | Logistic regression algorithm pre-processed by using the under-sampling approach (This model is constructed by the same predictor variables as in U_pDT) |
Ba_DT_9 | Decision tree algorithm with 9 predictor variables, combined with bagging |
Ba_LR_9 | Logistic regression algorithm with 9 predictor variables, combined with bagging |
Ba_DT_10 | Decision tree algorithm with 10 predictor variables proposed by Endo et al. [10], combined with bagging |
Ba_LR_10 | Logistic regression algorithm with 10 predictor variables proposed by Endo et al. [10], combined with bagging |
Ba_DT_16 | Decision tree algorithm with 16 predictor variables proposed by Delen et al. [8], combined with bagging |
Ba_LR_16 | Logistic regression algorithm with 16 predictor variables proposed by Delen et al. [8], combined with bagging |
Ba_DT_20 | Decision tree algorithm with 20 predictor variables, combined with bagging |
Ba_LR_20 | Logistic regression algorithm with 20 predictor variables, combined with bagging |
Ba_pDT | Pruning decision tree algorithm combined with bagging |
Ba _rLR | Logistic regression algorithm combined with bagging (This model is constructed by the same predictor variables as in Ba_pDT) |
Ad_DT_9 | Decision tree algorithm with 9 predictor variables, combined with AdaboostM1 |
Ad_LR_9 | Logistic regression algorithm with 9 predictor variables, combined with AdaboostM1 |
Ad_DT_10 | Decision tree algorithm with 10 predictor variables proposed by Endo et al. [10], combined with AdaboostM1 |
Ad_LR_10 | Logistic regression algorithm with 10 predictor variables proposed by Endo et al. [10], combined with AdaboostM1 |
Ad_DT_16 | Decision tree algorithm with 16 predictor variables proposed by Delen et al. [8], combined with AdaboostM1 |
Ad_LR_16 | Logistic regression algorithm with 16 predictor variables proposed by Delen et al. [8], combined with AdaboostM1 |
Ad_DT_20 | Decision tree algorithm with 20 predictor variables, combined with AdaboostM1 |
Ad_LR_20 | Logistic regression algorithm with 20 predictor variables, combined with AdaboostM1 |
Ad_pDT | Pruning decision tree algorithm combined with AdaboostM1 |
Ad_rLR | Logistic regression algorithm combined with AdaboostM1 (This model is constructed by the same predictor variables as in Ad_pDT) |
Statistical analysis is utilized to find the differences in predictive performance among the models. The differences in the performances of the models are detected by using ANOVA test, in which the model is treated as a factor. Multiple comparison tests are also conducted using Tukey’s HSD test to identify the distinctive models. The significant level for the entire differences test is defined at 0.05.
Results
Efficiency of all techniques
The comparative results of models using all techniques and standard data mining models
Model | Accuracy | Sensitivity | Specificity | g-mean | AUC |
---|---|---|---|---|---|
DT_9 | 0.912 | 0.140 | 0.991 | 0.374 | 0.772 |
LR_9 | 0.913 | 0.156 | 0.990 | 0.394 | 0.829 |
S_DT_9 | 0.791 | 0.475 | 0.823 | 0.626 | 0.700 |
S_LR_9 | 0.759 | 0.645 | 0.771 | 0.705 | 0.783 |
C_DT_9 | 0.772 | 0.669 | 0.792 | 0.727 | 0.758 |
C_LR_9 | 0.752 | 0.752 | 0.752 | 0.752 | 0.829 |
U_DT_9 | 0.748 | 0.748 | 0.749 | 0.748 | 0.798 |
U_LR_9 | 0.749 | 0.732 | 0.767 | 0.749 | 0.825 |
Ba_DT_9 | 0.911 | 0.151 | 0.990 | 0.386 | 0.797 |
Ba_LR_9 | 0.913 | 0.157 | 0.990 | 0.394 | 0.829 |
Ad_DT_9 | 0.902 | 0.197 | 0.974 | 0.438 | 0.752 |
Ad_LR_9 | 0.913 | 0.157 | 0.990 | 0.394 | 0.787 |
ANOVA for average g-mean
Sources of variance | Sum of squares | d.f. | Mean square | F | p-value |
---|---|---|---|---|---|
Between Groups | 3.239 | 11 | 0.294 | 4335.466 | 0.000 |
Within Groups | 0.007 | 108 | 0.000 | ||
Total | 3.246 | 119 |
Tukey’s HSD test for g-mean
Model | Different subset | ||||||
---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 6 | 7 | |
DT_9 | 0.374 | ||||||
Ba_DT_9 | 0.386 | 0.386 | |||||
LR_9 | 0.394 | ||||||
Ba_LR_9 | 0.394 | ||||||
Ad_LR_9 | 0.394 | ||||||
Ad_DT_9 | 0.438 | ||||||
S_DT_9 | 0.626 | ||||||
S_LR_9 | 0.705 | ||||||
C_DT_9 | 0.727 | ||||||
U_DT_9 | 0.748 | ||||||
U_LR_9 | 0.749 | ||||||
C_LR_9 | 0.752 |
In Table 9, the results present that SMOTE, CSC, and under-sampling can significantly improve the predictive performance of both DT and LR; AdaboostM1 can only improve the predictive performance of DT; and bagging can improve the predictive performance of neither DT model nor LR model. However, the results show that LR outperforms DT in terms of g-mean value for all cases with and without the use of SMOTE, CSC, under-sampling, bagging and AdaboostM1. The C_LR_9 model has the highest g-mean.
Efficiency of feature selection
The comparative results of models with feature selection using all techniques
Model | Accuracy | Sensitivity | Specificity | g-mean | AUC |
---|---|---|---|---|---|
S_DT_9 | 0.791 | 0.475 | 0.823 | 0.626 | 0.700 |
S_LR_9 | 0.759 | 0.645 | 0.771 | 0.705 | 0.783 |
S_DT_10 | 0.835 | 0.363 | 0.884 | 0.566 | 0.726 |
S_LR_10 | 0.772 | 0.492 | 0.800 | 0.627 | 0.720 |
S_DT_16 | 0.869 | 0.310 | 0.926 | 0.536 | 0.731 |
S_LR_16 | 0.796 | 0.471 | 0.830 | 0.623 | 0.727 |
S_DT_20 | 0.871 | 0.311 | 0.929 | 0.537 | 0.733 |
S_LR_20 | 0.791 | 0.476 | 0.824 | 0.626 | 0.726 |
C_DT_9 | 0.772 | 0.669 | 0.792 | 0.727 | 0.758 |
C_LR_9 | 0.752 | 0.752 | 0.752 | 0.752 | 0.829 |
C_DT_10 | 0.723 | 0.734 | 0.722 | 0.728 | 0.774 |
C_LR_10 | 0.723 | 0.766 | 0.719 | 0.742 | 0.818 |
C_DT_16 | 0.804 | 0.557 | 0.829 | 0.679 | 0.673 |
C_LR_16 | 0.662 | 0.810 | 0.647 | 0.724 | 0.814 |
C_DT_20 | 0.805 | 0.552 | 0.831 | 0.677 | 0.672 |
C_LR_20 | 0.591 | 0.824 | 0.567 | 0.684 | 0.787 |
U_DT_9 | 0.748 | 0.748 | 0.749 | 0.748 | 0.798 |
U_LR_9 | 0.749 | 0.732 | 0.767 | 0.749 | 0.825 |
U_DT_10 | 0.744 | 0.767 | 0.720 | 0.743 | 0.795 |
U_LR_10 | 0.743 | 0.762 | 0.724 | 0.743 | 0.817 |
U_DT_16 | 0.746 | 0.745 | 0.748 | 0.746 | 0.786 |
U_LR_16 | 0.749 | 0.727 | 0.771 | 0.749 | 0.826 |
U_DT_20 | 0.746 | 0.744 | 0.748 | 0.746 | 0.785 |
U_LR_20 | 0.753 | 0.743 | 0.764 | 0.753 | 0.829 |
Ba_DT_9 | 0.911 | 0.151 | 0.990 | 0.386 | 0.797 |
Ba_LR_9 | 0.913 | 0.157 | 0.990 | 0.394 | 0.829 |
Ba_DT_10 | 0.911 | 0.117 | 0.992 | 0.341 | 0.784 |
Ba_LR_10 | 0.911 | 0.126 | 0.991 | 0.354 | 0.818 |
Ba_DT_16 | 0.912 | 0.186 | 0.987 | 0.429 | 0.801 |
Ba_LR_16 | 0.913 | 0.177 | 0.989 | 0.418 | 0.829 |
Ba_DT_20 | 0.912 | 0.189 | 0.987 | 0.432 | 0.801 |
Ba_LR_20 | 0.914 | 0.187 | 0.989 | 0.430 | 0.835 |
Ad_DT_9 | 0.902 | 0.197 | 0.974 | 0.438 | 0.752 |
Ad_LR_9 | 0.913 | 0.157 | 0.990 | 0.394 | 0.787 |
Ad_DT_10 | 0.905 | 0.146 | 0.983 | 0.379 | 0.773 |
Ad_LR_10 | 0.911 | 0.112 | 0.993 | 0.334 | 0.783 |
Ad_DT_16 | 0.890 | 0.247 | 0.956 | 0.486 | 0.749 |
Ad_LR_16 | 0.914 | 0.177 | 0.989 | 0.418 | 0.779 |
Ad_DT_20 | 0.891 | 0.247 | 0.958 | 0.487 | 0.748 |
Ad_LR_20 | 0.914 | 0.180 | 0.990 | 0.422 | 0.794 |
ANOVA for average g-mean of models using feature selection
Sources of variance | Sum of squares | d.f. | Mean square | F | p-value |
---|---|---|---|---|---|
Between Groups | 8.994 | 39 | 0.231 | 2266.112 | 0.000 |
Within Groups | 0.037 | 360 | 0.000 | ||
Total | 9.031 | 399 |
Tukey’s HSD test for g-mean of models using feature selection
Model | Different subset | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | |
Ad_LR_10 | 0.334 | |||||||||||||
Ba_DT_10 | 0.341 | 0.341 | ||||||||||||
Ba_LR_10 | 0.354 | |||||||||||||
Ad_DT_10 | 0.379 | |||||||||||||
Ba_DT_9 | 0.386 | |||||||||||||
Ba_LR_9 | 0.394 | |||||||||||||
Ad_LR_9 | 0.394 | |||||||||||||
Ad_LR_16 | 0.418 | |||||||||||||
Ba_LR_16 | 0.418 | |||||||||||||
Ad_LR_20 | 0.422 | 0.422 | ||||||||||||
Ba_DT_16 | 0.429 | 0.429 | ||||||||||||
Ba_LR_20 | 0.430 | 0.430 | ||||||||||||
Ba_DT_20 | 0.432 | 0.432 | ||||||||||||
Ad_DT_9 | 0.438 | |||||||||||||
Ad_DT_16 | 0.486 | |||||||||||||
Ad_DT_20 | 0.487 | |||||||||||||
S_DT_20 | 0.537 | |||||||||||||
S_DT_16 | 0.536 | |||||||||||||
S_DT_10 | 0.566 | |||||||||||||
S_LR_16 | 0.623 | |||||||||||||
S_DT_9 | 0.626 | |||||||||||||
S_LR_20 | 0.626 | |||||||||||||
S_LR_10 | 0.627 | |||||||||||||
C_DT_20 | 0.677 | |||||||||||||
C_DT_16 | 0.679 | |||||||||||||
C_LR_20 | 0.684 | |||||||||||||
S_LR_9 | 0.705 | |||||||||||||
C_LR_16 | 0.724 | |||||||||||||
C_DT_9 | 0.727 | 0.727 | ||||||||||||
C_DT_10 | 0.728 | 0.728 | ||||||||||||
C_LR_10 | 0.742 | 0.742 | ||||||||||||
U_LR_10 | 0.743 | 0.743 | ||||||||||||
U_DT_10 | 0.743 | 0.743 | ||||||||||||
U_DT_16 | 0.746 | |||||||||||||
U_DT_20 | 0.746 | |||||||||||||
U_DT_9 | 0.748 | |||||||||||||
U_LR_9 | 0.749 | |||||||||||||
U_LR_16 | 0.749 | |||||||||||||
C_LR_9 | 0.752 | |||||||||||||
U_LR_20 | 0.753 |
The correlation-based feature subset selection method can reduce the information burden (i.e., the number of predictor variables), but still retain the quality of classification. This occurrence is in accordance with the study of Hall and Smith [30], which states that using a larger number of predictor variables cannot increase the performance of models for machine learning if these variables are correlated with one another.
Feature pruning effect
The comparative results of models using feature pruning
Model | Accuracy | Sensitivity | Specificity | g-mean | AUC |
---|---|---|---|---|---|
S_DT_9 | 0.791 | 0.475 | 0.823 | 0.626 | 0.700 |
S_LR_9 | 0.759 | 0.645 | 0.771 | 0.705 | 0.783 |
S_pDT | 0.728 | 0.703 | 0.731 | 0.717 | 0.770 |
S_rLR | 0.747 | 0.717 | 0.750 | 0.734 | 0.811 |
C_DT_9 | 0.772 | 0.669 | 0.792 | 0.727 | 0.758 |
C_LR_9 | 0.752 | 0.752 | 0.752 | 0.752 | 0.829 |
C_pDT | 0.740 | 0.748 | 0.740 | 0.744 | 0.795 |
C_rLR | 0.770 | 0.719 | 0.776 | 0.747 | 0.824 |
U_DT_9 | 0.748 | 0.748 | 0.749 | 0.748 | 0.798 |
U_LR_9 | 0.749 | 0.732 | 0.767 | 0.749 | 0.825 |
U_pDT | 0.740 | 0.749 | 0.731 | 0.740 | 0.791 |
U_rLR | 0.745 | 0.703 | 0.787 | 0.743 | 0.823 |
Ba_DT_9 | 0.911 | 0.151 | 0.990 | 0.386 | 0.797 |
Ba_LR_9 | 0.913 | 0.157 | 0.990 | 0.394 | 0.829 |
Ba_pDT | 0.911 | 0.107 | 0.994 | 0.324 | 0.724 |
Ba_rLR | 0.912 | 0.142 | 0.991 | 0.377 | 0.823 |
Ad_DT_9 | 0.902 | 0.197 | 0.974 | 0.438 | 0.752 |
Ad_LR_9 | 0.913 | 0.157 | 0.990 | 0.394 | 0.787 |
Ad_pDT | 0.911 | 0.161 | 0.988 | 0.397 | 0.822 |
Ad_rLR | 0.910 | 0.130 | 0.990 | 0.359 | 0.745 |
ANOVA for average g-mean value of models using feature pruning
Sources of variance | Sum of squares | d.f. | Mean square | F | p-value |
---|---|---|---|---|---|
Between Groups | 5.896 | 19 | 0.310 | 2062 | 0.000 |
Within Groups | 0.027 | 180 | 0.000 | ||
Total | 5.923 | 199 |
Tukey’s HSD test for g-mean of models using feature pruning
Model | Different subset | ||||||||
---|---|---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |
Ba_pDT | 0.324 | ||||||||
Ad_rLR | 0.359 | ||||||||
Ba_rLR | 0.377 | 0.377 | |||||||
Ba_DT_9 | 0.386 | ||||||||
Ba_LR_9 | 0.394 | ||||||||
Ad_LR_9 | 0.394 | ||||||||
Ad_pDT | 0.397 | ||||||||
Ad_DT_9 | 0.438 | ||||||||
S_DT_9 | 0.626 | ||||||||
S_LR_9 | 0.705 | ||||||||
S_pDT | 0.717 | 0.717 | |||||||
C_DT_9 | 0.727 | 0.727 | |||||||
S_rLR | 0.734 | 0.734 | 0.734 | ||||||
U_pDT | 0.740 | 0.740 | |||||||
U_rLR | 0.743 | 0.743 | |||||||
C_pDT | 0.744 | 0.744 | |||||||
C_rLR | 0.747 | ||||||||
U_DT_9 | 0.748 | ||||||||
U_LR_9 | 0.749 | ||||||||
C_LR_9 | 0.752 |
Some interesting points are observed between C_rLR and C_LR_9. First, C_rLR models need lesser information than C_LR_9 (four variables versus nine variables) on model construction. Second, C_rLR predicts five-year survivability with the lowest total number of misclassified instances (i.e., 49,446 instances) while the number of misclassified instances of C_LR_9 model is 53,340. Third, the C_rLR model has the highest accuracy in predicting the five-year survivability of breast cancer patients correctly.
The improvement of the proposed method
The comparative results (data from the same database and period as used by Delen et al.[8])
Model | Accuracy | Sensitivity | Specificity | g-mean | AUC |
---|---|---|---|---|---|
Proposed method (C_rLR) | 0.751 | 0.762 | 0.750 | 0.756 | 0.842 |
Previous method (LR) | 0.903 | 0.272 | 0.985 | 0.517 | 0.849 |
Proposed method (C_pDT) | 0.758 | 0.756 | 0.758 | 0.757 | 0.820 |
Previous method (DT) | 0.903 | 0.279 | 0.984 | 0.524 | 0.769 |
The comparative results (data from the same database and period as used by Endo et al.[10])
Model | Accuracy | Sensitivity | Specificity | g-mean | AUC |
---|---|---|---|---|---|
Proposed method (C_rLR) | 0.723 | 0.748 | 0.719 | 0.733 | 0.814 |
Previous method (LR) | 0.897 | 0.226 | 0.988 | 0.472 | 0.832 |
Proposed method (C_pDT) | 0.747 | 0.756 | 0.746 | 0.752 | 0.812 |
Previous method (DT) | 0.896 | 0.214 | 0.988 | 0.460 | 0.793 |
Discussion
The results demonstrated that CSC technique and sampling techniques (i.e., SMOTE and under-sampling) can significantly improve the performance of five-year prognosis models/classifiers for breast cancer patients (i.e., LR and DT). CSC technique often outperforms sampling techniques, this result is in accordance with the conclusion of McCarthy et al. [43]. While, the results show that AdaboostM1 can only improve the predictive performance of DT, and bagging cannot improve the predictive performance of DT and LR models.
This study proposes the best method to deal with imbalanced data set problem and to improve survivability prediction of breast cancer patients. The best method is the combination of CSC, a feature selection method, and a pruning process. CSC which solves the imbalanced data set problem by considering misclassification costs does not change the original data set. Moreover, feature selection method can improve the predictive performance of models by selecting the predictor variables most related to target variable; in addition, feature selection can solve the problem when there are correlated variables in the data set which harm the performance of the models.
Conclusions
This study has employed more comprehensive and most current data than the previous studies on the prognosis of breast cancer patients. We obtain the following conclusions: (i) the proposed technique to solve imbalanced problem, feature selection and pruning process can significantly improve the performance of two well-known five-year prognosis models/classifiers for breast cancer patients (i.e., LR and DT); (ii) CSC is superior to the other methods in improving the prognosis performance of both DT and LR with an imbalanced data set; (iii) the correlation-based feature subset selection method and the feature pruning process using information entropy can reduce the informative burden (i.e., the number of predictor variables) but still retain the quality of classification; (iv) by considering the results (Tables 9, 12 and 15), the performance of LR models outperform the DT models when these models are solely implemented, and when they employ CSC and SMOTE techniques, feature selection, and/or pruning process; (v) bagging cannot improve the predictive performance of DT model and LR model; while AdaboostM1 can only improve the predictive performance of DT. However, the improvement of DT is lower than of DT wrapped with CSC; (vi) although under-sampling technique can deal with imbalanced data set, it is not as good as CSC in terms of g-mean. Moreover it can discard potentially useful data.
For the low information-burden models, our study shows that the C_LR_9 model has the highest g-mean, but the C_LR_9 and C_rLR models are equally powerful statistically. Interesting phenomena are observed: (i) the performances of C_rLR are similar to the C_LR_9 model, but the earlier need fewer variables; (ii) C_rLR gives the highest accuracy to predict the survivability of patients and has the lowest total number of misclassified instances.
Future research can investigate the embedding of SMOTE and CSC into alternative classifiers, such as advanced population-based algorithms, to improve the prediction performance of five-year survivability of breast cancer patients.
Notes
Declarations
Acknowledgements
The authors gratefully acknowledge the editors, Professor Allan Tucker, and Dr. Ankit Agrawal for their helpful comments. This work is partially supported by the National Science Council, Taiwan, R.O.C.
Authors’ Affiliations
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