A Novel Multi-Neural Ensemble Approach for Cancer Diagnosis

ABSTRACT

Cancer is a complex worldwide health concern that resulted in 10 million cancer deaths in 2018; hence, early cancer detection is crucial. Early detection involves developing more precise technology that offers information about the patient’s cancer, allowing clinicians to make better-informed treatment options. This study provides an in-depth analysis of multiple cancers. This study also exhibits a good survey of the machine or deep learning techniques used in cancer research. Also, the study proposed a stacking-based multi-neural ensemble learning method’s prediction performance on eight datasets, including the benchmark datasets like Wisconsin Breast cancer dataset, mesothelioma, cervical cancer, non-small cell lung cancer survival dataset, and prostate cancer dataset. This study also analyzes the three real-time cancer datasets (Lung, Ovarian & Leukemia) of the Jammu and Kashmir region. The simulation findings indicate that the methodology described in our study attained the highest level of prediction accuracy across all types of cancer data sets. Additionally, the proposed approach has been statistically validated. The purpose of this investigation was to develop and evaluate a prediction model that might be used as a biomarker for malignancy based on anthropometric, clinical, imaging, and gene data.

Introduction

Cancer is a deadly issue responsible for most deaths worldwide that rise with an estimate of 18.1 million new cancer cases each year (Ferlay 2018). The study’s motivation is the alarming rate at which new cancer cases increase (Islami et al. 2018). According to the World Health Organization’s most recent data, 10 million cancer deaths occurred in 2020 alone, and millions of new incidences are recognized each year. Table 1 summarizes the study’s statistical findings on the tumors examined (Bray, Ferlay, and Soerjomataram 2020).

Table 1. Cancer deaths in the world (2018)

CANCER	NEW CASES	DEATHS
Lung	2,093,876	1,761,007
Breast	2,088,849	627000
Prostate	1,276,106	358,989
Cervical	570 000	311 000
Leukemia	437,033	309,006
Ovarian	295,414	184,799
Mesothelioma	30,443	25576

Lung malignant growth is the most widely recognized cancer, i.e., 11.6% of the total cases on the planet. Regardless of advances in chemotherapy, the forecast for malignant lung growth stays poor, with 5-year relative endurance fewer than 14% among men and approximately 18% among females in most countries (Bray, Ferlay, and Soerjomataram 2020). Tobacco use and impacts of cigarette smoking is the chief risk factor for malignant lung growth (Cruz, Tanoue, and Matthay 2011). Breast Cancer is the second most threatening cancer in the world. It has a high incidence and mortality rate (Key, Verkasalo, and Banks 2001). According to the latest cancer statistics mentioned in Table 1, Breast malignancy alone accounts for the majority of cancer deaths worldwide (Ferlay 2018). Ovarian Cancer (OC) is the seventh most generally analyzed malignant growth among ladies on the planet (3% of women died). OC is ordinarily detected at a late stage when the 5-year relative endurance rate is just 29%. Hardly any cases (15%) are determined to have restricted tumors (Stage 1) when the 5-year endurance rate is 92%. Strikingly, the general endurance rate for most cases runs between 30% and 40% over the globe and has seen increments (2%–4%) since 1995 (Allemani et al. 2014; Torre et al. 2018). OC risk factors incorporate natural and way of life factors, for example, asbestos and powder exposures and cigarette smoking (Reid, De Klerk, and Bill Musk 2011).

In 2018, 4.5% of people died of leukemia. As indicated by the review case surveys of leukemia, typical signs and side effects incorporate fever (17% to 77%), dormancy (12% to 39%), and dying (10% to 45%) (B. M. Reid, Permuth, and Sellers 2017). Around 33% of youngsters had musculoskeletal manifestations, especially in the spine and long bones, 75% had an expanded liver or spleen, in roughly 7% of kids at finding (Sinigaglia et al. 2008). Leukemia survivors require sequential complete blood record checking, just as age-and sex-explicit malignancy screening (Shouval et al. 2019). Grown-ups additionally present with protected side effects, for example, fever, tiredness, and weight reduction. They may have experienced shortness of breath, chest irritation, unreasonable wounding, nosebleeds, or abnormal menstrual periods in ladies (Cornell and Palmer 2012).

Early discovery of malignancy guarantees a unique possibility of expanding survivability of malignant growth patients (B. M. Reid, Permuth, and Sellers 2017). Various models dependent on clinical information are proposed in the prior studies and might be employed in emergency clinics or clinical investigation. These automated systems are noteworthy as these add to the more screening instruments (Breiman 2001; Wolpert 1992; Yoav and Schapire 1996). This study plans to assess how models grounded on the anthropometric, clinical, image, and gene information can help forecast various types of cancer (Wei et al. 2022; Coccia 2017; Chen et al. 2021; Korte et al. 2020; Coccia 2016). The learning architecture proposed in the current study depends on the predominance of neural systems and emphasizes the importance of automated learning for further development (Cho and Won 2003; Coccia 2019; Coccia and Bellitto 2018; Kourou et al. 2015a; Tan and Gilbert 2003; Xiao et al. 2018) and ensemble methods (Kavakiotis et al. 2016) in earlier investigations (Adem, Kiliçarslan, and Cömert 2019; Bourlard and Kamp 1988; Hu and Zebo 2019; Kononenko 2001; Lecun, Bengio, and Hinton 2015; Levine et al. 2019; Masters 1993). The study’s purpose is to develop a revolutionary classification algorithm capable of accurately predicting cancer diagnosis. The significant contributions made by the study are as follows:

• The study proposed a firsthand approach to the ensemble (stack) multiple deep learning models with a gradient-boosting technique named stacking-based multi-neural ensemble to classify cancer datasets to predict cancer diagnosis, stage, and survival time.

• This study has focused on the limitations of previous studies, thereby presenting an improved approach.

• Three real-time cancer datasets (Lung, Ovarian & Leukemia) are collected from the Jammu & Kashmir region.

• The proposed model is tested on five benchmark datasets: the Wisconsin Breast cancer dataset, Mesothelioma, Cervical cancer dataset, non-small cell lung cancer (NSCLC) survival dataset, and prostate cancer dataset.

• The performance of the proposed models is compared with previous studies, and the proposed model, i.e., stacking-based multi-neural ensemble, attained better prediction results than all the previous studies.

All the implementation details of the established Prediction Model are accessible on Github to facilitate the model’s reusability by other researchers.

Medical data can now be found in multiple public and private data repositories, thanks to advances in database technology and the Internet. The healthcare industry is anticipated to create terabytes of data each year. Extracting valuable information for excellent healthcare is a difficult and vital task, and we now have many data in our databases to do so. However, the amount of information gleaned from it is minuscule. As a result, effective data organization, analysis, and interpretation are critical if tangible knowledge extraction is accomplished. In order to identify relevant patterns and hidden knowledge from these enormous datasets of medical data, multiple computational techniques are necessary. We often analyze massive and large observational datasets in the data mining process and then extract important hidden patterns for data classification. The automated learning techniques have now begun to experiment with clinical data.

In this study, we have assessed the proposed strategy on eight datasets. Two datasets are extricated from digitized images, three real-time cancer datasets, two electronic health records databases comprising clinical properties, and datasets dependent on gene expressions and clinical information. From a vast collection of literature in malignancy prediction modeling, deep learning approaches have signified their vastness effectively and accomplished incredible outcomes; however, none of the systems is entirely exact. The conclusive results of our study confirm that the proposed stacking-based multi-neural ensemble learning strategy utilizes the cancer patient’s data and produces more precise expectations than single classifiers. The remaining article is grouped into seven sections. Section 2 describes the review of related research studies and prediction models. Section 3 describes the proposed methodology employed in the current study along with the dataset analysis. Section 5 shows the simulation results and their discussion. Finally, the article is concluded in the last section.

Theoretical Framework

Several research works have been done in the field of cancer detection (Coccia 2019; Korbar et al. 2021; Deshmukh and Kashyap 2022; Zhang et al. 2022; Gupta M.; Kumar et al. 2021; Kohli et al. 2021; Kumar 2020; Gupta and Gupta 2021). Many researchers have used automated learning techniques for the prediction of cancer (Gupta and Gupta 2021; Kumar et al. 2020; Kumar and Mahajan 2019; Kumar and Single, 2021). Few such studies are mentioned in this section.

Lung Cancer: In 2017, Lynch (Lynch et al. 2017) led an examination work to anticipate malignant lung growth utilizing unsupervised learning and achieved Root Mean Square Error (RMSE) values (16.193 for k-Means). This study used approximately 10.4k lung cancer records from the Surveillance, Epidemiology, and End Results (SEER) program database. Also, some researchers have assessed the endurance period of lung cancer patients by examining data mining approaches on the lung cancer records from the SEER database, containing collaborative clustering-based techniques (D. Chen et al. 2009), Support Vector Machine (SVM), and Logistic Regression (LR) (Fradkin, Muchnik, and Schneider 2005), and unsupervised methods in 2017 (Lynch et al. 2017). A similar study was proposed in 2017 (Lynch et al. 2017) that examined the supervised classification models to predict lung cancer survival. The classification models employed in the study are Decision Trees (DTs), Gradient Boosting Machines (GBM), SVM & Ensemble model. The best results were achieved using the Ensemble model (RMSE = 15.3). This investigation established the superiority of ensemble learning over single classifiers. Yen-Chen (Y. Chen, Ke, and Chiu 2014) 2014 utilized Artificial Neural Network (ANN), to foresee the survival of Lung cancer patients with risk classification. The gene expression dataset used in the examination was gathered from different research centers. This examination accomplished a precision of 83%.

Breast Cancer: Another study performed in 2017 Kumar, Sai Nikhil, and Sumangali 2017) used the Wisconsin breast cancer dataset and investigated the performance of DTs, K-Nearest Neighbors (KNN), and Neural Networks (NN) for predicting breast cancer. A reexamining study conducted by Xiao in 2018 (Xiao et al. 2018) employed an ensemble classifier to predict breast cancer diagnosis. Xiao compared multiple-ensemble techniques and concluded the superior performance of stacking various classifiers. A research study published in 2019 (Saygili 2019) employed different machine-learning techniques to diagnose breast cancer. The best classification accurateness was attained by Random Forests (RF), followed by the neural technique. Many of the recent research works have employed deep learning strategies (Gupta and Gupta 2021) on big-size breast cancer datasets.

Prostate Cancer: A research article published in 2017 (Liu and Xiaomei 2017) employed deep-learning models to classify prostate cancer to predict cancer diagnosis. The accurateness achieved by the Convolutional Neural Networks (CNN) model is 78% (approx.). In another research work carried in 2019 (Yoo et al. 2019), a novel model based on CNN was applied for prostate cancer diagnosis. The data used in the study consisted of 427 patients, where 175 were cases, and 252 were controls. The recommended model attained an area under the receiver operating characteristic curve (AUC) of 0.87. A computation model based on deep learning was projected in 2020 (Tolkach et al. 2020) to predict prostate cancer. Classification precision of the deep learning architecture reaches 98%. Another research study in 2020 (Gupta and Gupta 2020) proposed an automatic diagnosis of prostate cancer. This study evaluated multiple Classification models like KNN, Naïve Bayes (NB), SVM, DT, and the best performance was achieved by neural learning models. Also, computer simulations demonstrate that the data balancing strategy increased predictive performance from 84% to 93% with balanced data. Recent research (Gupta and Gupta 2021) proposed multiple-balancing techniques for attaining high accurateness. Many of the research studies done to predict the prostate cancer diagnosis has successfully shown the importance of computer-aided diagnosis.

Cervical cancer: Cervical cancer was diagnosed using automated learning methodologies (Wu and Zhou 2017). The technique based on Support Vector Machine (SVM) was used for classification along with Principal Component Analysis (PCA) and Recursive Feature Elimination (RFE) techniques. SVM-PCA, SVM-RFE with different feature sets was proposed in the study, and SVM-PCA displayed the best performances attaining the highest classification score (93%). Another study carried in 2017 (Ceylan and Pekel 2017) proposed multiple-classification models to predict the risk of cervical cancer and compared the Bayesian model, DTs, and RF. RF achieved the highest accurateness, i.e., 82% (approx.). Cervical cancer was diagnosed using the proposed strategy of balancing the data with Smote and used PCA for dimension reduction in 2018(Abdoh, Rizka, and Maghraby 2018). The technique was compared with the feature set selected by the RFE technique. The proposed design achieved 97.4% accuracy. Cervical cancer diagnosis was done using stacked Autoencoders and softmax classification in 2019 (Fernandes, Chicco, and Cardoso 2018) and achieved a top AUC score of 97.25%. Also, recent research by (Gupta and Kumar Gupta, 2021b) investigated the performance of stacking ensemble of different classifiers on cervical cancer dataset.

Leukemia: In 2018, a research study (Mei et al. 2018) applied neural Learning to predict acute myeloid leukemia (AML). The dataset used in the study was taken from TCGA (The Cancer Genome Atlas) database. The implementation used stacked Autoencoders to formulate a categorized DL model. The model implemented in R language attained exceptional correctness of 83% in forecasting prognosis. A review article published in 2019 (Salah et al. 2019) emphasized the utilization of ML models to predict leukemia diagnosis. A total of 58 research studies were revised. A significant factor observed in this study was that none of the articles applied ML models in real‐world scenarios. More than 90% of articles utilized small and homogenous samples. A research study was done in 2019 (Shouval et al. 2019) worked on predicting the survival of leukemia patients after the Autologous Stem Cell Transplantation. A recent research study 2020 (Maria, Devi, and Ravi 2020) employed ML to predict diagnosis. The respective research presented a comparative study of SVM, KNN, Neural Networks, and NB for the classification of leukemia into its subtypes.

Ovarian Cancer: (Miao et al. 2018) used deep CNN for predicting the diagnosis of ovarian cancers. The 10-folder cross-validation validated simulation results. Also, classification accurateness improved from 72.76% to 78.20% by using the strategy proposed in the study. Another study conducted in 2019 (Kawakami et al. 2019) used 334 epithelial ovarian cancer (EOC) cases, out of which 101 cases belonged to the benign group, and the rest belonged to the malignant group. ML models comprising Gradient Boosting Machine (GBM), SVM, RF, NB, and Neural Network were used. The ensemble technique (GBM & RF) presented the top prediction performance of 92.4% AUC. A recent study 2020 (Mingyang et al. 2020) aimed to access the practical value of ML models in OC detection. The data comprised 349 patients with 49 features. The study established notable features. The learner produced a better forecast and outperformed the prevailing OC prediction approaches.

Mesothelioma: Research work (Mukherjee 2018) on the same feature set and attained 99% with SVM. The study made by Ilhan and Celik (Ilhan and Celik 2017) deployed Ensemble Learning with 10-fold Cross-validation and successfully achieved 100% accuracy in classification. Also, recent research (Gupta and Kumar Gupta, 2021a) explores the performance of multiple classifiers on the dataset. The research work (Kaur and Singh 2019) used K-NN and claimed 99.07% accuracy. A retrospective study (Hu and Zebo 2019) trained numerous deep learning algorithms and confirmed stacked sparse auto-encoder (SSAE) as the best model for MM diagnosis. Two feature selection methods, i.e., Genetic Algorithm (GA) and ReliefF methods, were used to select the features. Genetic Algorithms (GA) chose a set of 19 highly significant features and confirmed that GA and Stacked Sparse Autoencoder (SSAE) achieved the highest attainable accuracy (100%). All the above-stated studies claimed high accuracies but, after examination, we observed that an input feature (“diagnosis method”) used in the model duplicated the target diagnosis class, confirmed by (Chicco and Rovelli 2019). This trivial feature makes the model virtually perfect yielding high estimation accuracy. Hence, we don’t advocate their results as it violates the fundamentals and can’t be considered. Recent work done by (Chicco and Rovelli 2019) on the same dataset confirmed that the accuracy stated by (Orhan et al. 2012) was trivial, and Probabilistic Neural Network (PNN) could not perform well, obtaining an accuracy of 0.52. Their study made the first move to address the repetitive feature in the dataset. Also, they handled the imbalance problem of the data by using the under-sampling technique. The highest accuracy was 0.82 and was recorded using Random Forest Classifier on the balanced set. Under-sampling established its effectiveness to upgrade the prediction results, even though it imposes the constraint of omitting a portion of valuable data. Table 2 summarizes the literature review of the cancer research studies.

Table 2. Analysis table

Study	ML Methods	Limitations of the Study
(Ilhan and Celik 2017)	DT, SVM and NN were employed and SVM achieved 100% accurateness	Replicated attribute is used which makes model trivially efficient
(Mukherjee 2018)	SVM & Multilayer Perceptrons (MLPs) were used for classification and SVM achieved 99.8% accuracy	Replicated attribute should be removed and class imbalance is not addresses
(Chicco and Rovelli 2019)	Classifiers used are DT,PNN,MLP,RF and RF achieved 82% accuracy	Enhancement can be done by smearing alternate data balancing techniques
(Wu and Zhou 2017)	SVM was used with RFE and PCA and SVM-PCA performed better	Other classifiers should be compared to establish the worth of particular technique
(Fernandes, Chicco, and Cardoso 2018)	Deep supervised Autoencoder were utilized in the study to achieve AUC score of 0.69	Insignificant prediction results
(Zahras 2018)	Deep Convolutional Neural Networks attained accuracy>90	Classification model evaluation must be done on parameters like AUC, MCC
(Devi et al. 2016)	Artificial Neural Networks achieved accuracy > 90	Highly imbalanced data is used without handling class imbalance
(Nilashi and Ibrahim 2017)	Three methods PCA-Fuzzy, PCA-SVM, and PCA-KNN were used PCA-Fuzzy performed the best with 93% AUC	Unbalanced distribution of instances across the data set’s numerous classes
Kumar, Sai Nikhil, and Sumangali 2017)	An ensemble of SVM-Naive Bayes-J48 was proposed that achieved 97% accuracy	Data balancing should be addressed
(Parthiban 2017)	Particle Swarm Optimization(PSO) – SVM,K-means and fuzzy were compared and PSO-SVM performed best (95% acc)	Robustness of the proposed algorithm should be checked in other benchmark datasets
(Saygili 2019)	ML techniques used were SVM, KNN, NB, J48, RF and MLP, the best acc (98%) was achieved by RF	A broader comparison of classification models should be analyzed
(Wang, Wang, and Chang 2016)	GA, Majority Voting, Extreme Learning Machine was implemented and GA attained highest acc (98.8%)	Development of a meta-heuristic algorithm to optimize the voting center’s selection of gene groupings is necessary
(Piao, Piao, and Ho Ryu 2017)	Techniques used were BaggingC4.5, BoostC4.5, BaggingSVM, BoostSVM and best performance was given by Bagging SVM (97.5 acc)	Proposed model is unsuitable for low-dimensional data
(Lynch et al. 2017)	Learning techniques used are Hierarchical Clustering, K-Means Clustering, and clustering achieved 15.6 RMSE	It is necessary to analyze a bigger variety of quantitative and categorical data.
(Sara, Asadi, and Kattan 2019)	Classifiers used are MLP, KNN, and C4.5 But C4.5 achieved highest AUC (85%)	Predictions showed some inconsistencies across the data sets
(Y. Chen, Ke, and Chiu 2014)	ANN prediction models and chi square techniques are used to obtain Acc = 83.3%	Different cancer subtypes need to be explored in order to improve cancer patients’ prognosis approaches
(Xiao et al. 2018)	Hybrid Model of KNN, SVMs, DTs, RFs is proposed to achieve AUC = 98.8	The research did not evaluate the dataset and did not go into detail about the features employed.
(Liu and Xiaomei 2017)	CNN is used classification and attained Acc = 78%	Insignificant classification accurateness
(Yoo et al. 2019)	Prediction model used is CNN to achieve AUC score of 87%	The dataset used is intrinsically skewed and does not accurately reflect reality
(Tolkach et al. 2020)	Deep learning employed for cancer prediction obtained 98% accuracy	Model should be tested on other datasets also to establish its significance
(Gupta and Gupta 2020)	Prediction models used are KNN, NB, SVM, DT and ANN; best prediction was made on oversampled data by ANN (93%)	Random Oversampling was employed to balance data which may overfit the classifier
(Mei et al. 2018)	Stack Auto encoder was implemented on R to predict the cancer diagnosis with 83% accuracy	moderately small size of cohorts
(Maria, Devi, and Ravi 2020)	SVM, KNN, Neural Networks, and NB were used to make prediction	The study has limited scope for cancer researches other than leukemia
(Miao et al. 2018)	Deep CNN was proposed for classification	The accuracy achieved by the model is not significant enough
(Kawakami et al. 2019)	ML Models like GBM, SVM, RF, NB, and Neural Network are used where ANN did best (92% AUC)	Limited data size

Proposed System

This section holds the flowchart of the cancer prediction procedure, algorithm of the proposed classification model, description of the hyperparameters used, and the proposed architecture. Missing value imputations are done using k-Nearest Neighbors (“An Introduction to Kernel and Nearest Neighbor Nonparametric Regression” 1992) (k-NN) imputation methods. Next, data is transformed using data scalar procedures. K-fold (K = 10) Cross-Validation (CV) approach was adopted, wherein MLP models were built on a training set and assessed on a test set. The training set corresponded to 75% of the total amount of data. Figure 1 depicts the proposed workflow.

Figure 1. Proposed workflow.

Data Analysis

This section provides the description of the datasets that have been explored in this research. The eight datasets used in the study fall under the category of clinical databases, real-time databases, gene expression-based databases, and digitized datasets.

Clinical Databases

Cervical cancer and mesothelioma cancer clinical datasets utilized in this study are authentic electronic health records of patients. They are freely available on the UCI Machine Learning Repository (University of California, Irvine).

• Cervical Cancer Dataset (Fernandes, Cardoso, and Fernandes 2017): An aggregate of eight hundred fifty-eight cases depicting records of patients were diagnosed and tested. There are four target factors, specifically “biopsy,” “schiller,” “Hinselmann,” and “citology.” In the dataset, all occurrences exclusively have 32 features with multivariate factors by the direction provided by clinical experts; these are more viable than other element subsets. A considerable lot of the examples have “obscure” or “missing qualities.” The four target variables are decision-makers.

• Mesothelioma (Orhan et al. 2012): The dataset utilized right now is a genuine electronic health record of patients. The dataset overseers (Orhan et al. 2012) gave the principal examination of this dataset in 2011 and distributed the dataset openly in 2016. An aggregate of Three hundred and twenty-four (324) examples portraying records of patients was analyzed and tested. In the dataset, all cases independently have 35 columns, i.e., features. One of the dataset features named “diagnosis method” is replicating the target variable “class of diagnosis.” Henceforth, we exclude this feature from further analysis to improve the reliability of the study.

Real-Time Datasets

Three real-time cancer datasets, i.e., ovarian cancer, lung cancer, and leukemia dataset, are incorporated in the study. The patients diagnosed with cancer were selected from multiple hospitals and clinics of the Jammu and Kashmir Region. For each patient, the diagnosis results were histologically confirmed. Records of cancer patients and healthy volunteers with the consent of all the participants were included in the present study. In this study, we assembled Clinical, demographic, and anthropometric information for all participants under similar conditions. The predictors identical in all the three datasets are age, weight, height, BMI.

• Ovarian Cancer Dataset (Verma et al. 2019): Ovarian cancer dataset was used in the study (Verma et al. 2019). Later on, we gathered more data and a total record of 697 participants was collected comprising 248 ovarian cancer patients (mean age 58.7 years, range 22–89) and 449 controls (mean age 56.44 years, range 25–89). Collected data includes menopausal status (that determine the pre/post or bleeding after menopause again), Pre/Post Menopause (for each participant, this status expressed whether patient experience menopause earlier or later), age of menarche i.e. age of onset of menses, presence of breast cancer nodules (stating whether the patient is diagnosed with breast nodules also), and use of oral contraceptives. These clinical features have been marked as important risk factors (B. M. Reid, Permuth, and Sellers 2017). The target variable is ovarian code that determines whether a person has ovarian cancer or not. The statistical description of the ovarian cancer dataset is provided in Table 3. Range and missing values are given for each predictor.

Table 3. Statistical description of ovarian cancer dataset

S.No.	Variables	Range	Missing
1.	Age (years)	[22,85]	0
2.	Weight (kg)	[40,90]	0
3.	BMI (kg/m2)	[14,38]	0
4.	Menopausal Status	[0,2]	0
5.	Pre/Post Menopause	[0,1]	2
6.	BC Nodules	[0,1]	17
7.	Age at Menarche	[0,1]	48
8.	Oral Contraceptive use	[0,1]	3
9.	Ovarian Code	[0,1]	0

These clinical features have been marked as important risk factors (B. M. Reid, Permuth, and Sellers 2017). The target variable is ovarian code that determines whether a person has ovarian malignant growth or not.

• Lung Cancer Dataset (Bhat et al. 2019): The lung Cancer dataset was first used in the study (Bhat et al. 2019). Then we incorporated new records in the dataset, and the final dataset comprises 225 lung cancer patients. Out of 225, 10 patients belong to Stage 1, 69 to stage II, 96 to stage III, and 50 to Stage IV. Out of 225, there were 187 males and 38 females identified with Lung Cancer. Clinical information about lung cancer patients (mean age 61 years, mean BMI 22 kg/m2) was registered. The age range of onset of cancer is [29, 84]. The risk factors or symptoms of lung cancer included in creating the dataset are weakness or weight loss, hoarseness of voice, pain in the chest, dyspnea, cough, fever, and tobacco intake (Cruz, Tanoue, and Matthay 2011). Other factors included in the dataset are the age of onset of cancer, duration of onset of cancer, Gutkha, and alcohol intake (Tumors 2008). These clinical features have been marked as significant risk factors in the research studies (Cooley 2000; Skaug, Eide Msci, and Gulsvik 2007; Monila 2008). Table 4 depicts the statistical description of the dataset. Smoking and age of onset are expressed in terms of years. Duration is defined in terms of months. Cough is recorded in terms of days. The target variable is “Stage,” which determines the cancer stage of the patient. Due to inadequacy in stage-I records, we have excluded stage-I patients from further analysis. As most rows are missing from a few of the predictors like cough, hoarseness of voice, dyspnea, and fever, these features are excluded from the future analysis.

• Leukemia Dataset (Bhat et al. 2019): An absolute record of 613 members was made containing 207 Leukemia patients (mean age 40.47 years, run 3–93) and 407 healthy people (mean age 49.18 years, extend 14–89). Out of 207, 140 males and 67 females were determined to have leukemia, i.e., More records of male leukemia patients are included in the dataset. The hemoglobin tally differs from 8.6 (mean) in cases to 9.7 (median) in controls. Gathered information incorporates the smoking status, the alcoholic propensities, the proximity of fever, unusual augmentation of spleen or liver (Splenomegaly/Hepatomegaly), and hemoglobin tally of the patient. These clinical highlights have been set apart as significant hazard factors in prior studies (Davis, Viera, and Mead 2014). Dataset description is given in Table 5.

Table 4. Statistical description lung cancer dataset

S.No	Variables	Missing Values
1	Age	0
2	Weight	0
3	BMI (kg/m^2)	0
4	Sex	0
5	Age of Onset	0
6	Duration	0
7	Smoking	0
8	Gutkha	25
9	Alcohol	16
10	Cough	142
11	Hoarseness of Voice	127
12	Dyspnea	89
13	Fever	98
14	Pain in Chest/ Other Parts	58
15	Weakness	32
16	Stage	0

Table 5. Statistical description of Leukemia dataset

S.No	Variables	Range
1	Gender	[0,1]
2	Age (years)	[3,93]
3	Height	[1.3,6.4]
4	Weight (kg)	[10,90]
5	BMI (kg/m^2)	[9,63.6]
6	Smoker	[0,1]
7	Alcoholic	[0,1,2]
8	Fever	[0,1]
9	Splenomegaly/Hepatomegaly	[0,1]
10	Hemoglobin Count(gm/dL)	[3,14]
11	Case/ Control	[0,1]

Variable 7 i.e. “Alcoholic” depicts whether person consumes alcohol (2), does not consume alcohol (2) and sometimes/occasionally drinks (1). Hemoglobin count is a significant factor as it depicts the amount of red blood cells (RBC) in the body and is expressed in terms of gm/dL (grams per deciliter). The objective variable is “case/control” that decides if an individual is a case (leukemia patient) or control (healthy person).

Digitized Image Datasets

The breast cancer Wisconsin dataset and prostate cancer dataset are obtained from the digitized images. Both the datasets are online accessible on the Kaggle data vault.

• Breast Cancer Wisconsin Dataset (Publisher, Bennett, and Mangasarian 2011): The cancer dataset comprises 569 occasions in which 357 belong to the benign class and 212 belong to the malignant class. Absolute 32 highlights figured from a digitized picture of a breast mass’s fine needle suction (FNA) are available. The highlights/properties utilized in the dataset portray qualities of the cell cores present in the picture, and “diagnosis” is the objective/target variable that determines the status of breast cancer diagnosis outcome.

• Prostate Cancer Dataset: This dataset is accessible from the Kaggle database (https://www.kaggle.com/sajidsaifi/prostate-cancer). It comprises record of 100 occasions and ten factors. One variable indicates the distinguishing proof number; the other 8 are numerical factors. The objective variable is “determination result,” which is all out having two classifications to be specific Malignant (M) and Benign (B). Dangerous class contributes to 62% of situations, whereas 38% have a place with benign class. Accordingly, harmful cells cosmetics the dominant part class while generous cells contribute to framing the minority class. There emerges the issue of class imbalance as a class with more data points can overshadow the class with fewer instances

Gene Expression Based Datasets

Various examinations have detailed the utilization of quality articulation information and other high-dimensional genomic information for endurance expectation (Chaddad et al. 2017; Skaug, Eide Msci, and Gulsvik 2007; Sun et al. 2018; Xiao et al. 2018; Cho and Won 2003; Shedden et al. 2008; Størvold et al. 2007; Y. Chen, Ke, and Chiu 2014). For example, non-small-cell lung carcinoma (NSCLC) patients’ quality articulation crude information (CEL files) and clinical information downloaded from the NCI database, a vault of high-throughput gene expression data microarrays.

• Lung Cancer Survival Dataset: We investigated numerous informational indexes to evaluate the prognostic estimation of different parameters in lung disease. We utilized the survival time (< year and a half) as a high-risk group and survival time [18, 48] as the moderate-risk group, and survival time > 4 years as a low-risk group. This NSCLC information was recorded basically from four establishments and constituted of 442 NSCLC patients. Patients’ survival durations, ages, breakdown phases, treatment, and smoking history were all included in the clinical data. All gene expression data profiling was carried out using Affymetrix HG-U133A chips. The treatment response data includes age, race, sex, survival time, adjuvant chemotherapy, adjuvant radiation therapy, and stage statistics. Cases with missing survival time are omitted from further analysis. The summary of the patient’s information and NSCLC patients, along with classified risk groups, is depicted in Table 6.

  Table 6. Summary of NSCLC patients

  Variables	Categories	Patients
  Gender	Male	223
  	Female	219
  Risk	Low	166
  	Intermediate	145
  	High	131
  N_Stage	N0	299
  	N1	87
  	N2	53
  	NX	1
  	T0	251
  T_Stage	T1	150
  	T2	28
  	T3	11
  ADJUVANT_CHEMO	No	233
  	Yes	120
  	Unknown	89
  ADJUVANT_RT	No	256
  	Yes	121
  	Unknown	65

Classification Model

Given the accomplishment of neural networks in biomedicine in earlier studies, we resorted to employing deep learning architectures (Gupta and Gupta 2021; Gupta and Kumar 20212022; Kumar et al. 2021). Henceforth, to construct learning models that can learn the unknown relationships among various classifiers, we embrace the Stacking-based ensemble learning of neural classifiers.

Ensemble Learning: Taking into account the way that ensemble learning can integrate various learning techniques. The resultant model that takes pluses of compound learning strategies would prompt superior performance. A few examinations have been portrayed in the writings to incorporate models to raise the exactness of the expectation. For example, Bagging was acquainted by Breiman (Breiman 2001) to consolidate outputs from decision trees produced by a few arbitrarily chose sub-sets of the training information and decisions in favor of the ultimate result. Boosting is an improved adaptation of Bagging that was advanced by Freund and Schapire (Vladimir et al. 2005). This strategy works by uplifting the weights of training samples in each iteration and finally joins the classification outcomes by weighted votes. Wolpert (Wolpert 1992) proposed using linear models to integrate results of the learning structures, otherwise called Stacking or blending. Contrasting the majority voting that takes just the linear connections among classifiers into thought, stacking classifiers can “learn” non-linear structures. Stacking utilizes a learning approach to integrate the models that make it a significantly more remarkable outfit strategy.

Multiple Layer Perceptrons: Rosenblatt constructed a single-layer perceptron that permits the neural systems to demonstrate a shallow neural system, wound up forestalling this network from performing non-linear classification (Rosenblatt 1958). Quick forward to 1986, when Hinton, Rumelhart, and Williams distributed a paper ”Learning representations by back-propagating errors,” presenting ideas about Backpropagation and hidden layers – subsequently bringing forth Multilayer Perceptrons (MLPs)(Rumelhart and Hintont 1986). In the forward pass, the data stream flows from the information layer through the shrouded (“hidden”) layers to the final (“output”) layer, and the selection of the last layer is estimated against the ground truth labels. Hidden Layers are neuron hubs stacked in the middle of sources of info and outcomes, permitting neural systems to learn intricate features gradually. In Backpropagation, weights are updated repeatedly to minimize the error rate utilizing the chain rule of calculus, partial derivatives of the error function. Such strategy provides us a gradient or a scene of blunder. Also, this may balance the parameters as it can estimate the error in various ways, including by Mean Square Error (MSE).

Measures and Parameters of Variables

Model Hyperparameters are properties that govern the entire training process. They include variables that decide the system structure (for instance, Number of Hidden Units) and the factors which determine how the system is prepared (for example, Learning Rate). Model hyperparameters are set before preparing (before upgrading the loads and predisposition). Hyperparameters are significant since they straightforwardly control the classification performance. Also, it has a substantial effect on the execution of the model under training. Optimization Hyperparameters are connected more to the advancement and preparing process like learning rate and number of epochs. In addition, model Hyperparameters are more associated with the structure of the model, like hidden layers and hidden units.

• Learning rate: If the model’s learning rate is significantly below than optimum quality, it will take significantly longer (hundreds or thousands) of epochs to reach optimum state. Then again, on the off chance that the learning rate is a lot bigger than ideal worth, at that point it would overshoot the perfect state and the calculation probably won’t merge. We chose the learning rate = 0.001 in the wake of tuning the neural model.

• Epochs: We used 500 epochs for the training phase of each MLP classifier. The intuitive manual method is to train the model for as much iterations as the validation error continues to decrease.

• Hidden units: It is one of the more perplexing hyper parameters. The number of the hidden units is proportional to the learning limit of the model. We used units of 50, 150, and 200 in MLP 1, MLP 2, and MLP 3, respectively. Another heuristic regarding the first hidden layer is that empirical observation indicates that increasing the number of hidden units above the number of inputs results in improved performance on a variety of tasks.

• Layers: MLP_1 is fabricated using two hidden layers while MLP_2 is prepared using three hidden layers. Consequently, MLP_3 is constructed with four hidden layers.

• Optimizer: AdaM represents Adaptive Momentum. It joins the Momentum and RMS prop in a solitary methodology making AdaM an exceptionally incredible and quick streamlining agent. Adaptive Moment Estimation (Adam) computes adaptive learning rates for each parameter and favors flat minima on the error surface. As followed, we calculate the decay average of the previous squared gradients ($S_t)$ and past gradients $C_t$ in eq. (i(i) $C_t={\alpha }_1{C}_{t-1}+\left(1-{\alpha }_1\right)gt$(i) ) and (ii).

(i) $C_t={\alpha }_1{C}_{t-1}+\left(1-{\alpha }_1\right)gt$(i)

(ii) $S_t={\alpha }_2{s}_{t-1}+\left(1-{\alpha }_2\right)g{t}^2$(ii)

$C_t$ and $S_t$ are approximations of the gradients’ initial moment (the mean) and secondary moment (the un-centered variance). The biases were countered using ${\hat{\mathrm{C}}}_{t}and{\hat{\mathrm{S}}}_t$ i.e. bias-corrected first and second moment estimates respectively. These are mathematically expressed in equation (iii) and (iv).

(iii) ${\hat{\mathrm{C}}}_t=\frac{C_t}{1-{\alpha }_1^t}$(iii)

(iv) ${\hat{\mathrm{S}}}_t=\frac{S_t}{1-{\alpha }_2^t}$(iv)

Finally, the ADAM rule is expressed in eq. (v).

(v) ${\phi }_{t+1}={\phi }_t-\frac{\eta {\hat{\mathrm{C}}}_t}{\sqrt{{\hat{\mathrm{S}}}_t+\epsilon }}$(v)

• Activation function: For input layer, ReLU activation function is used. We utilized the Sigmoid as the activation function in the hidden and output layer. It is a rather straightforward architecture, yet complex enough to serve as a valuable function.

• Rectified Linear Units (ReLU): ReLU function guarantees that if y is more prominent than zero, our yield remains y; else if y is negative, our yield is zero. In short, we select the most extreme among 0 and y. ReLU is expressed mathematically in equation (vi).

(vi) $f\left(y\right)=max\left(0,y\right)$(vi)

• Sigmoid activation: The enactment work utilized in the inside layer of ANN is Sigmoid. The arrival estimation of sigmoid capacity is monotonically expanding, lies between 0 and 1 or from −1 to 1. Sigmoid capacity is characterized scientifically in eq. (vii).

(vii) $S\left(x\right)=\frac{1}{1+e^{-y}}$(vii)

A sigmoid function is a statistical function with a characteristic “S”-shaped curve that is called the sigmoid curve.

Friedman Ranking Test

The Friedman Test is a non-parametric variant to ANOVA with Repeated Measures. It is used to detect there is or is not a statistical substantial distinction of three or more groups that contain the same participants. The Friedman test is used to determine the classifiers’ ranks. At the 0.5 and 95% confidence levels, the null hypothesis (H0: there is no significant variation in classifier performance) is discarded. Thus, the alternative hypothesis (H1) is supported, implying a considerable difference exists between the classification results. Bonferroni–Holm adjustments were employed to determine the significance of the multi-neural ensemble above other classifiers.

Working Methodology

The dataset denoted by X is made of x belonging to a set of attributes, and y denotes the target column. Also, z represents the size of the data. The base learners (MLP₁, MLP₂ & MLP₃) are represented by M₁, M₂ & M_3, respectively. The algorithms work by training each base learner applying MLPs on original data (X) and saving it as S₁, S₂, and S₃ (M₁, M₂, & M_3, respectively).Then a new dataset (P₁) is generated to hold predictions (p) made by the S₁, S₂, and S₃. Then the prediction dataset (P₁) made using base learners is passed as input through meta-model GDC or G and stored in S^’. Finally, the desired model is obtained. The algorithm of the stacking-based neural ensemble model is given in Figure 2.

Figure 2. Algorithm of the stacking-based neural ensemble model.

(MLP₁, MLP₂ & MLP₃) are represented by M₁, M₂ & M_3, respectively, predictions (p), prediction dataset (P₁)

The approach used in this study attempts to use a Gradient-boosting classifier (GBC) to stack deep neural networks, to construct a multi-model ensemble model to predict cancer in normal and tumor conditions. The selected features in each of the cancer datasets are supplied to the three neural models. After that, the GBC is used to stack the outputs of the three base learners to acquire the last forecast outcome. Figure 3 shows the learning architecture proposed in the study.

Figure 3. Proposed stacking based neural ensemble model.

Multilayer Perceptrons_1 (MLP_1), Multilayer Perceptrons_2 (MLP_2), and Multilayer Perceptrons_3 (MLP_3), Prediction (P)

Gradient Boosting Classifier (GBC) basically works by updating the weights of the wrongly classified instances in the subsequent layers. The error (€) is calculated using the Equation (viii), where s_m denotes all the instances in the training data and s < S (S = number of weak learners).

(viii) ${\text{euro}}_s=\frac{{\sum }_{i=1}^I{\beta }_i^{\left(s\right)}\ast y}{{\sum }_{i=1}^I{\beta }_i^{\left(s\right)}}$(viii)

$\beta =\frac{1}{i}whereirepresentsthedata-size$

$Z\left(q_m\right)isthehypothesisthatallinstances\left(q\right)arepredictedcorrectly$

Here $\gamma$ is the conditional function assessing the hypothesis $Z\left(q_m\right)$, $y=1$ if the condition $\gamma$ is true else 0 and is calculated in the Equation (ix).

(ix) $y=\gamma \left(q_i\ne Z_s\left(q_m\right)\right)$(ix)

Then the misclassified cases are assigned a weight on the succeeding layer using the equation (x).

(x) ${\alpha }_s=log\frac{1-{\text{euro}}_s}{{\text{euro}}_s}$(x)

Weights of data instances are updated in each iteration as shown in the equation (xi).

(xi) ${\beta }_i^{\left(s+1\right)}={\beta }_i^{\left(s\right)}\ast exp\left({\mu }_s\ast \gamma \left(q_s\ne Z_s\left(q_i\right)\right)\right)$(xi)

The principal behind weight updation approach is to tempt learning where the classification models learn from the mistakes of the models at preceding layers. Further $\gamma$ = 0 implies no Updation in the weight of the instance given in Equation (xii).

(xii) ${\beta }_i^{\left(s+1\right)}={\beta }_i^{\left(s\right)}$(xii)

In case of misclassification, weight updation for the particular instance is given in Equation (xiii).

(xiii) ${\beta }_i^{\left(s+1\right)}={\beta }_i^{\left(s\right)}\ast \mathrm{e}\mathrm{x}\mathrm{p}\left({\alpha }_s\right)\hspace{0.17em}$(xiii)

After the s repetitions, the final output is given in the Equation (xiv).

(xiv) $f_s\left(q\right)=sign\left(\sum _s^S{\alpha }_s\ast Z_s\left(q\right)\right)$(xiv)

Thus, Gradient Boosting Classifier (GBC) works on the basis of weighted vote scheme where the working of the classification models depends on the prediction performance of (n-1)^th classifiers.

Execution Details

The models were created using a Dell −15JPO9P computer equipped with an Intel Core i7-8550 U processor running at 1.80 GHz and 8 GB of Random-Access Memory (RAM). All machine learning algorithms are implemented in Python 3.7 via Anaconda Navigator.

Results and Discussion

This segment holds the experimental outcomes gathered after applying the proposed classification procedure. The graphs used to display the simulation results are plotted using “matplotlib” library in python.

The evaluation parameters used for the assessment of the prediction models are described in Table A1. These evaluation parameters lay the standard for evaluating the advantages and shortcomings of the AI-based learning approaches. In Table A1, true positive (P) refers to the correctly recognized cases, false positive rate (Q) refers to the cases that are negative and wrongly identified by the model, true negative rate (R) refers to the outcomes that are correctly predicted as negative by the technique, and false-negative rate (S) refers to the negative cases wrongly predicted by the model. The description of commonly used evaluation parameters for instance accuracy (Acc), Specificity (Spec.), Sensitivity (Sens.), F-measure, Receiving operator characteristic (ROC) curve, and Area under the curve (AUC) is given in Table A1 (appendix).

• Clinical Datasets: The proposed architecture performed best on both the datasets containing clinical data.

•  Cervical Cancer: The proposed Stacked_Model achieved 98.9% accurateness. The MLP with a single hidden layer realized the lowest prediction results are revealed in the Figure 4.

  Figure 4. Cervical cancer.

  

•  Mesothelioma: The stacked MLP model attained highest prediction accuracy (94%). Neural networks with less hidden layers performed better than those with more layers as presented in the Figure 5.

  Figure 5. Mesothelioma.

  

•  Real Time Datasets: The stacked model acquired the best prediction accuracy on all the three real-time datasets of J&K cases.

•  Ovarian Cancer: Inferring from Figure 6, the best prediction accuracy on the Ovarian Cancer dataset was attained by the proposed stacked model (98% approximately) followed by the neural network built using three or more hidden layers.

  Figure 6. Ovarian cancer.

  

•  Lung Cancer: Figure 7 shows that the best prediction accuracy on the Lung Cancer dataset was attained by the proposed stacked model (95.7%) followed by the MLPs with two or more hidden layers (84%).

  Figure 7. Lung cancer.

  

•  Leukemia: Figure 8 expresses that the most appreciable accurateness of 99% was achieved using Stacked Model can predict leukemia.

  Figure 8. Leukemia.

  

•  Digitized Image Datasets: The best performance was displayed by the proposed learning technique followed by the MLP_2 on the datasets derived using digitized images.

•  Breast Cancer: Breast Cancer prediction accuracy (99% approx.) is obtained with the proposed technique. The neural architecture with more layers performed better as compared to the MLP with less hidden layers as depicted in Figure 9.

  Figure 9. Breast cancer.

  

•  Prostate Cancer: Figure 10 displays the accuracy results achieved using all the neural techniques. The proposed model predicts prostate cancer with the highest accuracy (87%).

  Figure 10. Prostate cancer.

  

•  Gene Expression Dataset: The proposed machine learning algorithm worked the best on gene expression-based dataset.

•  Lung Cancer Survival: Figure 11 illustrates that the accuracy achieved by the proposed model predicts the survival of lung cancer patients with the highest accuracy (88.47%) followed by MLP_1.

  Figure 11. Lung cancer survival.

  

Prediction Results of the Proposed Model Accuracy

The final stacked neural model was assessed on each of the cancer datasets using different performance assessment parameters. The classification model was validated using a 10-Fold Cross-Validation approach. The performance of the model was investigated using evaluation parameters (Powers 2020) like Accuracy (Acc), Area under the Curve (AUC), F1_Score (F1), Mathew’s Correlation Coefficients (MCC), Specificity (Spec.), Sensitivity (Sens.). The prediction results thus attained are depicted in Table 7. The description of evaluation parameters is given in Table A1.

Table 7. Assessment of stacked model

Dataset	Cancer	Acc	AUC	F1	MCC	Sens.	Spec.
Clinical	Cervical	98.5	98.6	97	98.4	97.8	98.9
	Mesothelioma	94.1	93.5	88.2	94.1	96.8	91.4
Real-Time	Ovarian	97.62	97.68	95.35	97.79	95.19	99.95
	Lung	95.7	95	94.9	90.62	96.6	92.5
	Leukemia	99	99	99.3	99.5	99.5	99.3
Digital	Breast	98.94	98.6	97.77	98.81	99.75	97.89
	Prostate	87	88.46	65.88	81	90	87.12
Gene-expression	Lung Cancer Survival	88.47	88.38	77.16	88.64	86.31	90.97

Table 7 infers that the prediction architecture proposed in the study performs well on all the cancer datasets. Following inferences need to be highlighted:

• The Stacked Neural model worked well with both cervical cancer and Mesothelioma dataset attaining a great prediction score.

• The prediction model worked well with the three real-time ovarian cancer datasets (binary), lung cancer dataset (multi-class problem) where the target is to predict stage (stage 2, 3 and 4), and leukemia dataset (binary target). The proposed prediction model performed exceptionally well on all the parameters concerning the Wisconsin breast cancer dataset.

• The projected model worked well on NSCLC gene-expression dataset achieving appreciable prediction outcomes where the target is to predict the survival time of the lung cancer patients.

Comparison of the Proposed Model

To evaluate the effectiveness of the proposed study, we compared several approaches to predicting cancer or patient survival using the benchmark datasets (Cervical Cancer, Mesothelioma, Breast Cancer, and NSCLC gene expression-based lung cancer survival data. Comparisons based on the prediction accurateness (accuracy score) achieved by several research studies are summarized, and the highest accuracy scores are bold-faced in Table 8.

Table 8. Stacked model results

Dataset	study	Classification Model	Accuracy
Cervical Cancer	(Wu and Zhou 2017)	Support Vector Machines	93%
	(Ceylan and Pekel 2017)	Random Forests	82%
	(Fatlawi 2017)	Decision Trees	55.7%
	(Abdoh, Rizka, and Maghraby 2018)	Random Forest-PCA	97.4%
	(Adem, Kiliçarslan, and Cömert 2019)	Stacked Auto encoders	97.25
	Our study	stacking-based multi-neural ensemble	99%
Mesothelioma	(Orhan et al. 2012)	Probabilistic Neural Networks	53%
	(Nilashi and Ibrahim 2017)	fuzzy rule & CART	93%
	(Mukherjee 2018)	Support Vector Classifier	72%
	(Chicco and Rovelli 2019)	Random Forests	82%
	Our study	stacking-based multi-neural ensemble	94%
Breast Cancer	(Seera and Peng Lim 2013)	DT-RF	98.8%
	(Sumbaly 2014)	J48	94.42
	Kumar, Sai Nikhil, and Sumangali 2017)	SVM-Naive Bayes-J48	97.3%
	(Saygili 2019)	RF	98.7%
	Our study	stacking-based multi-neural ensemble	99%
NSCLC	(Y. Chen, Ke, and Chiu 2014)	Artificial Neural Networks	83%
	Our study	stacking-based multi-neural ensemble	88%

Table 8 reasons that the proposed classification technique, i.e., stacking-based multi-neural ensemble system, shows an incredible performance on all cancer datasets. Our proposed strategy performed better than the techniques employed in previous research studies.

Statistical Analysis

Using Friedman statistical significance tests (WALs and Kelleher 1971) and Holms post-hoc analysis, the proposed stacking-based multi-neural ensemble is statistically compared to three deep learning approaches for each dataset (Holm 1979). Table 9 contains the average Friedman ranks (the higher the rating, the better (Evans 2019)) and the adjusted p.

Table 9. Statistical results

ML Methods	Friedman Rank	Adjusted P
MLP_1	2.432	0.000478
MLP_2	3.2	0.005372
MLP_3	3.68	0.011821
Stacked Model	6.2	(Control)

Friedman rankings of each classifier demonstrated that the suggested stacked model beat the MLP 1, MLP 2, and MLP 3 algorithms significantly (at 0.05).

Based on the results, we perceive that the proposed gradient boosting-based multi-neural approach produces noticeable results superior to each of the neural classification models. Due to the complication and high mortality of cancer, diagnosis precision is critical. Consequently, improvement in diagnosis prediction by applying machine learning systems is of great aid to cancer cure. According to the interpretations in an earlier study (Kourou et al. 2015a), neural networks have been used in 70% of cancer research studies. This interpretation encouraged us to integrate multiple neural models for attaining a more precise classification model. In the study, we presented an evaluation of the proposed multi-neural technique and the three different MLP models acting solo. Also, Simulation results on the eight data sets express that the proposed strategy yields greater accurateness than all the other learners performing individually. The sensitivity analysis shown in Figure 12 specifies that the single classification model displays uneven performance for different data sets.

Figure 12. Sensitivity analysis.

Conclusion

A gradient boosting-based multi-neural approach is presented to predict cancer diagnosis, stage and survival. Multiple cancer datasets like real-time datasets, clinical, image-driven datasets, and gene expression data have been analyzed. The multi-neural ensemble model based on stacking ensembles the outputs of the three neural classifiers. Employing gradient boost learning at the second level enables the ensemble method to recognize the intricate relationships among the classifiers are automatically to achieve better prediction. This exploratory investigation conveys that the proposed stacking-based deep learning model can be an integral asset for a viable biomarker of various tumors. An ideal classifier must achieve higher sensitivity as diagnosing tumorous patients as nonmalignant would be a significant hazard. For cancer studies, this misclassification can be more hazardous than categorizing a healthy patient as malignant. Proposed gradient boosting used in the ensemble stage spontaneously acquires complicated structures. The instance labels are learned, such that the yield of MLPs and the associations amid them are considered. The gradient boosting learner works in a step-wise fashion by placing more weight on the instances that have been misclassified in the former stage. Subsequently, the appreciable accurateness of cancer prediction is achieved. The classification outcomes achieved by the predictive model in each of the cancer datasets are exceptionally sound to advocate the worth of the proposed model in further studies and medicinal practices. The study has some limitations; for instance, the model has been evaluated on small-size datasets only, and there is a requirement to validate the model on considerably large-sized datasets. Also, the proposed approach has been evaluated on only cancer datasets; for the sake of generalizability, the proposed model needs to be validated on other disease datasets as well. Regarding future directions, we aim to analyze the performance of the proposed model on other disease datasets.

Cervical Cancer (Risk Factors) Data Set

https://archive.ics.uci.edu/ml/datasets/Cervical+cancer+%28Risk+Factors%29

Mesothelioma’S Disease Data Set

https://archive.ics.uci.edu/ml/datasets/Mesothelioma%C3%A2%E2%82%AC%E2%84%A2s+disease+data+set

Breast Cancer Wisconsin (Diagnostic)

https://archive.ics.uci.edu/ml/datasets/Breast+Cancer+Wisconsin+(Diagnostic)

Prostate Cancer Data Set

https://www.kaggle.com/sajidsaifi/prostate-cancer

Code Software: The python code along with all the developed for the cancer diagnosis prediction pronounced in this study made available on Github.com at the following URL: https://github.com/surbhigupta24/Stacking-Based-Multi-Neural-Ensemble-

All the data files used in the study along with python code are uploaded privately on https://github.com/ and can be made public afterwards or can be provided to readers.

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Data Availability Statement

The following are the links of online datasets: https://github.com/surbhigupta24/Stacking-Based-Multi-Neural-Ensemble-

Appendix

Table A1. Description of metrices

Metrics	Description	Formula
Accuracy (Acc.)	It identifies the total amount of cases appropriately identified by the model.	(P + Q)/ (P + Q + R + S)
Specificity (Spec.)	It identifies the negative cases correctly determined by the model.	R/ (R + Q)
Sensitivity (Sens.)	It outlines the number of genuine cases recognized from all correct cases.	P/(P + S)
F1-Score	It evaluates the model based on the harmonic mean of Pr and Re	2 × ((Pr × Re)/(Pr + Re))
Receiver Operating Characteristic (ROC)	It considers the true positive rate against the false-positive rate on a range of thresholds.	–
Area Under the Curve (AUC)	AUC measures the area under the ROC curve and is also scale-invariant.	–