A MATHEMATICAL APPROACH OF EXPLORATION TOWARDS EXTREME RISK FACTOR IN CANCER OF OPTIMAL CONDITIONHTML Full Text
A MATHEMATICAL APPROACH OF EXPLORATION TOWARDS EXTREME RISK FACTOR IN CANCER OF OPTIMAL CONDITION
Priyanka Majumder * 1, Apu Kumar Saha 1 and Mrinmoy Majumder 2
Department of Mathematics 1, Department of Civil Engineering 2, National Institute of Technology, Agartala, Barjala, Jirania - 799046, Tripura, India.
ABSTRACT: The aim of this present investigation is to identify the most important risk factor for cancer by means of a mathematical model. The study begins with considering some types of cancer viz. breast, colorectum as well as lung and bronchus cancer as most of the cancer patients suffer from these types of cancers. Teaching-Learning-Based Optimization technique is applied to sorting out the most lethal cancer among all cancer consider in this study and it is found that lung and bronchus cancer is the most fatal. Further, we investigate the risk factor associated to lung and bronchus cancer by means of Literature, Expert and Local Hospital survey. All the risk factor has their own importance for death from cancer in medical aspects. Multi-Criteria Decision Making technique is applied to recognize the most significant risk factor among all the factors in statistical scenario. It is identified that smoking is the most concerning risk factor. The information related from the study may help to take necessary measure to control the death rate due to lung and bronchus cancer.
Breast cancer, Colorectum cancer, Lung and Bronchus cancer, Optimization, MCDM, Control
INTRODUCTION: Human body contains millions of cells; it grows divides and dies in the conventional manner. Sometimes the system goes wrong and uncontrolled no of cells grows, which leads to cancer. The cancer cells Combine and form extra mass tissue known as tumor 1. Cancer is a common disease which spreads throughout the blood stream in the human body. Leukemia alters the blood cell and involve in its maturity and immaturity 2. Some of the tumors do not spread throughout the body, but grow uncontrollably like benign tumor 3.
Normal / healthy cell controls their growth and when they become unhealthy, destroys by themselves. In Asia high prevalence of chronic viruses like hepatitis B 4 and C, the Epstein Barr virus and human papilloma viruses (HPV) 4 increases the high risk of cancer.
Mutations in p53 gene 5 leads to cancer as well as nutrition 6 Plays a vital role in mortality of cancer 7. Exposure to aldehydes and formaldehyde associated with high risk of lymphoma cancer 8. Hypoxia 9 is a solid tumor growth in cancer which is common and disturbs molecular pathways 10. It is not possible to find out the specific cause of cancer. Cancer cells are modulated by culture condition and extracellular microenvironment condition 11. But there are many risks which increase the cancer, such as intake of tobacco, alcohol, poor diet, obesity, exposure to UV radiation, lack of physical activity 1.
According to the literature survey, there are so many lethal cancers namely breast, colorectum, lung and bronchus 12. Of the 7 million deaths from cancer worldwide in 2001, an estimated 2.43 million (35%) were attributable to nine potentially modifiable risk factors. Of these, 0.76 million deaths were in high-income countries and 1.67 million in low-and-middle-income nations.
Among lower and middle income regions, Europe and Central Asia had the highest proportion (39%) of deaths from cancer attributable to the risk factors studied. 1.6 million of the deaths attributable to these risk factors were in men and 0.83 million in women. Smoking, alcohol use, and low fruit and vegetable intake were the leading risk factors for death from cancer worldwide and in low and middle income countries. In high income countries, smoking, alcohol use, and overweight and obesity were the most important causes of cancer. Sexual transmission of human papilloma virus is a leading risk factor for cervical cancer in women in low and middle income countries. More than 12 million new cases of cancer occur annually worldwide. Of those 5.4 million occur in developing countries and 6.7 million in developing countries 13, 14.
Aline et al., developed the Proactive Molecular Risk Classifier for Endometrial Cancer (ProMisE), a molecular classification system based on The Cancer Genome Atlas genomic subgroups, and sought to confirm both feasibility and prognostic ability in a new, large cohort of ECs 15. Evaluate the relationship between health beliefs (perceived susceptibility to breast cancer, perceived benefits of AI treatment, and perceived barriers to AI treatment) and adherence to AIs by Moriah et al., 16. Filip et al., evaluated factors associated with stage-specific cancer therapy and survival, focusing on temporal trends and sociodemographic disparities 17. To identify the variability of short- and long-term survival outcomes among closed Phase III randomized controlled trials with small sample sizes comparing SBRT (stereotactic body radiation therapy) and surgical resection in operable clinical Stage I non-small cell lung cancer (NSCLC) patients by Pamela 18.
In the present study, we heave aimed to recognize the most fatal cancer (whose death rate is maximum) and to find the most important factor (MIF) responsible for causing cancer. To carry out study, we have obtained the regression function of death rate of each cancer that have been considerable in our study of the data given in 19. Next, we have optimized the death rate due to different cancers by Teaching Learning Based Optimization (TLBO). In the second part of the study we have found out the factors. Most lethal cancer among the cancers considered in our study y literature review, expert survey and survey from a local hospital. The Analytic Hierarchy Process (AHP) has been applied to identify the most important factor responsible for that cancer.
Background: Cancer is the name given to a collection of related diseases. In all types of cancer, some of the body’s cells begin to divide without stopping and spread into surrounding tissues. Cancer can start almost anywhere in the human body, which is made up of trillions of cells. Normally, human cells grow and divide to form new cells as the body needs them. When cells grow old or become damaged, they die, and new cells take their place 20. Fig. 1 showing a cancer cell. Fig. 2 showing the new cancer cases annually per 100,000 people (age-adjusted) in the world.
FIG. 1: A DIVIDING CANCER CELL (NATIONAL INSTITUTES OF HEALTH)
FIG. 2: RECENT CANCER SCENARIO IN THE WORLD
Breast Cancer: Breast cancer starts when cells in the breast begin to grow out of control. These cells usually form a tumor that can often be seen on an x-ray or felt as a lump. The tumor is malignant (cancer) if the cells can grow into (invade) surrounding tissues or spread (metastasize) to distant areas of the body. Breast cancer occurs almost entirely in women, but men can get breast cancer, too 21. Breast cancer is the most common malignancy affecting women worldwide 22. Breast cancer is a very important health issue in developed and developing nations of the world 23. In several developed countries, breast cancer incidence increases faster with age before age 50 than after 24. There are various type of risk factors for breast cancer, with some having greater importance than others. A review of the literature on such risk factors was thus undertaken, with these been grouped into four broad categories, namely: sociodemographic factors, reproductive factors, lifestyle factors and hormonal status. Table 1 shows all important risk factors of lung cancer. Equation 1 represents colorectal cancer risk factor ( ).
brf = sf + rdf + lf + hs........(1)
Where sf = b1
rdf = b2 + b3
lf = b4 + b5 + b6
hs = b7 + b8 + b9 + b10
TABLE 1: RISK FACTORS OF LUNG CANCER
|Type||Name of factor||Notation||Intrinsic factor||Extrinsic or environmental factor|
|Sociodemographic factors (sf)||Age||b1||√||×|
|Reproductive factors (rdf)||Age at menarche||b2||√||×|
|Age at first pregnancy||b3||√||×|
|Lifestyle factors (lf)||Diet||b4||×||√|
|Body weight (postmenopausal)||b5||×||√|
|Hormonal status (hs)||Oral contraceptives||b7||×||√|
|Hormone replacement therapy||b8||×||√|
Colorectum Cancer: Colorectal cancer develops in the colon or the rectum, also known as the large intestine. The colon and rectum are parts of the digestive system, also called the gastrointestinal (GI) system.
TABLE 2: RISK FACTORS OF COLORECTAL CANCER
|Type||Name of factor||Notation||Intrinsic factor||Extrinsic or environmental factor|
|Sociodemographic factors (sf)||Older age||cl1||√||×|
|Medical factors (mf)||Family history||cl3||√||×|
|Inflammatory bowel disease||cl4||√||×|
|Helicobacter pylori infection||cl6||√||×|
|Large bowel endoscopy||cl8||√||×|
|Hormone replacement therapy||cl9||√||×|
|Lifestyle factors (lf)||Smoking||cl12||√||√|
|Excessive alcohol consumption||cl13||√||√|
Diet factors (df)
|High consumption of red and processed meat||cl16||×||√|
|Fruit and vegetables||cl17||×||√|
|Cereal fibre and whole grain||cl18||×||√|
The digestive system processes food for energy and rids the body of solid waste 25. Colorectal cancer is the third and second most common cancer, respectively, in men and women worldwide 26 and is a major cause of morbidity and mortality 27. There are various risk factors for colorectal cancer, with some having greater importance than others. A review of the literature on such risk factors was thus undertaken, with these being grouped into four broad categories, namely: sociodemographic factors, medical factors, lifestyle factors and diet factors. Table 2 shows all important risk factors of lung cancer. Equation 2 represents colorectal cancer risk factor (clrf).
Lung and Bronchus: Lung cancer cells have defects in the regulatory circuits that govern normal cell proliferation and homeostasis. The transformation from a normal to malignant lung cancer phenotype is thought to arise in a multistep fashion, through a series of genetic and epigenetic alterations, ultimately evolving into invasive cancer by clonal expansion 28, 29. Lung cancer has been the most common cancer in the world 30. The incidence of cancer of the lung has increased precipitously since the early years of this century, and this disease is responsible for the deaths of many thousands of patients throughout the world 31. There are multiple risk factors for lung cancer, with some having greater importance than others. A review of the literature on such risk factors was thus undertaken, with these being grouped into two broad categories, namely: factors inherent to the individual (intrinsic factors) and factors extraneous to the individual (extrinsic or environmental factors). Table 3 shows all important risk factors of lung cancer. Equation 3 represents Lung cancer Risk Factor (lrf).
TABLE 3: RISK FACTORS OF LUNG CANCER
|Name of factor||Notation||Intrinsic factor||Extrinsic or environmental factor|
|Heredity and genetic susceptibility||l1||√||×|
|Previous respiratory diseases||l7||√||×|
|Tobacco and smoking||l8||×||√|
|Composition of tobacco smoke||l9||×||√|
|Pre-existing lung disease||l15||×||√|
|Pneumonia and mycobacterial disease||l17||×||√|
|Human papilloma virus||l18||×||√|
|Human immunodeficiency virus||l19||×||√|
|Second-hand tobacco smoke||l20||×||√|
|Other environmental pollutants||l22||×||√|
|Other occupational exposures||l23||×||√|
Methods: In this study apply one optimization techniques (OT) viz. TLBO and one MCDM method viz. AHP. OT is apply for identifying the fatal cancer whose death rate is maximized and to find the MIF responsible for causing cancer apply MCDM.
Teaching Learning Based Optimization (TLBO): TLBO is one of the population based algorithm suggested by Rao et al., 32, 33 where a group of students is considered the population and different subjects offered to the learners are analogous with the various design variables of the optimization problem. The main goal of this optimization is 'in a classroom every individual attempts to learn something from teacher to improve themselves'. This algorithm is based on two period viz. teaching phase and learner phase.
Phase I: During the Teacher Phase, the teaching role is assigned to the best individual (Xteacher). The algorithm attempts to improve other individuals (Xi) by moving their positions towards the position of the Xteacher by taking into account the current mean value of the individuals (Xmean). This is constructed using the mean-values for each parameter within the problem space (dimension), and represents the qualities of all students from the current generation. Eq. (4) simulates how student improvement may be influenced by the difference between the teacher’s knowledge and the qualities of all students. For stochastic purposes, two randomly-generated parameters are applied within the equation: r ranges between 0 and 1; and TF is a teaching factor, which can be either 1 or 2, thus emphasizing the importance of student quality.
Xnew = Xi+ r. (Xteacher – (TF . Xmean))..............(4)
Phase II: During the Learner Phase, student (Xi) tries to improve his / her knowledge by peer learning from an arbitrary student Xii, where i is unequal to ii. In the case that Xii is better than Xi, Xi is moved towards Xii (Eq. (5)). Otherwise, it is moved away from Xii (Eq. (6)). If student Xnew performs better by following Eq. (5) or (6), he / she will be accepted into the population. The algorithm will continue its iterations until reaching the maximum number of generations.
Xnew = Xi+ r. (Xii _ Xi)...................(5)
Xnew = Xi+ r. (Xi _ Xii)...................(6)
The Analytical Hierarchy Process (AHP): The Analytical Hierarchy Process (AHP) is a decision-aiding method developed by Saaty 34, 35, 36, 37. It aims at quantifying relative priorities for a given set of alternatives on a ratio scale, based on the judgment of the decision-maker, and stresses the importance of the intuitive judgments of a decision-maker as well as the consistency of the comparison of alternatives in the decision-making process 34.
Saaty 34, 35, 36, 37 developed the following phase for applying the AHP:
Phase I: Define the problem and determine its goal.
Phase II: Structure the hierarchy from the top (the objectives from a decision - maker's viewpoint) through the intermediate levels (criteria on which sub-sequent levels depend) to the lowest level which usually contains the list of alternatives.
Phase III: Construct a set of pair-wise comparison matrices (size n × n) for each of the lower levels with one matrix for each element in the level immediately above by using the relative scale measurement shown in Table 4. The pair-wise comparisons are done in terms of which element dominates the other.
Phase IV: There are n(n-1)/2 judgments required to develop the set of matrices in step 3. Reciprocals are automatically assigned in each pair - wise comparison.
Phase V: Hierarchical synthesis is now used to weight the eigenvectors by the weights of the criteria and the sum is taken over all weighted eigenvector entries corresponding to those in the next lower level of the hierarchy.
Phase VI: Having made all the pair-wise comparisons, the consistency is determined by using the eigenvalue, λmax to calculate the consistency index, CI as follows: CI = ( λmax – n) / (1 - n), where n is the matrix size. Judgment consistency can be checked by taking the consistency ratio (CR) of CI with the appropriate value in Table 5. The CR is acceptable, if it does not exceed 0.10. If it is more, the judgment matrix is inconsistent. To obtain a consistent matrix, judgments should be reviewed and improved.
Phase VI: Phase III - VI are performed for all levels in the hierarchy.
TABLE 4: PAIR-WISE COMPARISON SCALE FOR AHP PREFERENCES 34, 35, 36, 37
|Verbal judgments of preferences||Numerical rating|
|Equally to moderately||2|
|Moderately to strongly||4|
|Strongly to very strongly||6|
|Very strongly preferred||7|
|Very strongly to extremely||8|
TABLE 5: AVERAGE RANDOM CONSISTENCY (RI) 24, 25, 26, 27
|Size of matrix||1||2||3||4||5||6||7||8||9||10|
FIG. 3: FIGURE DEPICTS THE BASIC METHODOLOGY OF IDENTIFYING THE MIRF OF CANCER
In the present study apply OT and MCDM method for selection of most important risk factor (MIRF) for fatal cancer. Here OT is applied for selection of fatal cancer and MCDM is applied for selection for the most impotent risk factor of fatal cancer which is selected by OT. Fig. 3 depicts the basic methodology of identifying the MIRF of fatal cancer.
Application of OT: The statistical technique multiple regression analysis (MRA) is used for developing the mathematical models by using the death rate data listed in Table 6. Here five objective functions are constructed with the help of Table 6. Using MINITAB 17 statistical software we obtain the objective function of each cancer. Each type of cancer is selected as input and average values are taken as output for this software and then obtain Regression. Here each Regression is considered as an objective function. All this data are collected from Cancer Statistics, 2016 19. Here this data is selected because each year, the American Cancer Society estimates the numbers of new cancer cases and deaths that occurs in the United States in the current year and compiles the most recent data on cancer incidence, mortality, and survival.
TABLE 6: DEATH RATES FOR SELECTED CANCERS INDIFFERENT STATES OF USA ET 2008 TO 2012
|State||Beast||Colorectum||Lung and Bronchus||Average|
|District of Columbia||29||16.6||33.9||26.5|
Equation 6a, 6b and 6c represents cancer function with respect to breast, Colorectum, Lung and Bronchus respectively. Upper bound and lower bound are selected maximum and minimum value of each cancer data.
Max ZBreast = 51.8 – 6.76 X1+0.372 X12-0.006151 X13..(6a)
Subject to X1 ≥ 15.1
X1 ≤ 29
Max ZColorectum = –42.4+8.9X2–0.39X22+0.0.0050 X23..(6b)
Subject to X2 ≥ 10.2
X2 ≤ 16.6
Max ZLung and Bronchus = 9.66+0.029 X3+0.00745 X32-0.000074 X33 ..(6c)
Subject to X3 ≥ 15.6
X3 ≤ 55.2
The validity of the regression model is further tested by plotting a probability distribution shown in Fig. 4, 5 and 6. The probability values of the response parameters are scattered near to 95% line, which indicates perfect fitting of the developed regression model.
One of the aims of the present investigation is to find the fatal cancer. We select that cancer whose death rate is maximized. So in this study, we maximize the objective functions 6a, 6b and 6c also all this function 6a, 6b and 6c represents the death rate of each considering cancers.
Application of MCDM: In the present study, we have aimed 42 recognize the most important risk factor of fatal cancer (Whose death rate is maximum). The selection of that factors used AHP techniques. The steps below provide the methodology adopted to look for the weights of importance for each and every factor of the fatal cancer by the MCDM method.
Selection of Criteria: In the present study the relative score of percentage of is required for weights of importance of the criteria The following steps are required for finding the relative score alternatives:
a. Literature Survey (C1): A survey has been carried out within the literature of related fields from where it is found that the effect of each parameters which can Induce effects of the fatal cancer. The score of literature survey is given by equation 7.
Let, f = No. of literature which prefer the alternative.
F = Total number literature studied.
S(A1) = Score of literature survey = (f/F)%…........ (7)
Where S(C1) denotes the percentage of C1
b. Expert Survey (C2): A survey has been carried out within experts in related fields are participants were asked to suggest about the fatal cancer parameters that important for analysis of fatal cancer. According to responses received from the experts a percentage was given to the factors according to Equation 8. Here Expert survey denoted by C2.
Let, r = No. of expert survey, which prefer the criteria.
R= Total number expert survey.
S(C2 )= Score of expert survey= (r/R)%………… (8)
Where S(C2) denotes the percentage of C2
c. Local Hospital Survey(C3): A survey from local patient from cancer hospital has been carried out. Participants were asked to suggest about the fatal cancer parameters which can induce effect on the fatal cancer. According to the response from the local patient a percentage was given to the factors according to Equation 9. Here Local survey denoted by C3.
Let, g = No. of local survey, which prefer the criteria.
G = Total number local survey.
S(C3) = Score from local survey = (g/G) %……… (9)
Where S(C2) denotes the percentage of C2.
Selection of Alternatives: Some environmental factors will be found from a survey. We collect those factors as alternatives which are commonly found from three surveys and this survey. All these alternatives are denoted by Ai.
RESULTS AND DISCUSSION: The results for this present investigation can be sub-divided into two parts, viz., results of the OT to estimate the fatal cancer and lastly use selection of most important environmental risk of that fatal cancer use MCDM. All the three results are described in detail in the following three different Sections 5.1 and 5.2.
Result from OT: Table 7 shows the optimal value of the objective function and Fig. 7a, 7b and 7c represents the convergence graph of the objective function. Using TLBO it is found that the death rate of Lung and Bronchus cancer is maximum with respect to other two considering cancers. So it is clear that Lung and Bronchus cancer is the fatal cancer. In this study, we take population size 30 and number of iteration taken 100.
TABLE 7: TABLE SHOWING THE OPTIMAL VALUE OF CANCER
|Name of cancer||Design variable (Normalized Form)||Optimal result (Normalized Form)||Number of iteration and populations ize|
|Breast||0.269536||0.314971||100 and 30|
|Colorectum||0.168776||0.33625||100 and 30|
|Lung and Bronchus||0.561689||0.348779||100 and 30|
Here all of the objective function solved by MATLAB code of TLBO. Aronchick 38, Gasperino 39, Ruano-Ravina et al., 40 they also say that Lung and Bronchus is now the leading cause of cancer death in men and women.
Result from MCDM: The percentage of the parameters with respect to each of the criteria is presented in Table 8. Table 9 shows the pair-wise comparison of each factor with respect to each criteria. Table 10 shows the final aggregations of AHP. According to OT result, it was found that lung and bronchus cancer is fatal. There are so many environmental factors are responsible for that cancer. According to literature, expert and local hospital survey, it was found that tobacco and smoking, second-hand tobacco smoke, diet and environmental pollutants are more responsible for lung and bronchus cancer. Here, all these factors are considered as an alternative. Here tobacco and smoking, Second-hand tobacco smoke, diet and environmental pollutants are denoted by A1, A2, A3 and A4 respectively.
TABLE 8: PERCENTAGE OF PAPERS, EXPERT AND LOCAL HOSPITAL SURVEY
According to the result of AHP it was found that Tobacco and smoking are the most important risk factor for lung and bronchus cancer because the weights of A1 is greater than other risk factors. Vincent et al., 41, Spiro 42, Hecht 43 also suggested that smoking is very risky for Lung and Bronchus cancer.
TABLE 9: PAIR-WISE COMPARISON OF ALTERNATIVES WITH RESPECT TO CRITERIA
|Criteria||Comparison of Alternatives||CR (%)||Principal Eigen value||Iterations||Delta||Priority (%)|
Local Hospital Survey
TABLE 10: TABLE SHOWING EIGEN VECTOR WEIGHT FOR EACH OF THE CRITERIA AND ALTERNATIVES CONSIDERED
|Criteria||Weights of Criteria||Alternatives||Overall Eigen vector Priority of risk factor||Rank|
CONCLUSION: In this study, we first find the regression of death rate of cancer by making use of different kinds of cancers data. Investigation performed on three types of cancer viz. breast, colorectum as well as lung and bronchus cancer. The conclusions drawn from the above analysis are as follows:
a. Lung and bronchus cancer is significant over other type of cancer.
b. Smoking is the most risk factor for lung and bronchus cancer.
ACKNOWLEDGEMENT: Thank you very much to the reviewers for the kind suggestion to improve our manuscript.
CONFLICT OF INTEREST: I have no conflict of interest into the manuscript.
- Nair LS, Mahesh S, Smitha LS, Sujathan K and Remani P: Expression of Canavalia gladiata lectin in leukemic cells. J Cancer Sci Ther 2011; 3(4).
- Shewale MT and Patil SB: Detection of Brain Tumor Based On Segmentation Using Region Growing Method. International Journal of Engineering Innovation and Research 2016; 5(2): 173-6.
- McBee Jr WC, Gardiner AS, Edwards RP, Lesnock JL and Bhargava R: MicroRNA analysis in human papilloma virus (HPV)-associated cervical neoplasia and cancer. J Carcinogene Mutagene 2011; 1(1).
- Deepthi CN, Pavan VVL, Kumar A, Babu R and Indirapriyadarshin IU: Role of Tumor Suppressor Protein p53 in Apoptosis and Cancer Therapy. J Cancer Sci Ther S 2011; 17: 2.
- Turconi G: Healthy Aging: Nutritional Intervention to Improve and Extend Quality of Life among Older People. Nutrition and Food Sciences 2010.
- Liu CY, Chang LC and Yang SW: Metastatic hepato-cellular carcinoma to the nasal cavity: a case report and review of the literature. Journal of Cancer Science and Therapy 2011; 3(4): 81-3.
- Schinasi L and Leon ME: Non-Hodgkin lymphoma and occupational exposure to agricultural pesticide chemical groups and active ingredients: a systematic review and meta-analysis. International journal of environmental research and public health 2014; 11(4): 4449-527.
- Nair A: Amplified Hypoxia Induced Tumor-Cell Death 2010.
- Ahmed HG, Mohammed AI and Hussein MO: A comparison study of histochemical staining of various tissues after Carnoy’s and formalin fixation. Sudan Journal of Medical Sciences 2011; 5(4).
- Nagy MA: HIF-1 is the Commander of Gateways to Cancer. J Cancer Sci Ther 2011; 3(2): 35-40.
- Veettil SK, Lim KG, Chaiyakunapruk N, Ching SM and Hassan MR: Colorectal cancer in Malaysia: its burden and implications for a multiethnic country. Asian journal of surgery 2017; 40(6): 481-9.
- Garcia M, Jemal A, Ward EM, Center MM, Hao Y, Siegel RL and Thun MJ: Global cancer facts and Wgs. American Cancer Society, Atlanta 2007.
- Ferlay J: (GLOBOCAN 2002) Cancer incidence, mortality and prevalence worldwide. IARC Cancer Base No. 5, version 2.0. http://www-depdb.iarc.fr/globocan/GLOBO frame.htm. 2004.
- Talhouk A, McConechy MK, Leung S, Yang W, Lum A, Senz J, Boyd N, Pike J, Anglesio M, Kwon JS and Karnezis AN: Confirmation of ProMisE: A simple, genomics - based clinical classifier for endometrial cancer. Cancer 2017; 123(5): 802-13.
- Brier MJ, Chambless DL, Gross R, Chen J and Mao JJ: Perceived barriers to treatment predict adherence to aromatase inhibitors among breast cancer survivors. Cancer 2017; 123(1): 169-76.
- Kaniski F, Enewold L, Thomas A, Malik S, Stevens JL and Harlan LC: Temporal patterns of care and outcomes of non-small cell lung cancer patients in the United States diagnosed in 1996, 2005, and 2010. Lung Cancer 2017; 103: 66-74.
- Samson P, Keogan K, Crabtree T, Colditz G, Broderick S, Puri V and Meyers B: Interpreting survival data from clinical trials of surgery versus stereotactic body radiation therapy in operable Stage I non-small cell lung cancer patients. Lung Cancer 2017; 103: 6-10.
- Siegel RL, Miller KD and Jemal A: Cancer statistics, 2016. CA: A Cancer Journal for clinicians 2016; 66(1): 7-30.
- El-Hajj ZW and Newman EB: How much territory can a single coli cell control? Frontiers in microbiology 2015; 6: 309.
- Record RA, Scott AM, Shaunfield S, Jones MG, Collins T and Cohen EL: Lay Epistemology of Breast Cancer Screening Guidelines Among Appalachian Women. Health communication 2017; 32(9): 1112-20.
- Torre LA, Bray F, Siegel RL, Ferlay J, Lortet-Tieulent J and Jemal A: Global cancer statistics, 2012. CA: a cancer journal for clinicians 2015; 65(2): 87-108.
- Luo SX, Liu JE, Cheng AS, Xiao SQ, Su YL and Feuerstein M: Breast Cancer Survivors Report Similar Concerns Related to Return to Work in Developed and Developing Nations. Journal of occupational rehabilitation 2018; 14: 1-0.
- Kelsey JL: A review of the epidemiology of human breast cancer. Epidemiologic reviews 1979; 1: 74-109.
- Society AC: Colorectal Cancer Facts & Figures 2014–2016. Color Cancer Facts Fig 2014; 1-32.
- Siegel RL, Miller KD and Jemal A: Cancer statistics, 2018. CA: a cancer journal for clinicians 2018; 68(1): 7-30.
- Ferlay J, Soerjomataram I, Dikshit R, Eser S, Mathers C, Rebelo M, Parkin DM, Forman D and Bray F: Cancer incidence and mortality worldwide: sources, methods and major patterns in GLOBOCAN 2012. International journal of cancer 2015; 136(5).
- Lemjabbar-Alaoui H, Hassan OU, Yang YW and Buchanan P: Lung cancer: biology and treatment options. Biochimica et Biophysica Acta (BBA)-Reviews on Cancer 2015; 1856(2): 189-210.
- Belinsky SA: Unmasking the lung cancer epigenome. Annual review of physiology 2015; 77: 453-74.
- Stewart BW, Wild CP. World cancer report 2014. Health 2017.
- Sheron N: Alcohol and liver disease in Europe–Simple measures have the potential to prevent tens of thousands of premature deaths. Journal of hepatology 2016; 64(4): 957-67.
- Rao RV, Savsani VJ and Vakharia DP: Teaching learning-based optimization: a novel method for constrained mechanical design optimization problems. Computer-Aided Design 2011; 43(3): 303-15.
- Rao RV, Savsani VJ and Vakharia DP: Teaching learning-based optimization: an optimization method for continuous non-linear large scale problems. Information Sciences 2012; 183(1): 1-5.
- Saaty TL: The analytic hierarchy process New York. Nachhaltigkeit im Einkauf von Logistik dienstleistungen 1980; 137.
- Saaty TL: Decision making for leaders. IEEE Transactions on Systems, Man, and Cybernetics 1985; 3: 450-2.
- Saaty TL: How to make a decision: the analytic hierarchy process. European Journal of Operational Research 1990; 48(1): 9-26.
- Saaty TL and Kearns KP: Analytical planning: The organization of system. Elsevier 2014.
- Aronchick JM: Lung cancer: epidemiology and risk factors. In Seminars in roentgenology Elsevier 1990; 25(1): 5-11.
- Gasperino J: Gender is a risk factor for lung cancer. Medical hypotheses 2011; 76(3): 328-31.
- Ruano-Ravina A, Figueiras A and Barros-Dios JM: Lung cancer and related risk factors: an update of the literature. Public health 2003; 117(3): 149-56.
- Ruano-Ravina A, Figueiras A and Barros-Dios JM: Lung cancer and related risk factors: an update of the literature. Public health 2003; 17(3): 149-56.
- Spiro SG: The management of lung cancer. Lung 1982; 160(1): 141-55.
- Hecht SS: Tobacco smoke carcinogens and lung cancer. JNCI: Journal of the National Cancer Institute 1999; 91(14): 1194-210.
How to cite this article:
Majumder P, Saha AK and Majumder M: A mathematical approach of exploration towards extreme risk factor in cancer of optimal condition. Int J Pharm Sci & Res 2018; 9(9): 3732-42. doi: 10.13040/IJPSR.0975-8232.9(9).3732-42.
All © 2013 are reserved by International Journal of Pharmaceutical Sciences and Research. This Journal licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
P. Majumder *, A. K. Saha and M. Majumder
Department of Mathematics, National Institute of Technology, Agartala, Barjala, Jirania, Tripura, India.
23 December, 2017
02 March, 2018
11 March, 2018
01 September, 2018