The glucose level linkages with breast cancer markers

The glucose level linkages with breast cancer (BC) biomarkers are focused in the article adopting probabilistic modeling with a real data set surveyed from 64 BC women and 52 normal women along with 10 interested study factors. It is derived that mean glucose levels are over for BC women (P=0.02224) than normal. Mean glucose levels are inversely linked with insulin (P< 0.00001), interaction effects of leptin and adiponectin (leptin*adiponectin) (P=0.08834), homeostasis model assessment score insulin resistance (HOMA-IR) and leptin (HOMA-IR*leptin) (P<0.00001), while they are directly linked with HOMA-IR (P<0.00001) and leptin (P<0.00001). The variance of glucose levels is inversely linked with leptin (P=0.00022), insulin (P=0.01365), monocyte chemoattractant protein-1 (MCP-1) (P=0.01153), insulin*HOMA-IR (P=0.00022), age*resistin (P=0.03974), age*HOMA-IR(P=0.03102), while it is directly linked with HOMA-IR (P<0.00001), resistin (P=0.02182) and age (P=0.00133). Glucose levels are higher for BC women, and they increase along with the increased levels of HOMA-IR, leptin, and the decreased levels of insulin, HOMA-IR*leptin, leptin*adiponectin.


Introduction
Worldwide, diabetes mellitus (DM) and cancer are normal diseases with an outrageous impression on human health. Epidemiologic studies present that DM individuals are always at higher risk of cancer [1][2][3][4]. Several research reports have illustrated that there is a direct link between obesity and cruelty of BC [5][6][7]. A current report has established the linking between BC markers and body mass index (BMI) [7]. Linking between the BC prognosis and metabolic syndrome has been recorded in [8][9][10][11]. It is noted that metabolic syndrome is acquainted as a summation of at least three of the following metabolic risks such as obesity, high serum triglycerides, elevated serum glucose, higher blood pressure, lower highdensity lipoprotein cholesterol [8,10]. The principal mechanisms of the linking between obesity, BC progression and metabolic syndrome have yet to be completely demonstrated, and the previous epidemiological studies remain contradicting [12][13][14][15][16]. A mechanism proposes that it is for higher oestrogen levels that are adjusted from cholesterol [17]. Glucose metabolisms, insulin, resistin, lipid and leptin are postulated as probable intermediate mechanisms that are responsible for developing links between BC markers and obesity [9,11,13,[18][19][20]. A positive linking between triglycerides and BC markers has been noted in [16]. Also, high insulin and leptin levels are linked with reduced levels of high-density lipoprotein that is supposed to increase risk of BC [19,20].
Cancer research articles are mainly based on preliminary statistics such as usual multiple regression [8,11,16], Cox model analysis [4], logistic regression, Kaplan Meier analysis [20], which are inappropriate for physiological heteroscedastic data analysis. Very few earlier research articles have focused the interaction effects as the component of the linking between glucose levels and BC markers. Recently, some BC marker probabilistic models for resistin, MCP-1, leptin and adiponectin have shown many complicated linkages with glucose levels [21][22][23][24]. The current report derives all the findings herein based on the probabilistic models of glucose levels with the BC markers along with the rest factors. The report is arranged as follows. The next section presents materials & methods, and the subsequent sections present results & discussions, and conclusions. study subjects were not identified with BC family history and malignant disease.

Materials
The selected BC women with normal BMI, or obesity had been treated in the Gynaecology Department of the same hospital. These study subjects were detected BC for the first time adopting positive mammography and histologically confirmed tests. Moreover, these BC patients were free from any infection, or acute disease during the entry study time. The same doctor researcher extracted all the interested clinical information along with anthropometric data from each selected unit during the first counseling. Finally, only 116 (64 BC and 52 normal women) were taken in the study, and the rest 38 study units were excluded due to obesity with BMI>40 kg/m 2 .

Statistical methods
The report aims to derive the probabilistic model of glucose levels based on the remaining as the explanatory variables. It is identified that the response glucose level is heteroscedastic, which should be modeled applying joint generalized linear models (JGLMs) that is clearly presented in [27][28][29]. It is found that the joint gamma model fit gives better results so it is presented very shortly herein.

Joint Gamma Models:
Here glucose level = i y say, is the interested study continuous random response variable along with its unequal variance ( termed as variance function. Note that the variance has two parts namely,  , it is gamma, and it is Poisson, or Normal obeying as Joint mean and dispersion of glucose level= i y models following gamma distribution are presented by Maximum likelihood (ML) method is applied to estimate mean parameters, while the restricted ML (REML) method is adopted to estimate dispersion parameters [27].

Statistical and graphical analysis
The random response glucose level is treated as the dependent variable and the rest others are treated as the explanatory variables. Note that the response glucose level is heterogeneous, which is modeled by JGLMs under gamma distribution. The best model is selected based on the lowest Akaike information criterion (AIC) value that reduces both the squared error loss and predicted additive errors [30, p. 203-204]. A few insignificant effects are added in both the models due to marginality rule introduced by Nelder [31]. JGLMs for glucose level gamma fit outcomes are summarized in Table 1. The derived glucose level JGLM gamma fit (Table 1) is a data obtained model, so it should be accepted through graphical diagnostic checking, which is revealed in Figure 1. Figure 1(a) presents the glucose level gamma fitted absolute residuals against the glucose level fitted values, which is a flat straight line except right tail. This reveals that variance is equal with the running means. In addition, absolute residuals are randomly dispersed at a point of the fitted value, except only two absolute residuals. Figure 1(b) represents the glucose level gamma fitted mean normal probability plot ( Table 1) that does not identify any lack of fit. Figures 1(a) and 1(b) confirm that gamma fitted glucose level JGLMs are close to the true model (Table 1).  (Table 1) Table 1  Gamma fitted glucose level mean () model (from Table 1 From Table 1, it is found that mean glucose levels are directly linked with SUT (1=normal; 2= BC patients) (P=0.02224), interpreting that glucose levels are over for BC women than normal. This is frequently noticed in reality, which implies that DM study units have a higher BC risk. Mean glucose levels are inversely linked with insulin (P<0.00001), concluding that glucose levels decrease as the insulin levels increase. This is the mechanism of balancing glucose levels of human beings. Mean glucose levels are directly linked with HOMA-IR (P<0.00001), or leptin (P<0.00001), it concludes that glucose levels increase if HOMA-IR, or leptin levels rise. Even though the HOMA-IR and leptin levels are directly linked with mean glucose levels, their joint interaction effect HOMA-IR*leptin (P<0.00001) is inversely linked with it. In addition, adiponectin (P=0.43713) is insignificantly linked with mean glucose levels, but the interaction effect leptin*adiponectin (P=0.08834) is inversely partially linked with mean glucose levels.

Results & Discussion
The variance of glucose levels is directly linked with age (P=0.00133) and HOMA-IR (P<0.00001), while their joint interaction effect age*HOMA-IR (P=0.03102) is inversely linked with it. These indicate that glucose levels are highly scattered in older women, and also for the subjects with higher HOMA-IR scores. But due to their joint interaction effect, variance of glucose levels is not so highly scattered. In addition, similarly as age, resistin (P=0.02182) is also directly related with the variance of glucose levels, while their joint interaction effect age*resistin (P=0.03974) is inversely linked with it. The interpretations are similar to age & HOMA-IR. Again, HOMA-IR is directly related, and insulin (P=0.01365) is inversely related with the variance of glucose levels, while their joint interaction effect insulin*HOMA-IR (P=0.00022) is inversely associated with it. On the other hand, leptin (P=0.00022) and MCP-1 (P=0.01153) are inversely linked with the variance of glucose levels, concluding that scatteredness of the glucose levels is higher if the leptin levels, or MCP-1 levels decrease. fully new in the diabetes and BC literature, therefore these outcomes are little reported in the similar earlier published reports.

Conclusions
The linkages of glucose levels with some BC markers along with BMI, age and insulin are focused in the report based on JGLMs. Note that the accepted gamma fitted model satisfies lowest AIC value, graphical testing, and smaller standard error of the estimates. The current results of glucose levels are very little focused in the earlier reports. It is expected that these linkages of glucose level will be held for any similar data set, which is not verified herein as we have not any similar data in hand. Glucose levels are higher for BC women, and they increase along with the increased levels of HOMA-IR, leptin, and the decreased levels of insulin, HOMA-IR*leptin, leptin*adiponectin. Medical experts can interpret the role of glucose levels for BC women from this report. Moreover, it may provide very clear activities of glucose levels for the BC women. DM women should be more careful on BC risk.