Diastolic Blood Pressure Determinants for Prostate Cancer Patients

Research Article

Austin J Clin Cardiolog. 2022; 8(3): 1099.

Diastolic Blood Pressure Determinants for Prostate Cancer Patients

Das M1, Gong R2, Sahoo RK3, Devi RS4, Banik S5 and Das RN6*

1Department of History, The University of Burdwan, Burdwan, West Bengal, India

2Department of Informatics and Mathematics, Mercer University, Macon, GA, USA

3Shool of Statistics, G. M. University, Sambalpur, Odisha, India

4Department of Statistics, Moreh College, Moreh, Manipur, India

5Department of Physical Sciences, Independent University, Bangladesh, Dhaka, Bangladesh

6Department of Statistics, The University of Burdwan, Burdwan, West Bengal, India

*Corresponding author: Rabindra Nath Das, Department of Statistics, The University of Burdwan, Burdwan, West Bengal, India

Received: October 20, 2022; Accepted: November 19, 2022; Published: November 26, 2022

Abstract

The association between the hypertension risk factors such as diastolic and systolic blood pressure with the Prostate Cancer (PC) risk factors is controversial. The report derives the determinants of the Diastolic Blood Pressure (DBP) of the PC patients. It is derived herein that mean DBP is directly associated with serum Haemoglobin (HG) (P=0.017), and Systolic Blood Pressure (SBP) (P<0.001), while it is negatively associated with the subject’s age (P<0.001). Variance of DBP is higher for normal subjects (P=0.004) than PC patients. Variance of DBP is higher for Cardiovascular Disease (CVD) history (P=0.060) subjects than normal, PC patients with Bone Metastases (BM) (P=0.002) than normal, and heart patients identified by Electrocardiogram (EKG) (P=0.046) than normal and benign. These associations of DBP for PC patients are derived based on the statistical Joint Generalized Linear Models (JGLMs) method. It is concluded herein that mean DBP is independent of PC risk factors, while it is observed that DBP is highly scattered for PC patients with BM. For PC patients with hypertension, care should be taken on DBP, SBP and HG only.

Keywords: Bone metastases (BM); Diastolic blood pressure (DBP); Prostatic acid phosphatase (PAP); Prostate cancer (PC); Systolic blood pressure (SBP); Non-constant variance

Introduction

Hypertension and PC are commonly critical conditions among senior men throughout the world [1]. Generally, PC is the most common cancer in senior men, and most of them are suffering from hypertension [2-5]. Consequently, SBP and DBP are at higher levels for these hypertension PC patients [6-11]. The universal agestandardized prevalence of elevated hypertension risk factor, namely blood pressure (BP) (SBP ≥140 mmHg or DBP ≥90 mmHg) in men was estimated as ≥20% in 2015 [12].

It is well known for several decades that the elevated BP is a sign for development of any disease, which reflects a long cumulative exposure in ageing-related diseases such as PC and diabetes [13]. Note that hypertension is associated with inflammation that is a hallmark of cancer development [5,14]. The inflammatory cells in the prostate microenvironment linked to precursor lesions for PC in the prostate gland, known as proliferative inflammatory atrophy, have been found [13,14]. It was observed that systemic prediagnostic inflammatory biomarkers including high sensitive C-reactive protein and white blood cells were linked to PC development [6,13,14].

The earlier reported linkages between hypertension and PC risk factors was controversial [2,8]. The present article aims to derive the explanatory factors (or determinants) of DBP for PC patients using an appropriate probabilistic model. In the PC literature, the relationship of DBP with PC biomarkers or risk factors is not clear. In addition, most of the earlier articles tried to derive the association of DBP for PC patients based on percentage, meta-analysis, correlation, confidence intervals etc, which are not appropriate [1,2,8,10-12,15- 18]. The article investigates the following hypertension PC research queries.

• Is DBP associated with PC biomarkers? What are the determinants of DBP for PC patients? This is the principal hypertension query in PC epidemiology.

• How can one obtain the determinants of DBP?

• What are the effects of DBP on PC patients?

The article examines these above queries adopting the sections materials & methods, statistical analysis, results & discussions, and conclusions. The identified DBP determinants are presented in (Table 1), while the explanatory factors are derived by joint generalized linear models (JGLMs), and the effects of DBP are focused in the discussion section.

Materials and Methods

Materials

The present study considers a data set on a randomized clinical trial performed on 474 PC subjects with third or fourth stage PC. The contributor of the data set was D.P. Byar, who published a few analyses of the data set along with his coauthors [19,20]. The data set was well described in the book by Andrews and Herzberg [21]. For every subject, the following factors were noted: 1. Study unit’s stage (=S-stage=F1) (0= no cancer; 1= PC); 2. Estrogen (mg) (=RX=z2); 3. Months of follow up (=D-time=z3); 4. Survival status (Alive=F4) (0=Alive; 1= Dead due to PC; 2= Dead due to heart or vascular; or cerebrovascular; or pulmonary embolism; or other cancer; or respiratory disease; or other specific non-cancer; or unspecified non-cancer; or unknown cause); 5. Age(=z5); 6. Weight (= Wt= z6); 7. Performance Rating (=PFR=F7) (0= normal activity; 1= confined to bed; 2= in bed < 50% daytime; or in bed >50% daytime); 8. Cardiovascular Disease History (=CVDH=F8) (0=no, 1=yes); 9. Systolic Blood Pressure (=SBP=x9); 10. Diastolic Blood Pressure (=DBP=z10); 11. Electrocardiogram Code (= EKG=(F11) (0=normal; 1=benign; 2= rhythmic disturb & electrolyte; or heart block; or conduction; or heart strain; or old Myocardial Infarction (MI); or recent MI); 12. Serum Haemoglobin (=HG=z12); 13. Size of primary tumour (SZ=z13); 14. Index of tumour stage and histolic grade (= SG= z14); 15. Serum prostatic acid Phosphatase (=PAP=y); 16. Bone metastases (=BM=F16) (0=no, 1=yes); 17. Date of study (S-date=z17). In the data set there are some attribute and continuous variables. In the current study, DBP is treated as the dependent or response variable, and the rest others are treated as the explanatory or dependent factors/ variables.

Statistical Methods

The considered response variable DBP is identified as heteroscedastic as the under taken PC data set is physiological. Therefore, the heteroscedastic response DBP can be modeled using stabilizing variance under a suitable transformation, but it is not always stabilized [22]. Note that the dependent variable DBP is nonconstant variance, which can be suitably modeled by Joint Generalized Linear Models (JGLMs) under lognormal, or gamma distribution [23,24]. JGLMs is described in the books by Lee et al. [23], and Das [25]. Very shortly, these two JGLMs are described as follows.

Log-normal JGLMs: For the positive response Yi (=DBP) with E(Yi=DBP) = μi (mean) and Var(Yi=DBP) = 2i sμi² = 2i s( ) i V μ say,where 2i s’s are dispersion parameters and V ( ) shows the variance function, commonly,

the log transformation Zi = log(Yi=DBP) is used to stabilize the variance Var(Zi) ≈ 2i s , while it may not be stabilized always [22]. For obtaining an advanced model, JGLMs for the mean and dispersion are derived. Herein for the response DBP, considering log-normal distribution, JGL mean and dispersion models (with Zi = log (Yi=DBP)) are as follows:

E(Zi)= μzi and Var(Zi) = szi²,

μzi=xit β and log (szi²)= git γ,

where xit and git are the explanatory factors/variables vectors attached with the regression coefficients β and γ, respectively.

Gamma JGLMs: For the above stated Yi’s (=DBP), the variance consists of two parts such as Vi) (depending on the mean parameters) and si² (independent of μi’s). The variance function V( ) indicates the GLM family distributions. For illustration, if V(μ ) =μ , it is Poisson, gamma if V(μ ) = μ² , and normal if V(μ )= 1 etc. Gamma JGL mean and dispersion models for DBP are as follows:

where g(-) and h(-) are the GLM link functions for the mean and dispersion linear predictors respectively, and xit, wit are the vectors of explanatory factors/variables connected to the mean and dispersion parameters, respectively. Maximum likelihood (ML) method is applied for computing mean parameters, and the Restricted ML (REML) method is adopted for obtaining dispersion parameters, which are illustrated in the book by Lee et al., [23].

Statistical & Graphical Analysis

The response DBP is modeled on the rest all explanatory factors/ variables adopting JGLMs using both the distributions such as gamma and log-normal. The best DBP fitted model is accepted based on the lowest Akaike Information Criterion (AIC) value that reduces both the predicted additive errors and the squared error loss [26; p.203-204]. Following the AIC criterion, JGL gamma model fit (AIC= 1433.133) of DBP is better than log-normal fit (AIC= 1448). Both the best DBP fitted JGLMs analysis results are shown in (Table 1). All the included factors in both the models are significant.

Citation: Das M, Gong R, Sahoo RK, Devi RS, Banik S and Das RN. Diastolic Blood Pressure Determinants for Prostate Cancer Patients. Austin J Clin Cardiolog. 2022; 8(3): 1099.