Association between cholesterol and cardiac parameters.

Transcription

1 Short communcaton Assocaton between cholesterol and cardac parameters. Rabndra Nath Das* Department of Statstcs, The Unversty of Burdwan, Burdwan, West Bengal, Inda Abstract It s well-known that atheroscleross s a prmary form of cardovascular dsease, n whch cholesterol plaques form n the artery walls, and consequently restrct blood flow. Ths leads to less oxygen for the heart muscle, yeldng cardac problems. The current report examnes the assocatons of total cholesterol and ts components wth the cardac parameters. In addton, the effects of the total cholesterol and ts components on cardac parameters are focused n the present report. Keywords: Cardac parameter, Cardovascular dsease, Jont generalzed lnear models, Hgh-densty lpoproten, Low-densty lpoproten, Total cholesterol, Very low-densty lpoproten. Accepted on March 10, 2017 Introducton There s no specfc cardovascular dsease (CVD) marker. Generally, total cholesterol (TC) s used as a cardac dsease marker as t s a prncpal cause of atheroscleross and heart dsease [1-4]. Several studes have shown the assocaton between TC and CVD [5-10]. Recently, the Prospectve Studes Collaboraton (usng meta-analyss) has shown the assocaton between CVD and TC n all ages and n both sexes [11]. Though the assocaton between TC and CVD mortalty s observed n all ages and n both sexes [11], buhe rsk decreases as the age ncreases, and t s mnmal more than age of 80 years [12]. However, there are several contradctons to the assocaton between TC and CVD. Specfcally, most of the Japanese epdemologcal studes have focused thahe hgh TC s not a rsk factor for stroke [13-16]. It s well-known that TC s the sum of low-densty lpoproten (LDL-C), hgh-densty lpoproten (HDL-C), and very lowdensty lpoproten (VLDL-C). Trglycerde s not ncluded n TC. TC below 200 (mg/dl) s treated as normal, and more or equal to 200 (mg/dl) s recognzed as hgh. The Centers for Dsease Control and Preventon has analyzed data from , and t has examned ncdence, prevalence, treatment, and control of hgh LDL-C levels [17]. It s observed that approxmately 71 mllon Amercan adults (33.5%) had hgh LDL-C levels, but only 34 mllon (48.1%) goreatment, and 23 mllon (33.2%) had ther LDL-C controlled [17]. It s known that TC and CVD are assocated n all ages n both the sexes [12], but a hgh LDL-C level s assocated wth a hgher rsk of CVD, whle a hgh level of HDL-C s assocated wth a lower rsk of CVD [18]. The medcal practtoners frst measure the total cholesterol levels to assess a patent s cardac rsk. For more specfc gudance, the doctors dvde the TC level by the HDL-C level. The CVD rsk s mnmzed by havng a lower TC level, and a hgher proporton of HDL-C level. The rato of TC to HDL-C should be less than 4 to 1. It s mentoned as n the above thahere may or may not be assocaton between the cholesterol and ts components wth the cardac parameters. The present report consders the followng hypotheses. Is there any assocaton between the cholesterol and ts components wth the cardac parameters? What are the effects 3 of cholesterol and ts components on the cardac parameters? These ssues are examned n the current report based on real data analyss. Background Most of the earler research artcles have used the statstcal technques such as meta-analyss, smple product moment correlaton coeffcent, Logstc regresson, classcal smple & multple regresson analyses, Ch-square test [3,5,7,9,11,17] whch are not approprate for the analyss of postve, heteroscedastc, correlated, non-normally dstrbuted data [19-21]. The physologcal contnuous random varables such as total cholesterol, low-densty lpoproten, hgh-densty lpoproten, rato of TC to HDL-C, blood pressures (basal, systolc, dastolc, maxmum), heart rates (basal, peak, maxmum), cardac ejecton fractons are mostly heterogeneous, postve, and non-normally dstrbuted [22-24]. Recently, a few artcles [6,9,11,22,24] have consdered the responses as postve, heteroscedastc and nonnormally dstrbuted, buhe assocatons of TC, LDL-C, HDL-C and the rato of TC to HDL-C wth the cardac parameters have not clearly focused. Based on the recent artcles [6,22,24,25], and along wth some new analyses, the present report focuses the assocatons of TC, LDL-C, HDL-C and the rato of TC to HDL-C wth the cardac parameters. Most of the earler research artcles have assumed the dstrbuton of the random varables (cholesterol and ts components) as Normal. Practcally, these random varables are non-normally dstrbuted [6,24]. Earler used statstcal technques are mostly based on Normal dstrbuton. The present data sets are postve, and ther varances are non-constant, dstrbutons are non-normal, and the earler used statstcal methods are napproprate. These ssues have motvated us to examne the assocaton between the cholesterol and ts components wth the cardac parameters. Methodology The responses TC, LDL-C, HDL-C, the rato of TC to HDL-C and cardac parameters are postve, heterogeneous and nonnormally dstrbuted. These responses are generally modeled ether by the gamma or the Log-normal jont generalzed lnear models (JGLMs) [20,22]. These two models and the analyss technques are well descrbed n [20-22]. Usng lnk functons, J Cholest Heart Ds 2017 Volume 1 Issue 1

2 Ctaton: Das RN. Assocaton between cholesterol and cardac parameters. J Cholest Heart Ds. 2017;1(1):3-7 two models one for the mean and the other for the varance are derved usng teraton process. For ready reference, these two models are shortly reproduced heren. For analyzng the postve response y 's, Nelder and Lee [26] have derved a modelng technque, known as the jont generalzed lnear models (JGLMs) whch s as follows. For the postve response Y, generally, the log transformaton Z =logy s used. Assumng the log-normal dstrbuton of Z a jont modelng of the mean and varance s such that E(Z )=µ z and Var(Z )=σ z2, µ z =x β and log (σ z2 )=g γ, where x and g are the row vectors for the regresson coeffcents β and γ n the mean and dsperson model, respectvely. For a postve response y, f 2 E ( ) = µ and Var ( y ) = σ V ( µ ), y where V ( ) s the varance functon and s are the dsperson parameters, and V( µ )= µ 2, then the jont gamma models for the mean and the varance parameters are 2 t 2 t ε = h ( σ ) = w γ and ε = h ( σ ) = w γ, t where g ( ) and x are GLM lnk functons for the mean and the varance, respectvely; and x, w are respectvely, the row vectors assocated wth the mean parameter β and the varance parameter γ. Maxmum lkelhood (ML) method s used for estmatng the mean parameters β, whle the restrcted ML (REML) s used for estmatng the dsperson parameter γ [20]. Materals The present report has consdered two secondary data sets whch are gven respectvely [6,24]. The data descrptons, collecton methods, patents populaton are clearly descrbed n the related papers. For ready reference, the factors/ covarates are descrbed heren. Frst data set The data set contans 366 subjects along wth 20 factors/ covarates wth all non-mssng nformaton (Table 1) [6]. It can be downloaded at wk/ Man/DataSets?CGISESSID=10713f6d891653ddcbb7ddbdd9cf fb79. The factors/ varables of the data set are age, sex (male=1, female=2), total cholesterol (TC), hgh densty lpoproten (HDL-C), lpd rato= cholesterol/hdl-c (Rato), glycosolated hemoglobn (GLYHB), stablzed glucose (STB.GL), subject's heght (Heght), subject's weght (Weght), body mass ndex (BMI), frame (1=small, 2=medum, 3=large) (Frame), locaton (1=Buckngham, 2=Lousa) (Locaton), frst dastolc blood pressure (BP.1d), frst systolc blood pressure (BP.1s), second dastolc blood pressure (BP.2d), second systolc blood pressure (BP.2s), subject's hp measurement (Hp), subject's wast measurement (Wast), ndex of fat dstrbuton (=wast/hps rato) (IFD), postprandal tme when labs were drawn (TIM.PN). The data set contans total cholesterol (TC), hgh densty lpoproten (HDL-C), lpd rato=cholesterol/hdl-c (Rato), and cardac parameters such as frst dastolc blood pressure (BP.1d), and frst systolc blood pressure (BP.1s). Only the analyss of TC s gven n [6]. The analyses of HDL-C, lpd σ 2 rato, BP.1d, and BP.1s have been derved based on both the log-normal and gamma models. Based on the current analyses and TC analyss from [6], the followng assocatons between TC and ts components wth the cardac parameters are reported as follows. * From [6], TC analyss shows the followng assocatons. The mean TC s separately negatvely nsgnfcantly assocated wth HDL-C (P=0.920) and the lpd rato (P=0.318), whle t s postvely sgnfcantly assocated wth the jont nteracton effect of HDL-C and lpd rato (P<0.001). The varance of TC s negatvely nsgnfcantly assocated wth the frst systolc blood pressure (BP.1s) (P=0.968), whle t s negatvely sgnfcantly assocated wth the frst dastolc blood pressure (BP.1d) (P<0.001), ndcatng thahe patents wth hgher BP.1d have lower TC varance. Buhe jont nteracton effect of BP.1s & BP.1d (P=0.084) s postvely sgnfcantly assocated wth the TC varance. *The hgh densty lpoproten (HDL-C) analyss shows the followng assocatons. The mean HDL-C s postvely sgnfcantly assocated wth the TC (P<0.001), and t s nversely sgnfcantly assocated wth the lpd rato (P<0.001). The mean HDL-C s negatvely nsgnfcantly assocated wth the frst systolc blood pressure (BP.1s) (P=0.188), whle t s postvely sgnfcantly assocated wth the frst dastolc blood pressure (BP.1d) (P=0.039). The varance of HDL-C s postvely sgnfcantly assocated wth the frst dastolc blood pressure (BP.1d) (P=0.058). *The lpd rato (TC/HDL-C) analyss shows the followng assocatons. The mean lpd rato s postvely sgnfcantly assocated wth the TC (P<0.001), and t s nversely sgnfcantly assocated wth the HDL-C (P<0.001). The varance of the lpd rato s negatvely sgnfcantly assocated wth the frst dastolc blood pressure (BP.1d) (P=0.002). *The frst dastolc blood pressure (BP.1d) analyss shows the followng assocatons. The mean frst dastolc blood pressure (BP.1d) s postvely nsgnfcantly assocated wth the TC (P=0.198). It s postvely sgnfcantly assocated wth the HDL-C (P=0.031) and the frst systolc blood pressure (BP.1s) (P<0.001). The varance of BP.1d s postvely nsgnfcantly assocated wth the BP.1s (P=0.192). *The frst systolc blood pressure (BP.1s) analyss shows the followng assocatons. The mean BP.1s s postvely nsgnfcantly assocated wth the TC (P=0.348), and t s postvely sgnfcantly assocated wth the BP.1d (P<0.001). All the above summarzed results are gven n Table 1. Second data set The data set s taken from Modelng of Bochemcal Parameters [24]. It contans 64 subjects wth 21 factors/ varables whch are age, sex, weght, heght, body mass ndex, obesty, lfestyle, detary habts lke eatng n outsde (no=0, yes=1), smokng habt (no=0, yes=1), types of ol consumpton, famly blood pressure (no=0, yes=1) (BP), famly hstory (FH) of dabetes melltus (no=0, yes=1) (DM), hypertenson wth coronary heart dsease (no=0, yes=1) (CHD), hstory of any drug ntake (no=0, yes=1), hstory of past llness (no=0, yes=1), fastng plasma glucose level (PGL), serum trglycerde (STG), total cholesterol (TC), low densty lpoproten (LDL-C), hgh densty lpoproten (HDL-C), fastng serum nsuln (FI). J Cholest Heart Ds 2017 Volume 1 Issue 1 4

3 Das Table 1. Assocatons of TC, HDL-C, lpd raton wth cardac parameters (1 st data set). Response Assocated wth Estmate Standard error t-value P-value Assocaton type HDL-C Insgnfcant Mean TC Lpd rato Insgnfcant HDL-C*rato <0.001 Postve BP.1s Insgnfcant Varance of TC BP.1d <0.001 Negatve BP.1s*BP.1d Postve TC <0.001 Postve Mean HDL-C Lpd rato <0.001 Negatve BP.1s Insgnfcant BP.1d Postve Varance of HDL-C BP.1d Postve Mean Lpd rato TC <0.001 Postve HDL-C <0.001 Negatve Varance of rato BP.1d Negatve TC Insgnfcant Mean BP.1d HDL-C Postve BP.1s <0.001 Postve Varance of BP.1d BP.1s Insgnfcant Mean BP.1s TC Insgnfcant BP.1.d <0.001 Postve Assocatons The above data set contans TC, LDL-C, HDL-C, and two cardac parameters famly blood pressure (no=0, yes=1) (BP), hypertenson wth coronary heart dsease (no=0, yes=1) (CHD). The analyses of TC, LDL-C and HDL-C are gven n [24]. Famly blood pressure and hypertenson wth coronary heart dsease are both categorcal characters. The analyses of these two cardac parameters are not gven n Modelng of Bochemcal Parameters [24]. Based on the analyses of TC, HDL-C and LDL-C [24], the assocatons of TC and ts components wth the two cardac parameters are presented heren. *Analyss of total cholesterol (TC) (Table 2) [24] shows that mean TC (or varance of TC) s postvely assocated wth HDL-C (P=0.001). Analyss of LDL-C [24] shows that mean LDL-C s postvely assocated wth TC (P<0.001), whle t s negatvely assocated wth the HDL-C (P<0.001). The mean LDL-C s postvely assocated the coronary heart dsease (CHD) (P<0.001), whle t s negatvely assocated wth the famly blood pressure (BP) (P<0.001). HDL-C analyss does not show any sgnfcant assocaton wth any cardac parameter for ths data set. All the summarzed results for ths data set s gven n Table 2. Concludng Remarks The current report focuses the assocatons between total cholesterol and ts components wth some cardac parameters. Here we have consdered TC, HDL-C, LDL-C, lpd rato (TC/ HDL-C). We have not consdered very low-densty lpoproten (VLDL-C), as we have no nformaton for VLDL-C n any set of consdered data. There are many cardac parameters such as basal, systolc, dastolc, maxmum blood pressures, basal, peak, maxmum heart rates and cardac ejecton fractons. Here we have only systolc, dastolc blood pressure, famly blood pressure and hypertenson wth coronary heart dsease (CHD). The present report has shown some assocatons between TC and ts components wth the systolc, dastolc, famly blood pressures and CVD. In addton, t has shown the assocatons between TC and ts components along wth the lpd rato. Moreover, t has shown the assocatons between the systolc and dastolc blood pressures. Serum trglycerde (STG) s not ncluded n TC, but TC s postvely assocated wth STG (P<0.001) (Table 2) [24]. Moreover, STG s negatvely assocated wth the HDL-C (P=0.024) and famly blood pressure (P=0.041). These two results are ncluded n Table 2. For the frst data set, jont nteracton effect of HDL-C and lpd rato (HDL-C*rato) s postvely sgnfcantly assocated wth the mean TC. Note that HDL-C and lpd rato (both nsgnfcant Table 2. Assocatons of TC, HDL-C, LDL-C wth cardac parameters (for 2 nd set data). Response Assocated wth Estmate Standard error t-value P-value Assocaton type Mean TC HDL-C Postve Serum trglycerde(stg) <0.001 Postve Varance of TC HDL-C Postve TC <0.001 Postve HDL-C <0.001 Negatve Mean LDL-C coronary heart dsease (CHD) Postve famly blood pressure (BP) <0.001 Negatve STG <0.001 Negatve Mean STG TC <0.001 Postve Mean STG HDL-C Negatve 5 J Cholest Heart Ds 2017 Volume 1 Issue 1

4 Ctaton: Das RN. Assocaton between cholesterol and cardac parameters. J Cholest Heart Ds. 2017;1(1):3-7 effects) are ncluded n the model due to margnalty rule by Nelder [27]. Nelder s margnalty rule states that f any hgher order nteracton effect s sgnfcant, then all ts lower order effects should be ncluded n the model. It s known that HDL-C s a part of TC, and the lpd rato s a drect functon of TC, so ther jont nteracton effect should be postvely assocated wth TC. Varance of TC s postvely assocated wth the jont nteracton effect of BP.1s and BP.1d (BP.1s*BP.1d). Mean and varance of HDL-C s also separately postvely assocated wth the BP.1d. Varance of lpd rato s negatvely assocated wth the BP.1d. For the second data set, mean LDL-C s postvely assocated wth coronary heart dsease (CHD), and t s negatvely assocated wth the famly blood pressure. These results show that TC and ts components are assocated wth cardac parameters and events. The consdered two data sets are not very good to examne the assocaton between TC and ts components wth the cardac parameters, as the frst data set s for the dabetc patents, and the second data set s for the young Indan medcal students under age 24 years. An deal data for ths study should be the cardac patents wth STG, TC, all the components of TC, and along wth all possble cardac parameters and events. The present report has shown some assocatons between TC and ts components wth the cardac parameters. The frst data set contans TC and HDL-C but no LDL-C, whereas the second data set contans all the three. For the second data set, LDL-C has shown many assocatons wth the cardac parameters than TC, but HDL-C has shown no assocaton (Table 2). It has establshed that TC and ts components have some effects on cardac parameters. Medcal practtoners and every ndvdual should care on total cholesterol and ts components. 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5 Das 22. Das RN. Hypertenson rsk factors who underwent Dobutamne stress echocardography. Interventonal Cardology: Open Access. 2016; 8(1): Das RN. Dabetes Melltus & Cardovascular Dsease: Co- Exstence? BAOJ Dabetes. 2016;2(1): Das RN. Modelng of Bochemcal Parameters. Model Asssted Statstcs and Applcatons. 2011;6(1): Das RN. Dabetes dsease progresson determnants. BAOJ Dabetes. 2016;2(2): Nelder JA, Lee Y. Generalzed lnear models for the analyss of Taguch-type experments. Appled Stochastc Models and Data Analyss. 1991;7: Nelder JA. The statstcs of lnear models: back to bascs. Statstcs and Computng. 1994;4: *Correspondence to: Rabndra Nath Das Department of statstcs The Unversty of Burdwan Burdwan West Bengal Inda Tel: E-mal: 7 J Cholest Heart Ds 2017 Volume 1 Issue 1