Department of Statistics, Walter Sisulu University, Mthatha, South Africa
Department of Statistics, University of Forte Hare, Eastern cape, South Africa
Faculty of Health Sciences, Walter Sisulu University, Private Bag X1, Mthatha, Eastern Cape, 5117, South Africa
Department of Internal Medicine, University of Kinshasa, Kinshasa, DR Congo
Division of Cardiology and Intensive Care, University of Maiden Ngouabi, Kinshasa, Congo
Emergency Department, University Hospital Center, Brazzaville, Congo
Division of Chemical Pathology, Stellenbosch University, Cape Town, Stellenbosch, South Africa
Abstract
Background
To provide a stepbystep description of the application of factor analysis and interpretation of the results based on anthropometric parameters(body mass index or BMI and waist circumferenceor WC), blood pressure(BP), lipidlipoprotein(triglycerides and HDLC) and glucose among Bantu Africans with different numbers and cutoffs of components of metabolic syndrome(MS).
Methods
This study was a crosssectional, comparative, and correlational survey conducted between January and April 2005, in Kinshasa Hinterland, DRC. The clustering of cardiovascular risk factors was defined in all, MS group according to IDF(WC, BP, triglycerides, HDLC, glucose), absence and presence of cardiometabolic risk(CDM) group(BMI,WC, BP, fasting glucose, and postload glucose).
Results
Out of 977 participants, 17.4%( n = 170), 11%( n = 107), and 7.7%(n = 75) had type 2 diabetes mellitus(T2DM), MS, and CDM, respectively. Gender did not influence on all variables. Except BMI, levels of the rest variables were significantly higher in presence of T2DM than nondiabetics. There was a negative correlation between glucose types and BP in absence of CDM. In factor analysis for all, BP(factor 1) and triglyceridesHDL(factor 2) explained 55.4% of the total variance. In factor analysis for MS group, triglyceridesHDLC(factor 1), BP(factor 2), and abdominal obesitydysglycemia(factor 3) explained 75.1% of the total variance. In absence of CDM, glucose (factor 1) and obesity(factor 2) explained 48.1% of the total variance. In presence of CDM, 3 factors (factor 1 = glucose, factor 2 = BP, and factor 3 = obesity) explained 73.4% of the total variance.
Conclusion
The MS pathogenesis may be more glucosecentered than abdominal obesitycentered in not considering lipidlipoprotein , while BP and triglyceridesHDLC could be the most strong predictors of MS in the general population. It should be specifically defined by ethnic cutoffs of waist circumference among Bantu Africans.
Background
Metabolic syndrome (MS) is defined by a cluster of cardiovascular risk factors such as obesity (abdominal obesity in particular), diabetes mellitus (DM), high blood pressure (BP)/hypertension, dyslipidemia, insulin resistance, and hypercoagulability
In subSaharan Africa, MS, obesity, dyslipidemia, DM, hypertension and DM are emerging with cardiovascular complications
Several statistical methods can be used to identify patterns of clustering in cardiovascular diseases such as DM and hypertension. One such important and useful technique is factor analysis – a multivariate technique
Methods
This study was a crosssectional survey conducted between January, and April 2005, in Kinshasa Hinterland with details previously published
The survey was specifically and extensively designed using a statistical multistage and stratified random model at each level to recruit a study sample with similar and representative characteristics of Kinshasa Hinterland demographic and socioeconomic structure and results comparable with global data on DM.
Each region contributed with a number of cluster (EDs) calculated by population number: 185, 112 inhabitants for the upper urban area of Gombe, 161,410 inhabitants of the semirural Kisero area, 153,265 inhabitants for the urban Lukemi area and 146,034 inhabitants for the deepest rural Feshi area. The sample size was calculated as Z^{2}xPxQx the expected prevalence of DM in each area, Q = 1P, d is the in the absolute accuracy of 2% ad f = 8.5 to correct the design effect.
The details of collection of weight, height, waist circumference (WC), systolic blood pressure (SBP), diastolic blood pressure (DBP), plasma fasting glucose and plasma post load glucose have been described elsewhere
Definitions
Body mass index (BMI) was obtained in dividing weigh (kg) by height (m)^{2}. In our setting with limited resources and lack of routinely measured insulin resistance (gold standard), we applied the criteria of MS diagnosis proposed by the International Diabetes Federation (IDF) as follows: raised systolic blood pressure (SBP > 130 mmHg) and diastolic blood pressure (DBP > 85 mmHg), elevated triglycerides (TG > 1.7 mmol/L), low highdensity lipoprotein cholesterol (HDL < 1.04 mmol/L in men and <1.29 mmol/L in women) levels, abdominal obesity defined by increased waist circumference (WC > 94 cm in men and >80 cm in women), and fasting plasma glucose (FPG > 5.6 mmol/L)(6).
CDM was defined by the constellation of 3 components of WHO – defined MS such as diabetes, hypertension, and BMI > =30 kg/m2. However, absence of CDM was defined in participants without prehypertension, abdominal obesity, BMI > =25 kg/m2, and CDM. The definition of diabetes was based on clinical arguments and the latest WHO/IDF criteria among persons with the fasting venous plasma glucose level > =126 mg/dL or Postload venous blood plasma level > =200 mg/dL
Statistical analysis
Data were presented as
Factor analysis is based on the following statistical model and definitions
Suppose we have a set of
Suppose for some unknown constants
Here, the
In matrix terms, we have
If we have
Also we will impose the following assumptions on
1.
2. E(
3. Cov(
Any solution of the above set of equations following the constraints for
Suppose Cov(
Note that for any Orthogonal Matrix
Analogous to Pearson's r, the squared factor loading is the percent of variance in that indicator variable explained by the factor. To get the percent of variance in all the variables accounted for by each factor, the sum of the squared factor loadings for that factor (column) was added and divided by the number of variables. This is the same as dividing the factor's Eigenvalue by the number of variables.
The Eigenvalue for a given factor measured the variance in all the variables which is accounted for by that factor. Eigenvalues measure the amount of variation in the total sample accounted for by each factor.
For determining the number of factors, the Kaiser criterion was used. The Kaiser rule is to drop all components with Eigenvalues under 1.0.
The Cattell scree test plotted the components as the X axis and the corresponding Eigenvalues as the Yaxis. As one moves to the right, toward later components, the Eigenvalues drop. When the drop ceases and the curve makes an elbow toward less steep decline, Cattell's scree test says to drop all further components after the one starting the elbow.
Varimax Rotation served to make the output more understandable and facilitated the interpretation of factors. This is an orthogonal rotation of the factor axes to maximize the variance of the squared loadings of a factor (column) on all the variables (rows) in a factor matrix, which has the effect of differentiating the original variables by extracted factor. This procedure yields results which make it as easy as possible to identify each variable with a single factor. To avoid theoretical supposed grounds, we used oblique Promax rotation as additional alternative to varimax rotation for suited clustering characteristics.
A Pvalue < 0.05 was considered as statistically significant. All analyses were performed using the Statistical Package for Social Sciences (SPSS) for windows version 18.0 (SPSS Inc) Chicago, Il, USA.
Results
Out of the original population (n = 977 with 458 males and 519 females), 170(17.4%), 107(11%), and 75(7.7%) were diagnosed for new T2DM, MS, and CDM, respectively.
Table
Variables of interest
Participants with incident types 2 DM
Absence of diabetic participants
P Values
Retrieved from “
Age (Years)
53 ± 13
36 ± 12
< 0.0001
BMI (Kg/m^{2})
24.4 ± 5.6
23.3 ± 5.4
0.881
WC (cm)
86 ± 14.7
78.7 ± 14.3
< 0.0001
SBP (mm Hg)
131.1 ± 31.1
117 ± 17
< 0.0001
DBP (mm Hg)
80 ± 16.7
70 ± 11.7
< 0.0001
FPG (mmd/L)
7.5 ± 2
5.1 ± 1
< 0.0001
Triglycerides (mmd/L)
3.8 ± 0.8
2.7 ± 0.9
< 0.0001
HDL – C (mmd/L)
1 ± 0.3
2 ± 0.6
< 0.0001
In the general population, factor analysis generated 2 factors which were explaining 55.4% of total variance: factor 1(Blood pressure with variance = 29.6%; DBP = 0.881 and SBP = 0.872), and factor 2(Dylipidemia with variance = 25.8%; HDLC = 0.886 and triglycerides = 0.872).
In MS participants, factor analysis generated 3 factors with total variance of 75.1%: factor 1(Dyslipidemia with variance = 29.5%; triglycerides = 0.911 and HDLC = 0.874), factor 2(Blood Pressure with variance = 27.9%; DBP = 0.869 and SBP = 0.837), and factor 3(Abdominal obesity + Dysglycemia with variance = 18.1%; WC = 0.836 and fasting plasma glucose = 0.609).
Absence of CDM(n = 572)
Table
Variables
Mean±SD
BMI (Kg/m^{2})
24.6 ± 8.80
Waist Circumference (CM)
79.8 ± 13.6
SBP (mmHg)
113.4 ± 12.4
DBP (mmHg)
66.6 ± 07.6
FPG (mg/dL)
82.0 ± 14.0
PostLoad PG (mg/dL)
123.21 ± 18.0
WC
FPG
Postload PG
BMI


0.132
P = 0.016
SBP


−0.114
P = 0.031
DBP


−0.125
P = 0.020
WC
0.035
0.146
P = 0.286
P = 0.008
BMI
SBP
DBP
BMI

0.104
0.052
P = 0.046
P = 0.197
SBP


0.128
P = 0.019
DBP



WC
0.200
0.063
−0.021
P < 0.0001
P = 0.286
P = 0.364
FPG
−0.086
−0.155
−0.118
P = 0.080
P = 0.006
P = 0.027
Factor analysis revealed two uncorrelated factors that cumulatively explained 48.1% of the observed variance of the absence of CDM. The number of those two factors was determined by the scree plot according to Eigenvalue (Figure
Eigen values among participants without cardiometabolic risk.
Eigen values among participants without cardiometabolic risk.
Twocomponent plot in rotated space among participants without cardiometabolic risk.
Twocomponent plot in rotated space among participants without cardiometabolic risk.
Factor 1
Factor 2
BMI
−0.131
0.738
SBP
−0.502
0.340
DBP
−0.455
0.114
WC
0.077
0.696
FPG
0.765
0.051
PostLoad PG
0.707
0.400
Presence of CDM
The mean values of variables analyzed in participants with CDM are presented in Table
Eigen values among participants with cardiometabolic risk.
Eigen values among participants with cardiometabolic risk.
Variables
Mean±SD
BMI (Kg/m^{2})
43.40 ± 20.20
PostLoad PG (mg/dL)
80.00±15.80
SBP (mmHg)
127.60 ± 26.70
DBP (mmHg)
80.00 ± 15.80
FPG (mg/dL)
93.40 ± 19.80
Waist Circumference (CM)
182.84 ± 101.10
These three factors could be identified as: Blood Glucose Metabolism Disordering (Factor 1; 35.6% of variance), Blood Pressure (Factor 2; 20.3% of variance), and obesity (Factor 3; 17.7% of variance) (Table
Factor 1
Factor 2
Factor 3
BMI
0.077
−0.025
0.760
SBP
−0.064
0.881
−0.137
DBP
−0.224
0.833
0.116
WC
0.025
0.001
0.769
FPG
0.906
−0.106
0.096
PostLoad PG
0.894
−0.179
0.031
Discussion
The present study identified MS combination for which factor analysis would be appropriate among Bantu Africans. For that reason, the steps involved in performing factor analysis procedure were described. Thus, factor analysis findings using SPSS software have been interpreted.
However, MS is a complex issue in health care. It does not have a simple cause, but multiple risk factors. Its natural course is influenced by genetic factors, personal (Host) attributes, environmental characteristics, or some interactions of both.
At our knowledge, this was the first study to characterize factor analysis of possible risks for clustering of some traditional cardiovascular risk factors in the general population, absence of CDM, presence of CDM, and presence of MS among Bantu Africans living in DR Congo(Central region).
The extent of T2DM, CDM (concurrent presence of 3 nonlipid components of MS), and MS defined by IDF 5 criteria such as 3 nonlipid components and 2 lipidlipoprotein components
Emerging burden of MS
Contrary to the previous myths, non communicable diseases (Diabetes, hypertension, MS, atherosclerosis) are no longer rare in Africa
MS pattern
The present study sought at identifying the physiogenic factors responsible for the clustering of cardiometabolic components. Factor analysis showed marked differences in the MS pattern between the groups of 3 components (CDM) and 5 components (MS).
Number of generated factors
In the general adult population, factor analysis identified 3 components for MS. This finding about MS was consistent with a study conducted in Asian Indians from the general population
In considering the entire population and the subpopulation without CDM, factor analysis generated only 2 factors. In all participants, the factors revealed such as hypertension(factor 1) and dyslipidemia(factor 2) cumulatively explainedb55.4%bof the total variance of the clustering pattern of atherogenic factors from MS. However, in the absence of CDM, BP was not loaded, while only dysglycemia(factor 1) and obesity/BMI and WC(factor 2) were revealed the first factors which cumulatively explained 48.1% of the total variance of the characterization of this group by the clustering of nonlipid components for MS.
The present study showed that no overlapping of variables on more than 1 factor indicated that more than 1 variable was responsible for the ultimate phenotype of the MS. Our findings demonstrated that factor analysis confirmed the general results from other factor analyses of the MS on different ethnic groups that had 35 factors revealed
Our findings with the clustering of the variables in MS as a result of multiple factors known modifiable in nature raised the following question: would it be more efficient to include all participants in one major factor analysis model? Indeed, factor analysis is practically limited to develop a singleparameter screening tool for MS in this study as mentioned in the literature
Factor analysis was applied to see whether there was a less complex space with fewer than the “n” dimensions of the variables that had been analyzed. It was found that a three dimensional space or a mixture of three factors could be used to explain a major part of the data. In more precise mathematical terms the global and examined variables without dyslipidemia(with paradoxes of triglycerides and HDLC) could be reduced to three factors with eigenvalues greater than one, which explained 73.4% of the variance in MS Africans. The loadings on these factors sorted out into three metabolic groupings.
Neither of the variables was loaded on all the three components. These three factors could be identified as Glucose Metabolism (Factor 1), Blood Pressure (Factor 2) and Obesity (Factor 3). This suggests that those nonlipid components clustered naturally rather than as a result of chance.
No overlapping of variables on more than one factor indicated that more than 1 variable is responsible for the ultimate phenotype of the fats. The present factor analysis confirmed global results from other factor analyses of fats among different populations that had 3 to 4 factors identified as nonmodifiable/genetic risk factors and modifiable/ environmental risk factors. The study attempted to observe among BMI, WC, SBP, DBP, FPG, and postload PG group  which ones go together and which ones do not
In many studies, fats play a pivotal role in the occurrence of the onset of CVD, andT2DM. However, lipid profile and fasting insulin are not available in the majority of health centers in developing countries.
Therefore, identification of nonlipid components of the metabolic syndrome would be helpful in understanding the etiology among Bantu Africans. Virtually no study has been performed on combination of the evaluated variables in Sub Saharan Africa.
Perspectives for Africa
This study highlighted the absence of obesity as a factor of MS in type 2 diabetic Bantu Africans. Moreover, obesity was the third factor of MS with lower variance in comparisons with variances of factor 1(Glucose) and factor 2(Blood pressure) among type 2 diabetic Africans with MS. As reported on the factor analysis of risk variables associated with MS in adult Asian Indians
Limitations and strengths
The advantages and disadvantages of factor analysis have been reported in medical, physical, marketing economic and environmental researches
Advantages of factor analysis
The rotation methods are useful in making the output more understandable and for ease of interpretation of the factors. The optimal variance of the squared loadings of a factor (Column) on all the variables (rows) in a factor matrix is due to varimax rotation (an orthogonal rotation of the factor axes). Factor matrix differentiates the original variables from extracted factors.
Groups of interrelated variables are identified and seen in their manner to be related to each other.
In multifactorial diseases, it is easy and inexpensive to perform factor analysis which can be used to identify hidden dimensions which may not be apparent from analysis.
Disadvantages of factor analysis
It is not possible to pick the proper rotation using factor analysis alone as all rotations represent different underlying processes and equally valid outcomes of standard factor analysis optimization.
Though not a strictly mathematical criterion, there is much to be said for limiting the number of factors to those whose dimension of meaning is readily comprehensible. The same limitation is reported about variance explained criteria.
The research is requested to choose the solution which generates the most comprehensive evaluation of data.
The Kraiser criterion is the default in SPSS and most computer programs but is not recommended when used as the sole cutoff criterion for estimating the number of factors.
Certain researchers prefer to keep enough factors to account for 80%90% of the variation. However, other researchers explain variance with a few factors, but lower than 50% (Parsimony).
Factor analysis cannot identify causality as interpreting factor analysis is based on using a “ heuristic” convenient solution even if not absolutely “true”. If important attributes (such as lipid components of fats) at primary health care in developing countries like DRC, the value of the procedure was reduced for BMI in absence of MS.
It requires strong background knowledge of biology and Pathophysiology or theory as multiple attributes may be highly correlated for no apparent reason. Varimax was an orthogonal rotation of the components to maximize the variance of the squared loadings (unrotated output accounted for by the first and subsequent factors) of a dimension (Column) on all the variables(Rows) in a factor matrix. Varimax rotation is the easiest and the most simple and common rotation option used in MS
Implementation of factor analysis
The implementation of Factor analysis is well established within robust statistical software such as SAS, BMDP and SPSS and R programming language with the factanal function (GPA rotations), and Open Opt
Conclusion
The factor analysis performed for this study suggests that the clustering of the nonlipid variables is sufficient to define CDM in black Africans at including glucose metabolism, Blood pressure and Obesity. Since 3 factors in sequencing dyslipidemia, hypertension, and abdominal obesitydysglycemia were identified for the Bantu Central African MS phenotype, more one major factor could be accounted for this specific MS. Early prevention and management (diagnosis and proper intervention) strategies for those modifiable loaded risk variables could reduce the burden of type 2 DM, MS, and emerging cardiovascular disease in Central Africa.
Competing interests
All authors declare that they have no competing interests.
Authors’ contributions
All the coauthors have seen and approved the final version of the manuscript and it is not currently under active consideration for publication elsewhere, has not been accepted for publication, nor has it been personally and actively involved in substantive work leading to the report, and will hold themselves jointly and individually responsible for its content. JBKLO was responsible for the field work. JNS performed review literature related to factor analysis. BLM conceived of the study, and participated in the study design. JNS and BLM performed statistical analyses. JTL, JNS, BLM, JBKLO, and GT participated in the coordination of writing of the study. All authors read and approved the final manuscript.
Acknowledgements
We thank the medical officers, interns, social workers, and nursing staffs from the University of Bandundu, the participants and the professionals of the laboratory of Lomo Medical for the ultrastructural technical assistance.