Logistic Regression Equation of Diabetes Risk Score among Nigerians
AN Adamu*, AE Ohwovoriole†, JK Olarinoye*, OA Fasanmade†, CO
Ekpebegh†, SB Adebayo‡
*Endocrinology and Metabolism Unit, Department of Medicine, University of Ilorin, Nigeria.
† Endocrinology and Metabolism Unit, Department of Medicine, University of Lagos, Nigeria.
‡Department of Statistics, University of Ilorin, Nigeria.
Address correspondence and reprint to Abdullahi N. Adamu, Department of Medicine, University of Ilorin
Teaching Hospital, Ilorin, Kwara State, Nigeria.
ABSTRACT
Background- The prevalence of type 2 diabetes is on the increase all over the world
and the developing nations will be worse hit by this pandemic. Type 2 diabetes could
exist for years without the person knowing about it, thus the need for an easy cost
effective screening method.
OBJECTIVE- To develop and validate a risk score, considering simple predictive risk
factors for developing Type 2 diabetes among Nigerians.
METHODOLOGY- The subjects used to determine the Logistic Regression Equation
were 234 persons with Type 2 diabetes Mellitus and 234 persons without diabetes were
recruited, all aged 40-70yrs and a questionnaire was applied on them. The questionnaire
contain pertinent information, and anthropometric measurements that portent risk of Type
2 diabetes Mellitus. The variables were tested for their association with Type 2 diabetes
comparing the two groups, in order of the level of significance in univariate analysis, into
logistic regression model using Stata® (Statacorp, College Station, Texas, USA). The
variables were retained if they made a significant (p <0.05) contribution according to the
likelihood ratio test. The Coefficient from the resulting model formed the risk score. The
regression equation coefficient results obtained is then applied on people living with
hypertension to asses the performance of the regression equation. Receiver operative
characteristic curve was plotted to determine the point of maximal efficiency of the
equation. Sensitivity, specificity, positive and negative predictive values were calculated.
The efficiency of the equation was also calculated.
RESULTS- age, sex, family history of diabetes, skin complexion, annual income, social
class, BMI, history of tobacco use, alcohol use, hypertension and physical activity are the
significant risk factors. The intercept of the analysis was; -129.04. The risk score with
maximal efficiency was 0.45. It has a sensitivity of 89.40%, specificity of 18.20%,
positive predictive value of 10.40, and negative predictive value of 95%. The efficiency
was 107.60%. The area under the curve of receiver operative characteristic curve is 0.54.
CONCLUSION- The risk of Type 2 diabetes can be easily predicted from the pertinent
risk factors that can be gotten through a standard questionnaire and BMI measurement.
This method will make screening for Type 2 diabetes easily implementable using an
inexpensive hand-held programmable calculator.
The prevalence of Type 2 diabetes is on the increase in all populations worldwide. The
current burden of diabetes is about 246 million in the adults with diabetes in the world
and it is expected to reach 380 million in the year 2025 (1). The impact of the upsurge in
prevalence of diabetes and other non-communicable diseases is to be hit worse by
1
developing nations, particularly Africa due to the ageing of the population and drastic
lifestyle changes accompanying urbanization and westernization (2). Diabetes Mellitus is
associated with a high rate of long-term complications in populations of African origin in
the face of difficult economic conditions (3). Several recent interventional studies have
undisputedly proved that Type 2 diabetes can be efficiently prevented by lifestyle
modification in high risk persons (4, 5&6). The challenge to the health care givers is to
identify the group of people who will benefit maximally from this intervention.
The purpose of screening is to differentiate an asymptomatic individual at high
risk from an individual at low risk for diabetes (7). Ideally, screening tests should be
rapid, simple and safe (8, 9). A positive screening test only means that the person is more
likely to have the disease than a person with a negative screening test. Screening for
diabetes can identify patients at an early stage of the disease; thus, identifying those that
will derive benefit of prevention and early treatment (10). Strategies to reduce the
proportion of undiagnosed cases through self-reported demographic, behavioral, medical
information and anthropometric measurements to assign a person to a higher or lower
risk group are less expensive than biochemical tests (7).
The available studies on risk score development and validation to screening for
type 2 diabetes used a larger population in a community or hospital setting, We aim to
develop a simple, practical, and easy scoring system by using fewer, high risk people
with systemic hypertension in a hospital and community setting to characterize
individuals according to their future risk of Type 2 diabetes.
METHODOLOGY:
Development of the risk score
A case control data of two hundred and thirty-four persons (234 x 2), each with Type 2
diabetes and without diabetes, was recruited. Those with Type 2 diabetes were regular
attendees to the Diabetes Clinic of the Lagos University Teaching Hospital. Those
without diabetes were recruited in the various wards of the same hospital, admitted for
diabetes unrelated illnesses and from among the members of a church congregation at the
Teaching Hospital Chapel as the number of in patients could not match the diabetes
number.
Inclusion and Exclusion Criteria; The diabetes subjects were on diet and/ or oral
glucose lowering agents’ treatment while persons without diabetes were not on
medications and not known to have diabetes before or were not on medications that could
alter glucose metabolism.
A questionnaire that included anthropometric, demographic and clinical parameters was
designed. Weight was measured with subjects wearing light clothes, to the nearest
500mg, while height was determined without shoes, to the nearest 0.5cm. Waist
circumference was measured midway between the lowest rib and the iliac crest, to the
nearest 0.5cm, hip circumference was determined at the level of the greater trochanter, to
the nearest 0.5cm. Body mass index (BMI) was calculated by dividing the weight (kg) by
the height squared (m2) categorize into 1, BMI<30kg/m2, 2 BMI ≥30-34.9kg/m2, 3 3539.930kg/m2, 4 >4030kg/m2. Waist to hip ratio was computed by dividing waist
circumference with the hip circumference. Demographic and clinical parameters were:gender coded as; 1 male, 2 female, age coded as ;1 <40yrs and 2 ≥40yrs, family history of
2
diabetes involving the parents and siblings coded as; 1 if non of the family members has
diabetes and 2 if any of the family members has diabetes , physical activity most of the
day of the week coded as 1 if activity per week is less than 30min three times per week, 2
if physical activity is 30min three times per week, 3 if physical activity is more 30min
three times per week, alcohol intake coded as; 1 if the subject does not got drunk at least
4days of the week and 2 if the subject usually got drunk at least 4days of the week , The
socioeconomic stratification was done by categorization of educational attainment,
income and occupation and by assigning scoring system to the categories. Educational
category is; None=1, Basic Arabic and Islamic education/Primary/ modern school=2,
Secondary =3, Advanced Teacher Training/Polytechnic = 4 and University=5.
Occupation social status is; Unemployed= 1, Petty Trading/Artisans=2 (includes driving,
tailoring, small scale farming, hairdressing, plumbing, bricklaying etc. ), Clerk/Typist= 3,
Teaching/Middle Level civil servants= 4, Professionals= 5 ( includes top civil servants
and businessmen ). Income per year category is based on minimal wage in Nigeria (11) in
naira currency as follows; Nil income or < 67009 =1, 67010 – 71372 = 2, 71373 –
134079 = 3, 134080 – 242068 = 4, 242070 – 340332 = 5, >340332 = 6. The summation
of the categorical scores (Socioeconomic Class (sec) score Grading) were also assessed
as follows; 1 SEC <9, 2 SEC = 9 – 11, 3 SEC =12 – 14, 4 SEC >15. Skin complexion
categorized into 1, black and 2, brown, 3 light. Tobacco use is categorize into; 1 smokes
less than 5 sticks in the last five years and 2 smokes more than five sticks in the last five
years. Hypertension is categorized into; 1 not known to have hypertension and 2 being a
person with hypertension. For female gender additional information were requested:
parity categorize into 1, less than 3 children and 2, more than 3 children, history of giving
birth to a child weighing ≥4.0kg, past history of gestational diabetes, and history of
contraceptive use, categorize into 1, oral and injectables and other type of family
planning and non at all.
The aim was to produce a simple risk score calculation that could be conveniently used in
primary care and by non medical personnel. Consequently, only parameters that were
easy to assess without laboratory tests and clinical measurements not requiring special
skills were used.
Test of the risk score
Two hundred and six persons with systemic hypertension on life-style modification and/
or drug(s) for the control of blood pressure attending the hospital were sequentially
recruited in a cross sectional study. One hundred and thirty one (62.62%) had OGTT
done. The study period was three months, spanning from January to March 2004. The
same questionnaire as above was applied to the subjects.
Exclusion criteria included- established secondary forms of hypertension, chronic renal
failure and chronic liver disease.
Performance of OGTT
At 7.30am, on the day of OGTT, fasting venous blood was taken and 75gm of anhydrous
glucose dissolved in 200mls, chilled water was ingested at once by the subjects. A repeat
venous sample was taken at 9.30am.
Handling of blood specimens
3
Blood samples were immediately centrifuged after collection to separate plasma from red
cells. Plasma aliquots were frozen at -80oC until analyses. Plasma glucose was analyzed
according to the method of Trinder (11). 2 hour post glucose venous plasma glucose
estimation of ≥11.1mmol/l is considered to have diabetes using OGTT as a gold standard
(12).
Approval was obtained from the Ethical Committee of the Lagos University Teaching
Hospital. An informed consent was obtained from the subjects before commencing the
studies.
Statistical Method
The data was entered into Microsoft Excel® later transferred to Stata (Statacorp, College
Station, Texas,) USA for the analysis. Descriptive statistics of the samples were done in
which continuous variables were compared with student t-tests, categorical variables with
chi-square tests. Logistic regression analysis was done in which the variables were tested
for their association with incident cases of diabetes using backward stepwise logistic
regression. The logistic regression analysis with diabetes as dependent variable and the
predictive risk factors for diabetes were used as independent variables was performed
using the logit and logistic commands of stata software. Variables were retained if they
made a significant (<0.05) contribution according to the likelihood ratio test. The ßcoefficient for known risk factors for Type 2 diabetes from the resulting model formed
the risk score. The mean (SD) of probability of having diabetes using the significant
variables total score for subjects with diabetes were calculated. It was used as landmark
to differentiate those that have diabetes and those that do not.
1
Probability of having Type 2 diabetes=
_________________
  
 
 
1+e – ( + 1 1 + 2 2……. n n)
Where e = exponential
α = constant
β= coefficient score of a particular variable
xi= are the continuous or dichomous explanatory variables.
Statistical Method on Test of the Score
A 2x2 table was made to calculate the performance of the risk score using 2hour plasma
glucose value as gold standard. Thus, sensitivity, specificity, predictive value and
efficacy of the test were done. Sensitivity is the proportion of a diseased population that
is identified by the screening test as positive-the true positive, specificity is the proportion
of the healthy population that is identified as healthy by the screening test- the true
negatives, positive predictive result is the proportion of positive results in a mixed
population of sick and healthy people, negative predictive value is the proportion of
negative results in a mixed population of sick and healthy people while efficiency is the
percentage that the sum of the true positives and the true negatives is of the grand total
population. Receiver Operative Characteristic Curve (ROC) was plotted, and the area
under the curve and the 95% CI were estimated.
Table 1 Shows the Statistical 2x2 of OGTT against risk score test.
4
Gold Standard Test (OGTT)
-ve
Risk Score Test
+ve
-ve
TN
FN
TN+FN
+ve
FP
TP
FP+TP
TN+FP
FN+TP
TN+FN+FP+TP
TP: true positive, FP: false positive, FN : false negative, TN: true negative..
Results
Descriptive features of the samples
The age matched features of the subjects used to determine the risk score showed that
most of the predictive risk factors were significantly in favour of those without diabetes
except the height and the duration of hypertension that was not remarkable. The percent
number of people with hypertension, alcohol use and smoking was higher among
diabetes than those without diabetes as shown in table 2.
Of the 131 subjects who completed the study, they consisted of 87 (66%) females and 44
(34%) males. Using 2hr post-glucose assay of ≥200mg/DL on OGTT, 107(81.68%) do
not have the disease while 24(18.32%) have the disease.
The subjects with diabetes are significantly older, had longer duration of hypertension,
BMI, more percentage of family history of diabetes, having baby weighing more than
4kg and history of gestational diabetes among female category. Those without diabetes
have percentage significantly better physical activity per week, job description and
steroid contraceptive use. Annual income and gender differences in the two categories
were not different as shown in table 3.
The pertinent logistic regression factors that contributed to the risk of diabetes with
diabetes as a dependent factor is shown in table 4 with the odd ratio and its 95%
confidence interval, coefficients and the P values. The categorization of the factors put a
particular risk factor as significant if any of categories is significant as seen in BMI
category, if any of the category is close to 0.05 is also considered to be significant as seen
in skin complexion category 2 with P value of 0.07. Other factors that have P value at
marked variant from P value of ≤ 0.05 are not included.
The intercept of the equation was; -129.04.
The mean of the final risk score and standard deviation is 0.34 ± 0.11; a score range of
this result and it performance is shown in table 5.
Table 2 Features of subjects used to develop the Risk Score
FEATURES
Subjects (n=234)
controls (n=234)
p-value
Overall Age (Yrs)
52.31 ± 6
( 37 - 69)
51.81 ± 8
(31 - 84)
>0.05
5
Age of males (Yrs)
50.72 ± 9
( 38 - 84)
52.55 ± 8
( 31 - 70)
76.04 ± 10
( 50 - 111.3)
1.63 ± 0.06
( 1.41 - 1.8)
28.57 ± 3
( 19.28 - 41.91)
96.24 ± 10.4
( 70 - 136)
103.67 ± 12
( 75 - 160)
0.93 ± 0.08
( 0.74 - 1.18)
26 (20.63)
< 0.05
Hypertension (%)
46.58 ± 6
(38 - 69)
44.29 ± 5
( 37 - 67)
71.96 ± 5
( 56 - 100.0)
1.60 ± 0.05
( 1.5 - 1.64)
27.98 ± 2
( 23.87 - 39.55)
89.02 ± 7
(56 - 113)
98.01 ± 10
( 58 - 123)
0.91 ± 0.06
( 0.78 - 1.15)
100 (79.36%)
Duration of
Hypertension (yrs)
Alcohol (%)
2.30 ± 2.3
( 0.00 - 20)
43 (57.33%)
1.8 ± 1.8
( 0.0O - 20)
32 (42.67)
>0.05
Smoking (%)
33 (78.57)
9 (21.43)
<0.05
Age of females (Yrs)
Weight (Kg)
Height (m)
Body mass index(kg/m2)
Waist circum. (cm)
Hip circum. (cm)
Waist/Hip
Table 3
< 0.05
<0.05
>0.05
< 0.05
<0.05
<0.05
<0.05
<0.05
<0.05
Features of those used to test the risk score
OGTT<200mg/dl OGTT≥200mg/dl
Current age
50.78±8.95
57.14±7.54
Duration of HBP
9.08±8.02
13.63±8.51
Females
11.43%(12)
12.5%(3)
males
88.57(95)
87.5%(21)
BMI
29.54±7.00
33.57±4.77
Family history of diabetes
24.76%(26)
60%(15)
Annual income
42.86%(45)
37.5%(9)
Birth of baby ≥4kg
0%(0)
33.33%(1)
History of gestational diabetes
16.66%(2)
33.33%(1)
Steroid Contraceptive use
25%(3)
0%(0)
Physical activity per week
93.33(98)
62.5%(15)
Job description
70.47%(74)
54.16%(13)
P value
<0.05
<0.05
>0.05
>0.05
<0.05
<0.05
>0.05
<0.05
<0.05
<0.05
<0.05
<0.05
Table 4 Logistic regression used to develop the risk score with diabetes as a dependent variable
Feature
OR(95%CI)
Coeff.
Age (Yrs)
0.90(0.86-0.95)
-1.00
Sex
2.14(1.03-4.42)
FhxDM
4.07(1.88-8.78)
Brown
light
SE
Z
P
0.02
-3.94
0.00
0.76
0.79
2.05
0.04
1.40
1.59
3.58
0.00
1.97(0.94-4.12)
0.68
0.74
1.81
0.07
1.44(0.60-3.40)
0.36
0.63
0.82
0.41
Skin. Comp
6
Annual Income
2
8.45e+09(4.62e+08-
22.86
1.25e+10
15.41
1.55e+11)
3
1.18e+10(5.17e+08-
0.00
0.00
23.19
1.88e+10
14.55
0.00
22.83
1.24e+10
15.24
0.00
22.21
6.62e+09
14.78
0.00
23.03
1.65e+10
14.09
0.00
0.15
0.11
-2.39
-2.51
2.67e+11)
4
8.26e+09(4.38e+081.56e+11
5
4.41e+09(2.32e+088.38e+10)
6
1.01e+10(4.10e+082.48e+11)
Social Cat
0.01
0.01
2
0.3(0.11-0.80)
-2.20
3
0.15(0.03-0.66)
-1.87
4
0.24
-1.41
0.22
-1.55
0.83(0.26-2.65)
0.75(0.23-2.39)
-0.19
-0.28
0.49
0.44
-0.32
-0.48
1.61(0.04-0.58 )
-1.83
0.10
-2.78
8.81(2.58-30.02)
2.17
5.51
3.48
0.33(0.16-0.69)
-1.09
0.12
-2.95
0.00
2
2.40(0.94-6.11)
0.84
1.14
1.84
0.06
3
2.88(1.21-6.86)
1.06
1.27
2.39
0.02
0.12
BMI
2
3
4
Tobacco
Hypertension
0.75
0.63
0.00
0.00
Phy.Act/week
FhxDM: Family history of diabetes, Skin. Comp; Skin complexion, BMI; Body mass index, Phy. Act/ week; Physical activity per
week.
The plasma glucose intra-assay coefficient is 3.53 while inter-assay is 9.03 both showing
a good assay method.
The performance of test at various cut-off points are as documented in table 5. As the cutoff point increase, the sensitivity increases and vice-versa for specificity. The overall
performance that has to do with efficiency which was highest at cut-off point of 0.45 is
107.60. This also matches with maximal curve line at topmost left corner of Receiver
operative characteristic curve (ROC) as shown in fig 1. The area under the curve (AUC)
of ROC is 0.54 with 95% confidence interval of 0.39-0.70.
Table 5 Performance of logistic score at various points
Sensitivity
Specificity
PPV
NPV
EFFICIENCY
0.23
18.33
81.69
45.20
54.20
52.67
0.34
71.43
24.24
16.66
80
95.67
0.45
89.40
18.20
10.40
95.00
107.60
7
ROC Curve
1.00
.75
Sensitivity
.50
.25
0.00
0.00
.25
.50
.75
1.00
1 - Specificity
Fig 1 Receiver Operative Characteristic Curve of Logistic Regression Analysis
Discussion
As part of the desire to adopt an easy and cost effective way to screen for Type 2
diabetes, effort was geared towards developing a risk score from the predictive risk
factors for Type 2 diabetes; we have developed a risk score equation based on age, sex,
family history of Type 2 diabetes, activity per week, Annual income, BMI, duration of
hypertension, Annual income and social category. For women additional factors like
history of delivery of baby weighing ≥4.0kg, history of gestational diabetes and history of
contraceptive were inputted into the logistic regression equation. It is presumed that the
validated risk score can easily be computed with the use of a programmable calculator.
This is the first study to assess the performance of a simple risk score using routinely
collected data as a screening tool for undiagnosed diabetes in; 1 African setting, 2. Using
data from people with systemic hypertension to test the risk score and 3. using limited
data to develop and test risk score. The use of limited data of 234 x 234 (864) subjects to
develop the risk score compare to a larger sampling size used in other studies is to enable
us assess whether a similar result could be obtained. The probability of having Type 2
diabetes in this study is 0.34 ± 0.11. The performance of risk score varies from place to
place depending on the cut off value, risk characteristic input into the risk score, the
biochemical measurement and its cut off value used as the gold standard.
The AUC is the objective measure of the performance of the risk score (13). The higher
it is the better the screening method at the cut off value. The AUC in this study is 0.54
which is similar to a multi-centre study involving Africa and India where AUC was 0.53
and 0.54 respectively (14). A comparative analysis of performance of risk score using
8
AUC shows that it has similar value of AUC in Africa and India, which is low compare
to other parts of the world. In the Arab world of Oman is 76-84% (15). The performance
among the Arabs using Oman as an example is similar to what obtains among the
Europeans. The results of similar studies carried out in Europe vary from 72-80% (15
&17).
A NPV value of 95% depicts that subjects with score 0.45 are unlikely to have diabetes
and thus can be excluded from any second stage procedure, usually fasting blood sugar or
OGTT. This is important for both the individual and health workers when making plans.
It also can be considered to save money when diagnostic tests can be targeted specifically
to those people who are more likely to have diabetes. The NPV reported in this study was
comparable with the study of Charlotte et al (16) and Griffin et al (17) who reported
NPV of 98.7% and 99% but better that one reported by Bahman (18) which was 83%.
The performance of this study is relatively comparable with others in terms of sensitivity
and specificity. The sensitivity of this study lies in between the sensitivity reported by
Charlotte et al and Griffin at al who reported sensitivities of 76% and 90% respectively
but higher than the sensitivity of 65% reported by Bahman (18). The poor performance of
the logistic regression equation in terms of specificity in this study could be due to the
nature of subjects used to develop the risk score in our study. An equal number of those
with type 2 diabetes and those without diabetes were used to develop the risk score in this
study, whereas, the other studies used population based samples to screen for type 2
diabetes and to develop the risk score.
Conclusions
This shows that despite low sample size we used to develop and test the risk score, we
got a comparable result with a study using a larger population but within the same
geographical and or socioeconomic region. Our result of high NPV and good sensitivity
is important in order to include maximum number of potential cases for biochemical
diagnostic testing. This tool is simple, feasible, acceptable,safe and cost-effective and
will reduce the number of invasive glucose tests.
Limitations
There are some differences in the method of development and test of the risk score
comparing it with other studies as per the number of subjects, the diabetes risk
characteristics and the biochemical gold standard used. While our study is a hospital
based with limited number of subjects for the development and test of the risk score,
other comparable studies used very large population and at times community based
information to develop and test the risk score. Also ethnic differences are known to affect
the prevalence of type 2 diabetes, prevalence of the risk factors and the extent to which
undiagnosed diabetes is associated with various risk factors (18-20).
Acknowledgement- I wish to sincerely thank Dr Solomon Griffin for opening my eyes
into this kind of study, and for making his original article available to me.
9
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