Effect of diabetes type-II on eye disease and its risk factors; a logit model analysis

Muhammad Faisal Fahim, Tayyab Raza Fraz, Sana Malik, Usama Yaseen. Effect of Diabetes type-II on Eye disease and its risk factors; A Logit Model Analysis. Cardiometry; Issue No. 29; November 2023; p. 90-94; DOI: 10.18137/cardiometry.2023.29.9094; Available from:

Diabetes is an alarming metabolic disease and its increasing day by day due to lifestyle compromises and other risk factors worldwide. There were 422 million people worldwide have diabetes, the majority living in under developed and low-and middle-income countries [1]. Prevalence of diabetes, pre-diabetes and associated risk factors: second National Diabetes Survey of Pakistan (NDSP), 2016–2017 stated Overall weighted prevalence of diabetes was 26.3% [2]. The world prevalence of diabetes among adults (aged 20– 79 years) will be 6.4%, affecting 285 million adults, in 2010, and will increase to 7.7%, and 439 million adults by 2030. Between 2010 and 2030, there will be a 69% increase in numbers of adults with diabetes in developing countries and a 20% increase in developed countries [3]. The overall prevalence of abnormal glucose tolerance (IGT + DM) was 20.5% in women and 15.9% in men. A larger percentage of subjects, both women and men, belonged to the age group 45–54 years (27%) [4]. Pooled Prevalence of diabetic retinopathy (DR) was found to be 28.78% with a variation of 10.6% to 91.3%. Out of 29 studies, DR was classified in 19 studies. Pooled Prevalence of VTDR in these 19 studies was found to be 28.2% (variation of 4% to 46.3%) of patient with retinopathy and 8.6% of all diabetics [5]. Diabetes mellitus affects most organs in the body. The manifestations of these effects are generally detected by changes in function that may or may not be peculiar to diabetes. Anatomical effects of diabetes on the eye, especially in the retina, can, however, be seen by direct observation through a dilated pupil with a hand-held ophthalmoscope. Retinopathy generally occurs early in the course of diabetes and, even though no other symptoms are present, may progress and threaten vision [6]. Cataracts are the most common age-related eye disease in the world. In the WES-DR, cataracts were more likely to cause severe loss of vision among people with late-onset diabetes than di- abetic retinopathy [7]. In the Framingham Eye Study and in the NHANES [8] cataract was more common among people with diabetes than among people of similar age without diabetes. In a population-based study of age-related eye disease, diabetes was associated with cortical cataract and cataract surgery [9]. Diabetes may also be causally associated with posterior subcapsular cataract. The rate of diabetes-related blindness increases with age and is greater in women than in men. Non-white women seem to be especially susceptible. In the USA, diabetic retinopathy was the fifth most common cause of legal blindness (defined as visual acuity of Snellen equivalent 20/200 or worse in the better eye) in about 4·8 people per 100 000 population7. The rationale of this study was created on critical thinking regarding diabetes mellitus and its silent effects on the eye of an individual with diabetes type-II. This can be crucial to think about eye disease related to diabetes as it already effects on different parts of body when the blood sugar is not controlled. This study aimed to evaluate the effect of Diabetes type-II on Eye disease and its risk factors in a tertiary eye care hospital of Karachi.

Methodology

This was cross-sectional study with retrospective data collection. Ethical approval was taken prior to study from Research Ethical Committee (REC) of Al-Ibrahim Eye Hospital, Isra Postgraduate Institute of Ophthalmology, Karachi. The data was retrieved from January to June 2019 from Hospital Information Management System (HIMS) software of the Institute. Non-probability purposive sampling method was used to collect data. Inclusion criteria were all the diabetics type-II patients came for routine check-up at Diabetes Eye Department irrespective of age, gender and duration of diabetes. Exclusion criteria were incomplete records / missing information. Parameters of data collection were age, gender, duration of diabetes (years), Fasting blood sugar (FBS), Random blood sugar (RBS) and visual acuity status.

Statistical analysis was done using STATA version 13.0 software for windows. All Continuous parameters were presented as mean ± standard deviation. For Categorical parameters frequency and percentages were reported. To see the significance between independent and dependent parameters logistics regression analy-sis/ Logit Model was performed. P-value ≤ 0.05 was considered to be statistically significant.

Logit Model

Assumed dependent variable “Y” to predict independent variable “X” = X1, X2, X3, ………… Xn) as predictive variables (explanatory variables). Variable “Y” is a binary coded as,

P (Y = 1) denotes the probability that patient had eye problem

P (Y = 0) denotes the probability that patient did not have eye problem

Independent “X” variable (Exogenous variable) = Diabetes type-II

Logit Link Function

A link function is simply a function of mean response variable “Y” that we use as the response instead of “Y” itself. We use the logit of “Y” as the response in our regression equation instead of just Y.

Ln (P/1-P) = β 0 + β 1 X 1 + β 2 X 2 + β 3 X 3 +……..+β k X k

Based on above Model, Present study Model is defined as,

Ln (P/1-P) = β 0 + β 1 X 1 (Diabetes FBS)+ β 2 X 2 (Age)+ β₃X₃(Gender) + β₄X₄(Duration of Diabetes)

Diabetes FBS defined as Fasting Blood Sugar

Age of patient defined as 20 – 80 years

Gender Male and Female

Duration of Diabetes defined as continuous variable in years.

The Logit function is the natural log of the odds that “Y” equals one of the categories. For mathematical simplicity, we assumed “Y” has only two categories and code them as 0 and 1.

Estimating Model Parameters (Coefficients)

Ordinary Least squares regression uses the minimum least squares method to obtain parameters so that the values of α and β were selected. This resulted in minimization the sum of squared deviations of the observed values of Y from predicted value. However, this model does not work similarly well for a categorical response variable.

Logistic regression uses the Maximum Likelihood Estimation obtain to estimate the model coefficients. This method produces values of α and β which maximize the probability of finding the observed set of data. Theoretically, it works like this: First create a likelihood function which states the probability of the observed data as a function of the unidentified parameters α and β. In univariate case, the influence to the likelihood function for a given value of the predictor X is,

P (Y =1|x)y* P (Y =0|x)1-y

Thus when Y=1, the influence is, P (Y=1|x)

When Y=0, the influence is, P (Y=0|x)

Since the sample observations are expected to be independent, the likelihood function for the data set is just the separate contributions:

L=π P (Y=1|x)y* P (Y =0|x)1-y

A more controllable form of this function is found by taking the natural logarithm of the likelihood function called the Log Likelihood function.

LL = ∑ yLog [ P (Y=1|x) ] + (1-Y) Log [P (Y=0|x)]

To obtain the values of the parameters that maximizes the above function, we differentiate this function with respect to α and β then set two resultant expressions to zero. An iterative method is used to resolve the equations and the resultant values of α and β are called Maximum Likelihood Estimates of those parameters. The similar method is used in the multiple predictor case where we would have (P+1) equations corresponding to the P predictors and the constant α.

Results

A total of 6090 cases were analyzed. Mean age of the participants was 51.01±10.8 years. There were 2954 (48.5%) male and 3136 (51.5%) female observed in this study. Table 1 shows the results of the binary logistic regression analysis with coefficients and their standard errors (S.E.), Wald test values, p values, odd ratios, and 95% confidence intervals for odds ratios. When all explanatory variables treat as continuous variables, we found that all variables which include age, height, rbs (random blood sugar) and duration of diabetes was statistically significant at the significance level 0.05 except weight and fbs (fasting blood sugar) for individual regression slope coefficients. For example, the coefficient for age is 0.044 and the corresponding standard error is 0.004, and the Wald value is indeed 10 as specified in Table 1. Since the relevant p-value for this test is < 0.05 therefore we reject the null hypothesis, hence there is strong evidence that age is important to include in the model given the other explanatory variables in the model. The Wald tests suggested that the age, height, rbs (random blood sugar) and duration of diabetes were statistically significant at the significance level 0.05 on each variable; it means that they should include in the model or weight and fbs (fasting blood sugar) should be removed from the model.

Table 1 also shows that the coefficient for age, height and rbs (random blood sugar), which suggests that higher age, height, rbs (random blood sugar) are associated with higher probabilities that the event will occur.

Odd ratios show the model of eye disease to predict the effect of Diabetes presence or absence in it. The odds ratio indicates that for every 1 unit increase in the age, height and rbs (random blood sugar) and the likelihood that presence of diabetes is present increases by approximately 1 percent.

Probability > chi2 – This is the probability of obtaining the chi-square statistic given that the null hy-

Table 1

The Wald test is used to test the set of hypotheses.

Variable		S.E.	Wald	p-value	Odds Ratio	95 % C.I for Odds Ratio.
Age	.0444782	.0042512	10.46	0.000	1.045482	(1.036, 1.054)
Weight	.0037434	.0034866	-1.07	0.283	.9962636	(.989, 1.003)
Height	.0268933	.0057019	4.72	0.000	1.027258	(1.015, 1.038)
FBS	.003308	.0021221	1.56	0.119	1.003313	(.999, 1.007)
RBS	.0039313	.0004937	7.96	0.000	1.003939	(1.002, 1.004)
Diabetes Mellitus (years)	-.2056712	.0345916	-5.95	0.000	.8141007	(0.760 0.871)
Constant	0.0173	0.01583	-4.45	0.0029	0.017	(0.0029, 0.103)

pothesis is true. In other words, this is the probability of obtaining this chi-square statistic (231.56) if there is in fact no effect of the independent variables, taken together, on the dependent variable. In this case, the model is statistically significant because the p-value is less than .000.

Number of obs = 6090

LR chi2(6)    = 231.56

Prob > chi2   = 0.0000

H ₀: β _i = 0 (The association is not statistically significant)

H ₀: β _i ≠ 0 (The association is statistically significant)

Wald Tast = —^в—. s . e .(в i )

• •    If the Wald test shows that the parameters for certain explanatory variables are zero, you can remove the variables from the model.

• •    If the test shows the parameters are not zero, you should include the variables in the model.

• •    Positive coefficients which are statistically significant indicate that the event becomes more likely as the predictor increases. Negative coefficients indicate that the event becomes less likely as the predictor increases.

• •    Odds ratios that are greater than 1 indicate that the event is more likely to occur as the predictor increases. Odds ratios that are less than 1 indicate that the event is less likely to occur as the predictor increases.

Discussion

The aim of this study was to know the effect of Diabetes type-II on Eye disease and its risk factors in a tertiary eye care hospital in Karachi. In this matter Binary logistics Regression analysis was performed to know the significance of eye disease on different parameters like age, gender, Height, Weight, FBS, RBS and Diabetes Mellitus (years).

Interpreting the Odds Ratio (OR) When an independent variable Xi increases by one unit (Xi+1), with all other factors remaining constant, the odds of the dependent variable increase by a factor exp(βi) which is called the odds ratio (OR) and ranges from zero (0) to positive infinity. It indicates the relative amount by which the odds of the dependent variable increase (OR > 1) or decrease (OR < 1) when the value of the corresponding independent variable increases by one (1) unit.

Logistics Regression analysis plays an important role in health sciences related data specifically the odds ratio (risk estimate). It evaluates risk and divide the cut off range of odds value into 1 and greater than 1. When risk occurs at odds ratio 1 then there is no risk and when odds ratio is greater than 1 then it indicates a risk in that variable and similarly as the odds ratio increases it indicates more risk.

A similar literature observed that diabetes is a fastest growing chronic and threatened disease around the globe. They stated that having diabetes is a big risk factor and its symptoms can occur at any stage of life [10].

Another literature stated that Diabetic retinopathy can develop in peoples with diabetes. If an individual had longer duration of diabetes, high hemoglobin levels, higher blood pressure can lead towards eye disease causation [11].

Another Literature also supported that Logistics Regression gives more accurate predictions among peoples with diabetes and its symptoms [12].

This hospital-based study demonstrated that expected association between eye disease increased duration of diabetes, age and other factors of diabetes were identified as modifiable risk factors.

Conclusion

This study reveals findings through binary logistics regression analysis. It indicates that there is an association found in the patients of eye disease with age, height, weight, RBS, FBS. This stated that there were some risk factors observed in these variables related to eye disease. Those who have the disease have risk factor to developed the others associated disease.

Acknowledgement

We acknowledge the support of Al-Ibrahim Eye Hospital and Diabetes Eye Department for Proving us data. We are also thankful to Dr. Saleh Memon (Director Research), Mr. Sikander Ali Sheikh (Asst. Director Out-reach Program) and Mr. Touseef Mahmood (Statistician) for their help and support.

Conflict of Interest

The authors declared that there is no conflict between them.

Financial Disclosure

We declared that no finances were taken from any source.