IDENTIFYING MOST INFLUENTIAL RISK FACTORS OF GESTATIONAL DIABETES MELLITUS USING DISCRIMINANT ANALYSIS

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1 Inter national Journal of Pure and Applied Mathematics Volume 113 No , ISSN: (printed version); ISSN: (on-line version) url: ijpam.eu IDENTIFYING MOST INFLUENTIAL RISK FACTORS OF GESTATIONAL DIABETES MELLITUS USING DISCRIMINANT ANALYSIS Priya Shirley Muller 1, M. Nirmala 2 1,2 Department of Mathematics Sathyabama University, Chennai priyamuller@gmail.com Abstract Gestational Diabetes Mellitus (GDM) is one of the common complications pregnancy. Women with GDM are at increased risk for adverse obstetric and perinatal outcome. Oral Glucose Tolerance Test (OGTT) is the crucial method for diagnosing GDM performed usually between 24th and 28th week of pregnancy. The proposed work focuses on early detection of GDM without a visit to the hospital for women who are pregnant for the second time onwards (multigravida patients). In recent years, prediction models using Discriminant Analysis (DA) have been developed in many areas of health care research. The application of the DA model revealed that the classifier is an efficient model for diagnosis of GDM without the conventional method of blood test by providing newly designed parameters as inputs to the model. AMS Subject Classification: 92B15, 92C50. Key Words and Phrases: Gestational Diabetes Mellitus, Diagnosis, Discriminant Analysis, Risk Factors. ijpam.eu

2 1 Introduction Diabetes Mellitus in India is a growing area of research as statistically the number has increased significantly mainly encouraged by decreasing levels of activity and increasing prevalence of obesity. Gestational Diabetes Mellitus is characterized by carbohydrate intolerance of varying severity with onset or first recognition during pregnancy. GDM has been associated with maternal, fetal and infant complications, including infant macrosomia and birth trauma, infant hypoglycemia, caesarean section, and increased medical costs. Although some women with diagnosed GDM will have persistent abnormal glycemia, most women will revert to normal carbohydrate metabolism after delivery. However, women with a history of GDM remain at increased risk of developing type 2 diabetes mellitus in the future. To standardize the diagnosis of GDM, the World Health Organization (WHO) has proposed using a 2-h 75 g OGTT usually at weeks [1]. If the patient has had gestational diabetes in a previous pregnancy, the OGTT will be carried out at weeks, followed by a repeat OGTT at 28 weeks if the first test is normal. Thus a pregnant woman susceptible to GDM would go through the routine blood test only during her 24 to 28 weeks of pregnancy. A number of studies have documented that early diagnosis of gestational diabetes reduced serious perinatal morbidity and also improved the woman s health-related quality of life [7] and hence is of paramount public health priority. 2 Literature Survey Jaafar et al., [2] proposed a method for diagnosing diabetes using back propagation neural network algorithm. The inputs to the system are plasma glucose concentration, blood pressure, triceps skin fold, serum insulin, Body Mass Index (BMI), diabetes pedigree function, number of times a person was pregnant and age. Zhang et al. [8] in their paper used fuzzy integral to structure the diagnostic model of gestational diabetes mellitus. The Sugeno measure was obtained by training of BP neural network. As the BP neural network is easy to get into local optimum, the algorithm of simulated annealing was used to optimize the BP neural network to obtain an approximate global optimal solution. Tran et al., [6] ijpam.eu

3 compared the discriminative power of prognostic models for early prediction of women at risk for the development of GDM using four currently recommended diagnostic criteria based on the 75-g OGTT. It was concluded that a simple prognostic model using age and BMI at booking could be used for selective screening of GDM in Vietnam and in other low- and middle-income settings. Our major motivation for this research is the increasing need for early identification of individuals at risk of developing GDM that could help decrease the incidence of morbidity and mortality of mother and child. 3 Methodology Discriminant Analysis is a commonly accepted statistical tool, which can generate excellent models. Since it is easily used and analyzed and provide coefficients such as probability ratio to express each independent variable s impact on the model, it is frequently applied in biomedicine models [4]. Discriminant analysis is a multivariable technique that separates distinct sets of observations and attributes new observations to predefined sets [3]. Statistical problem is to develop a law (diagnosis or classification function) on the basis of population size. The discriminant function score for a case can be produced with raw scores and unstandardized discriminant function scores. The discriminant function coefficients are, by definition, chosen to maximize differences between groups. The mean over all the discriminant function coefficients is zero, with a standard deviation equal to one. The mean discriminant function coefficient can be calculated for each group - these group means are called centroids which are created in the reduced space created by the discriminant function reduced from the initial predictor variables. Differences in the location of these centroids show the dimensions along which the groups differ. Once the discriminant functions are determined groups are differentiated, the utility of these functions can be examined via their ability to correctly classify each data point to their a priori groups. Classification functions are derived from the linear discriminant functions to achieve this purpose. For cases with an equal sample size for each group the ijpam.eu

4 classification function coefficient C j is as follows: C j = c j0 + c j1 x 1 + c j2 x c jp x p (1) for the j th group, j = 1... k, x = raw scores of each predictor, c j0 = a constant. If W = within-group variance-covariance matirix, and M = column matrix of means for group j, then the constant c j0 = ( 1/2)C j M j. For unequal sample size in each group, C j = c j0 + p ( nj ) c ij x i + ln N i=1 (2) n j = size in group j, N = total sample size. Once group means are found to be statistically significant, classification of variables is undertaken. DA automatically determines some optimal combination of variables so that the first function provides the most overall discrimination between groups, the second provides second most and so on. Computationally, a canonical correlation analysis is performed that will determine the successive functions and canonical roots. Classification is then possible from the canonical functions. Subjects are classified in the groups in which they had the highest classification scores. 4 Data Analysis The real time data was collected from past patient records from a multi-specialty hospital in Chennai, Tamil Nadu, India. The patient data sets of 188 records each consisting of ten parameters was extracted from the outgoing patient s records from January 2013 to May On consultation with gynaecologists, the study variables were chosen taking into account the several factors that are clinically relevant for a pregnant woman to develop GDM. Of the ten variables used in the model, the first three involve general information like age, family history of diabetes in first degree relatives and Body Mass Index (BMI). Fourth to eighth variables deal with previous pregnancy information such as presence of GDM, birth of a baby who weighed more than 3.8Kg, death of a baby before 20 weeks, birth of a baby with defects in spinal ijpam.eu

5 cord, heart or brain, death of a baby after 20 weeks respectively. The last two reveal information on history of urinary, skin or vaginal infections and polycystic ovary syndrome [5]. Among the ten variables, eight are binary variables, where 0 indicates nonoccurrence and 1 indicates occurrence. Figure 1: statistics Graph depicting the summary of patients history The details of the summary of the patients history statistics is depicted by a graph in Figure 1. Among the pregnant patients, an astounding 54.8% of them had either of their parents or both having diabetes and the patients who have had history of miscarriage are an alarming 39.9%. 5 Results and Discussions In this study, Discriminant Analysis model is used as a classifier to predict the outcome of GDM and hence assess the model accuracy to distinguish GDM and non-gdm patients and identify the significant risk factors of GDM. The results were analyzed using the Statistical Package for Social Sciences (SPSS) for Windows version Wilks lambda is used in an ANOVA F test of mean differences in DA, such that the smaller the lambda for an independent variable, the more that variable contributes to the discriminant function. Lambda varies from 0 to 1, with 0 meaning group means differ and 1 meaning all group means are the same. ijpam.eu

6 Table 1: Tests of Equality of Group Means in the Discriminant Analysis Model Variables Wilks Lambda F Value P Value Age * Family history of diabetes <0.001** Pre pregnancy body mass index <0.001** History of GDM <0.001** Delivery of a large infant * History of miscarriage ** Abnormal baby in previous pregnancy History of stillbirth Infections (Urinary, Skin, Vaginal) * History of Polycystic ovary syndrome Note: ** denotes significant at 1% level, * denotes significant at 5% level The F test of Wilks lambda shows which variables contributions are significant. The structure matrix table in SPSS shows the correlations of each variable with each discriminant function. These simple Pearsonian correlations are called structure coefficients or correlations or discriminant loadings. Wilks Lambda test with p<0.001 indicated discriminant analysis significance. The results indicated that of all the variables, history of GDM, pre pregnancy BMI and family history of diabetes had the smallest p-values and hence were most significantly associated with occurrence of GDM. Further, history of miscarriage was significant at 1% level while the variables age, delivery of large infant and history of infections were significant at 5% level. Discriminant functions are interpreted by means of standardized coefficients and the structure matrix. Standardized beta coefficients are given for each variable in each discriminant function and the larger the standardized coefficient, the greater is the contribution of the respective variable to the discrimination between groups. From table 2, it is concluded that the variable history of GDM plays a crucial role in discrimination between GDM and non GDM patients while the variables family history of diabetes, history of infections and history of miscarriage also contribute to a great extent. Table 3 shows that of the total 188 records of pregnant women, ijpam.eu

7 Table 2: Canonical Discriminant Function Coefficient Variables Unstandardized Standardized Coefficients Coefficients Age Family history of diabetes Pre pregnancy body mass index History of GDM Delivery of a large infant History of miscarriage Abnormal baby in previous pregnancy History of stillbirth Infections (Urinary, Skin, Vaginal) History of Polycystic ovary syndrome Constant Table 3: Classification Table Predicted Observed Output GDM Percentage Correct No Yes No Output GDM Yes Overall Percentage had GDM in current pregnancy of which 45 were correctly identified using the DA model 124 were the non GDM patients of which 112 were correctly identified. Table 4: Statistical Performance Measures Measures of Accuracy Percentage Sensitivity Accuracy Youden s index 0.61 The classification accuracy is used to measure the performance of DA. The properties that tell us about test accuracy are called ijpam.eu

8 sensitivity and specificity. In medical diagnostics, sensitivity is the ability of a model to correctly identify those with the disease (true positive rate), whereas specificity is the ability of the model to correctly identify those without the disease (true negative rate). Youden s index is a measure for classification accuracy of diagnostic test and calculated by sensitivity and specificity values of the test: Youden s index = Sensitivity + Specificity - 1. The index ranges from -1 to 1. A value of 1 means that there are no false positives or false negatives indicating the test is perfect. Hence, the larger the value of the index is, the higher the accuracy of the model. Sensitivity, specificity, accuracy and Youden s index for the model are shown in Table 4. Sensitivity of the DA model was calculated to be 70.31% while the specificity was found to be an astounding 90.32%. Youden s index was With an overall accuracy of 83.51%, the model has proved to be an efficient model for early detection of GDM among pregnant patients. 6 Conclusion A true increase in the prevalence of GDM, aside from its adverse consequences for infants in the newborn period, might also reflect or contribute to the current patterns of increasing diabetes and obesity. Therefore, the public health aspects of increasing GDM need more attention. Also in India more than 70% of population live in rural settings and facilities for diagnosing diabetes itself is limited. In this scenario, performing OGTT to diagnose GDM is not possible as the cost involved is prohibitive to perform three blood tests Hence the need is for a simple and economical test to diagnose GDM. With a staggering 83.51% overall accuracy, the DA model has proved to be an efficient classifier which helps to detect GDM in advance by using newly designed input parameters for multigravida pregnant women without even going to the hospital thereby reducing the cost for different medical tests and hence would be highly beneficial for pregnant women. Moreover, family history of diabetes, pre pregnancy BMI and history of GDM were found to be the most influential risk factors in detection of GDM, which will thereby help the patient to be aware in advance and take precautionary measures so that GDM can be averted. ijpam.eu

9 References [1] KG. Alberti, PZ. Zimmett, Definition, diagnosis and classification of diabetes mellitus and its complications, Part 1: diagnosis and classification of diabetes mellitus provisional report of a WHO consultation, Diabetic Medicine Journal, 15 (1995), [2] S. Farhanah, BT. Jaafar, DM. Ali, Diabetes mellitus forecast using artificial neural networks, Asian conference of paramedical research proceedings, Kuala Lumpur, Malaysia, (2005). [3] DW. Hosmer, S. Lemeshow, Applied Logistic Regression, John Wiley, New York (1989). [4] N. Mohamad, RI. Ismet, Rofiee M et al., Metabolomics and partial least square discriminant analysis to predict history of myocardial infarction of self-claimed healthy subjects: validity and feasibility for clinical practice, J Clin Bioinform Springer, 5, No. 3 (2015). [5] PS. Muller, SM. Sundaram, M. Nirmala, E. Nagarajan, Application of Computational Technique in Design of Classifier for Early Detection of Gestational Diabetes Mellitus, Applied Mathematical Sciences, 9, No. 67 (2015), [6] TS. Tran, JE. Hirst, MA. Do, JM. Morris, HE. Jeffery, Early Prediction of Gestational Diabetes Mellitus in Vietnam: Clinical impact of currently recommended diagnostic criteria, Diabetes Care, 36 (2013), [7] P. Wahi, V. Dogra, K. Jandial, R. Bhagat, R. Gupta, S. Gupta, et al., Prevalence of Gestational Diabetes Mellitus (GDM) and its Outcomes in Jammu Region, J Assoc Physicians India, 59 (2011), [8] C. Zhang, J. Song, Z. Wu, Fuzzy Integral be Applied to the Diagnosis of Gestational Diabetes Mellitus, Sixth International Conference on Fuzzy Systems and Knowledge Discovery, IEEE, 4(2009), ijpam.eu

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