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Logit Regression to predict the occurrence of diabetes using various medical predictor variables

Ramoji Rao Maruboina 21125054

Revanth Gadireddy 21125056

Ujjwal Kumar Shukla 21125076

Saroj Anjesh 170634

Project 2 (Group - 11)

MBA 652A - Statistical Modelling For Business Analysis

Presented to:

Prof. Devlina Chatterjee

IME Department

IIT Kanpur

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Introduction

Objective

  • Diabetes mellitus is a disease related to the levels of blood sugar. It has become imperative for people to identify symptoms and the causes for Diabetes mellitus.
  • Therefore, it is crucial to identify the causes beforehand to prevent oneself from getting the disease.
  • The objective of this study find the major causes for Diabetes in people using parameters such as Insulin, Blood Pressure, Age, Pregnancies, BMI and Glucose.

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Variables

Variable

Description

Type

Blood Pressure

Diastolic Blood Pressure

Continuous

Glucose

Plasma glucose concentration in an oral glucose tolerance test

Continuous

Pregnancies

Number of times the particular human got pregnancies is taken here

Discrete

BMI

It is a measure of weight(kg) to square of height(m2) ratio

Continuous

Age

Age in years

Continuous

Insulin

2-Hour serum insulin

Continuous

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Descriptive Statistics of the Dataset

(347, 7)

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Box plots

239

108

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Correlation Matrix

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Regression Models

Regressor

Model (1)

Model (2)

Model (3)

Model (4)

Blood Pressure

*

​

*

*

Glucose

*

*

*

*

Pregnancies

*

*

*

*

BMI

​

*

​

*

Age

​

*

*

*

Insulin

*

*

*

*

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Model 1

X1

Glucose

0.0213

(0.005)

X2

Insulin

0.0026

(0.001)

X3

Blood Pressure

-0.0616

(0.008)

X4

Pregnancies

0.1672

(0.041)

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ROC Curve and Confusion matrix – Model 1

​

​

Predicted

All

​

​

0

1

​

Actual

0

209

30

239

1

69

39

108

All

​

278

69

​

Accuracy

73.5

Sensitivity

0.56

Specificity

0.75

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Model 2

X1

Glucose

0.0110

(0.004)

X2

Insulin

0.0040

(0.001)

X3

Age

-0.0286

(0.017)

X4

Pregnancies

0.1713

(0.054)

X5

BMI

-0.0733

(0.015)

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ROC Curve and Confusion matrix – Model 2

​

​

Predicted

All

​

​

0

1

​

Actual

0

209

30

239

1

69

39

108

All

​

278

69

​

Accuracy

71.5

Sensitivity

0.56

Specificity

0.75

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Model 3

X1

Glucose

0.0210

(0.005)

X2

Insulin

0.0026

(0.001)

X3

Age

0.0047

(0.018)

X4

Pregnancies

0.1574

(0.056)

X5

Blood Pressure

-0.0626

(0.009)

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ROC Curve and Confusion matrix – Model 3

​

​

Predicted

All

​

​

0

1

​

Actual

0

208

31

239

1

62

46

108

All

​

270

77

​

Accuracy

73.2

Sensitivity

0.60

Specificity

0.77

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Model 4

X1

Pregnancies

0.1574

(0.057)

X2

Glucose

0.0210

(0.005)

X3

Blood Pressure

-0.0625

(0.012)

X4

Insulin

0.0026

(0.001)

X5

BMI

-5.925e-05

(0.020)

X6

Age

0.0047

(0.018)

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ROC Curve and Confusion matrix – Model 4

​

​

Predicted

All

​

​

0

1

​

Actual

0

208

31

239

1

62

46

108

All

​

270

77

​

Accuracy

73.2

Sensitivity

0.60

Specificity

0.77

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Coefficients and Std Errors

Regressor

Model (1)

Model (2)

Model (3)

Model (4)

Blood Pressure

-0.0616 **

(0.008)

​

-0.0626 ***

(0.009)

-0.0625 **

(0.012)

Glucose

0.0213 **

(0.005)

0.0110 **

(0.004)

0.0210 **

(0.005)

0.0210 **

(0.005)

Pregnancies

0.1672 **

(0.041)

0.1713 **

(0.054)

0.1574 **

(0.056)

0.1574 **

(0.057)

BMI

​

-0.0733 **

(0.015)

​

-5.925e-05

(0.020)

Age

​

-0.0286

(0.017)

0.0047

(0.018)

0.0047

(0.0018)

Insulin

0.0026 **

(0.001)

0.0040 **

(0.001)

0.0026 **

(0.001)

0.0026 **

(0.001)

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Omitted Variables

  • Diabetes Pedigree Function
  • Food habits
  • Workout time
  • Skin Thickness
  • Race

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Conclusion

  • Model 3 has been finalised as the main model as it gives a Pseudo R2 value of 0.1417 with five regressors whereas Model 4 gives a R2 value of 0.1417 with six regressors
  • From the model it is evident that more number of pregnancies will increase chances of getting diabetes
  • Higher the Glucose and insulin increases the chances of getting diabetes
  • Person with higher age will have excessive chances of getting diabetes compared to the person with lower age, where as Blood pressure also has favour affect towards diabetes

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  • A blood sugar level below 70 mg/dL is low and can harm you. A blood sugar level below 54 mg/dL is very low and is a cause for immediate action. Below 54 mg/dL is considered as outlier. (Premitable range 54 to 199)
  • 90 mm-Hg or greater diastolic pressure is considered as high blood pressure
  • Around 15 pregnancies in a lifetime and above is removed
  • Diastolic blood pressure below 50 mm HG is very low and it’s considered as outlier and removed.

​

Appendix

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