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Introduction

• Diabetes is a chronic disease caused by either insufficient insulin production by the pancreas or inefficient use of insulin by the body (WHO, 2023).
• Diabetes increases the risk of vision loss, kidney diseases, heart attacks, strokes, and amputations (WHO, 2023).
• The World Health Organisation estimates that diabetes will be the seventh major contributor to mortality worldwide in 2030 (Albert Einstein College of Medicine, n.d).
• According to World Health Organisation (2023), 8.5% of adults aged 18 years and older had diabetes. Diabetes caused 1.5 million deaths in 2019, with 48% of diabetes deaths occurring before age 70.

Introduction Cont.

• There are several types of diabetes (WHO, 2023):
  • Type 1 Diabetes -> Pancreas produces little or no insulin and requires daily insulin administrations.
  • Type 2 Diabetes -> Inability to produce enough insulin, or body resists insulin.
  • Gestational diabetes -> High blood glucose levels affecting pregnant women.
• Being overweight, having an inactive lifestyle and genetics are the three biggest contributors to type 2 diabetes (WebMD, 2021).

Problem Statement

• This study aims to provide insight into the potential associations between obesity and diabetes to support diabetes management and prevention.
• As stated in the introduction, being overweight or obese is one of the main factors contributing to diabetes.
• According to BMI (Body Mass Index), people classified as “overweight” are three times more likely to develop diabetes than those of normal weight (Obesity Action Coalition, n.d.).
• The following BMI categories are considered to be at high risk for developing type 2 diabetes:
  • Overweight -> BMI 25-29.9
  • Obesity -> BMI 30-39.9
  • Severe Obesity -> BMI >= 40
• The higher the BMI, the greater the risk of developing type 2 diabetes.

Problem Statement Cont.

• In this presentation, we will perform a hypothesis test to determine if the BMI of diabetic patients is the same as non-diabetic patients.
• The null hypothesis assumes that there is no difference in BMI between diabetics and non-diabetics.
• If the p-value is less than 0.05, we will reject the null hypothesis. This means that we have no evidence that diabetic patients have the same BMI as non-diabetic patients.
• If the p-value is greater than 0.05, this means that we have no statistical evidence to reject the null hypothesis.
• Other than hypothesis testing, we will also use descriptive statistics and visualizations to assess differences between 2 groups.

Data

• Pima Indian diabetes dataset was collected by National Institute of Diabetes and Digestive and Kidney Diseases.
• The Pima Indian diabetes dataset (UCI Machine Learning, 2016) was downloaded from: https://www.kaggle.com/datasets/uciml/pima-indians-diabetes-database
• The primary objective of this dataset is to predict diabetes based on machine learning algorithms.
• The Pima Indian has a higher diabetes mellitus prevalence, and it is a popular benchmark dataset for predicting diabetes (Chang et al., 2022).
• The dataset contains information on 768 females at least 21 years old from the Pima Indians of Arizona and Mexico.
• The sampling method used to collect the data is unknown. The dataset focuses on only Pima Indian women so the sampling method used is likely to be convenience sampling.
• This dataset consists of 768 observations and 9 variables. Variables in this dataset include pregnancies, Blood Pressure, Glocose, Skin Thickness, Insulin, BMI, Diabetes Pidegree function, age and outcome.

Data Cont.

• As mentioned in the problem statement, we will test the relationship between obesity and diabetes. Therefore, only BMI and Outcome will be used in this report.
• Outcome -> This is a categorical variable:
  • 0: Non-diabetic
  • 1: Diabetic
• BMI (Body Mass Index) -> BMI is calculated based on an individual’s height and weight. \[ BMI: \frac{weight (kg)}{[height (m)]^2} \]
• BMI is usually classified into different categories:
  • Underweight: BMI < 18.5
  • Normal Weight: 18.5 <= BMI <= 24.9
  • Overweight: 25 <= BMI <= 29.9
  • Obese: BMI >= 30

Descriptive Statistics and Visualisation

diabetes$BMI[diabetes$BMI == 0] <- mean(diabetes$BMI, na.rm = TRUE)
diabetes %>% boxplot(BMI ~ Outcome, data = ., ylab = "BMI")

Descriptive Statistics and Visualisation Cont.

diabetes_False <- diabetes[diabetes$Outcome == 0,]
diabetes_True <- diabetes[diabetes$Outcome == 1,]
d <- density(diabetes_True$BMI, adjust = 2)
d2<- density(diabetes_False$BMI, adjust = 2)
{plot(d, main="Density Plot of BMI", xlab = "BMI", col ="red", lwd = 2)
lines(d2, lwd = 2)
legend(65, 0.05, legend=c("Diabetic", "Non-diabetic"), col=c("red", "black"), lty=1:1, lwd = 2, cex=0.6, text.font=4, text.width = 7)}

Descriptive Statistics and Visualisation Cont.

• From the boxplot, we can see that people with diabetes tend to have higher BMI than people do not have diabetes.
• Interestingly, the lower quartile BMI of diabetic patients is even higher than the mean BMI of non-diabetic patients.
• In addition, there are several outliers at the upper end of the boxplot for diabetic patients, but only 2 outliers at the upper end of the boxplot for non-diabetic patients.
• Although a body mass index greater than 50 is uncommon, it can still happen. Upper outliers are not replaced or excluded, as they can still provide valuable information in our case.
• BMI is calculated based on an individuals’ height and weight. A BMI of 0 is not possible, it may be a missing value. Therefore, those numbers with a BMI of 0 were replaced accordingly with the mean value of each result.
• We can use density plots to identify differences in the distribution and central tendency of the two outcomes.
• From the density plot, we can see that the distribution is similar for diabetic and non-diabetic patients, but the central tendency is higher for diabetic patients.

Decsriptive Statistics Cont.

• The following table shows the summary statistics of BMI for diabetic and non-diabetic patients.
• As we can see from the table below, most of the summary statistics (mean, median, Q1, Q3, minimum, maximum) are significantly higher for diabetic patients than for non-diabetic patients.
• The sample size(n) for non-diabetic patients is larger than diabetic patients and there are no missing values in this data set.
• The standard deviations of two different outcomes are similar.

diabetes %>% group_by(Outcome) %>% summarise(Min = min(BMI,na.rm = TRUE), Q1 = quantile(BMI,probs = .25,na.rm = TRUE),  Median = median(BMI, na.rm = TRUE), Q3 = quantile(BMI,probs = .75,na.rm = TRUE), Max = max(BMI,na.rm = TRUE), Mean = mean(BMI, na.rm = TRUE), SD = sd(BMI, na.rm = TRUE), n = n(), Missing = sum(is.na(BMI))) -> table1
knitr::kable(table1)

Hypothesis Testing

BMI_nondiabetic <- diabetes %>% filter(Outcome == 0)
BMI_nondiabetic$BMI %>% qqPlot(dist="norm")

## [1] 443 152

Hypthesis Testing Cont.

BMI_diabetic <- diabetes %>% filter(Outcome == 1)
BMI_diabetic$BMI %>% qqPlot(dist="norm")

## [1]  63 171

Hypthesis Testing Cont.

• There are only a few patients’ data were collected in this dataset. It’s generally impossible to collect all the diabetic patient data, so it’s safe to assume that the population standard deviation is unknown.
• From the QQ plot, it’s obvious that most of the points seem to be following the normal distribution very closely. However, we can see points for diabetic patients falling outside the heads of the distribution, while points for non-diabetic patients falling outside the tails of the distribution.
• Due to the large sample size (n = 500, 268), normality assumption is not needed.
• The homogeneity of variance was tested using leveneTest. The p-value is significantly higher than the significance level (p >= 0.05), it’s safe to assume equal variance.

leveneTest(BMI ~ Outcome, data = diabetes)

Hypthesis Testing Cont.

\[H_0: \mu_1 = \mu_2 \]

\[H_A: \mu_1 \ne \mu_2\]

t.test(
  BMI ~ Outcome,
  data = diabetes,
  var.equal = TRUE,
  alternative = "two.sided"
  )

## 
##  Two Sample t-test
## 
## data:  BMI by Outcome
## t = -9.097, df = 766, p-value < 2.2e-16
## alternative hypothesis: true difference in means between group 0 and group 1 is not equal to 0
## 95 percent confidence interval:
##  -5.472549 -3.529894
## sample estimates:
## mean in group 0 mean in group 1 
##        30.88007        35.38129

Hypthesis Testing Cont.

• A two-sided t-test was conducted to test whether the BMI of diabetic patients is qual to BMI of non-diabetic patients.
• Our null hypothesis assumes that there is no difference between two groups, our alternative hypotheses assumes that the BMI of diabetic patients is different from non-diabetic patients.
• Our p-values suggest that if the null hypothesis were true, we would have approximately a 0 chance of observing the sample statistic or more extreme sample statistic than the one we have observed.
• If the null hypothesis is true, the probability of observing a sample mean difference of 4.50 is approximately 0.
• 0 is not within the confidence interval [-5.472549, -3.529894].
• According to the critical value method (p < 0.5), there was a statistically significant difference between BMI of diabetic and non-diabetic patients.
• Therefore, we reject null hypothesis H0.

Discussion

• From the hypothesis testing, we can conclude that there was a statistically significant difference between individuals with and without diabetes.
• Linked to our problem statement, all the analyses performed above (descriptive statistics, visualization, and hypothesis testing) suggest a strong association between obesity and diabetes.
• In addition, hypothesis testing suggests that BMI plays an important role in the management and prevention of diabetes.
• In addition to BMI, other factors such as age, gender, and ethnicity need to be considered when predicting diabetes to get a more comprehensive understanding of diabetes.
• The dataset we used for the study includes only diabetes data from the Pima Indians. Therefore, our conclusion may be biased.
• In the future, other sampling methods can be used such as a stratified sampling method, to obtain a more diverse dataset that is representative of the target population.
• The larger the sample size, the more accurate our statistical inferences will be. In this dataset, we only have 768 observations, and it would be desirable to collect more data in future studies to ensure that the sample is representative of the entire population.
• In conclusion, diabetes can be well prevented and managed through weight management, combined with a healthy diet and regular exercise. People with obesity should exercise regularly and control their diet to maintain weight loss and prevent excess weight.

References

• Albert Einstein College of Medicine. (n.d.). What is Global Diabetes. https://www.einsteinmed.edu/centers/global-health/global-diabetes-institute/about-us/global-diabetes/index.html
• Chang, V., Bailey, J., Xu, Q. A., & Sun, Z. (2022). Pima Indians diabetes mellitus classification based on machine learning (ML) algorithms. Neural computing & applications, 1–17. Advance online publication. https://doi.org/10.1007/s00521-022-07049-z
• Diabetes UK. (2022, September 8). BMIBody Mass Index (BMI) Calculator [Online image].https://www.diabetes.co.uk/bmi.html
• Drmohans. (2020, July 20). Does Obesity Always Mean T2DM (Type 2 Diabetes mellitus)? [Online image]. https://drmohans.com/does-obesity-always-mean-t2dm/
• Obesity Action Coalition. (n.d.). Understanding Obesity and Type 2 Diabetes. https://www.obesityaction.org/get-educated/public-resources/brochures-guides/understanding-obesity-and-type-2-diabetes-brochure/#:~:text=Being%20%E2%80%9Coverweight%E2%80%9D%20(BMI%20of,to%20your%20own%20insulin%20hormone.
• UCI Machine Learning. (2016). Pima Indians Diabetes Database [Data set]. Kaggle. https://www.kaggle.com/datasets/uciml/pima-indians-diabetes-database
• WebMD. (2021, May 16). Type 2 Diabetes Causes and Risk Factors. https://www.webmd.com/diabetes/diabetes-causes#:~:text=Although%20not%20everyone%20with%20type,cases%20in%20the%20United%20States.
• World Health Organization. (2023, April 5). Diabetes. https://www.who.int/news-room/fact-sheets/detail/diabetes