RPubs link information

• https://www.rpubs.com/mc168/1366045

Introduction

• Stroke involves blood flow interruption in brain, often lead to permanent brain damage
• World Stroke Organization reports stroke ranks as the third leading cause of both mortality and long-term disability globally
• Significant healthcare burden and reduced quality of life
• Many types of risk factors including biological (e.g. hypertension), lifestyle(e.g. smoking), demographic (e.g. age)
• Understanding risk factors help to develop effective prevention strategies, enabling early clinical intervention

Problem Statement

• Research question 1: Is the blood glucose level differed between stroke and non-stoke patients?
• We will check mean difference of average glucose level between stroke and non-stroke patients is statistically significant
  • Test method: Two-sample t-test
• Research question 2: Any association between residence type and stroke occurence?
• We will check if categorical association exists between residence type (urban versus rural) and stroke occurrence
  • Test method: Chi-square Test of Association

Data

• Dataset Source: The analysis uses the open Stroke Prediction Dataset (fedesoriano 2021) from Kaggle
• Dataset Context: Compiled from healthcare records, it focuses on predicting stroke risk based on demographic, clinical, and lifestyle factors
• Dataset Size: Comprises 5,110 observations (rows) and 12 features (columns), representing individual patient profiles
• The data is imbalanced, with a minority of stroke cases (approximately 4.9%, or 249 instances)

Data Cont.

• For this assignment, we will focus on avg_glucose_level, Residence_type, stroke
  • avg_glucose_level: numerical feature representing average glucose level in blood
  • Residence_type: categorical feature representing where the patient live, ‘Rural’ or ‘Urban’
  • stroke: numerical feature, 1 = patient had a stroke; 0 = patient did not
• Residence_type is converted into factor with level ‘Rural’ ‘Urban’
• stroke is converted into factor with level and labels ‘No’, ‘Yes’ to make it more descriptive
• There is no missing values in avg_glucose_level, Residence_type, stroke

dat_stroke <- read_csv("stroke_dataset.csv")

#Filter only important feature
stroke_ds <- dat_stroke[,c(8,9,12)]

Check data frame structure

str(as.data.frame(stroke_ds))

## 'data.frame':    5110 obs. of  3 variables:
##  $ Residence_type   : chr  "Urban" "Rural" "Rural" "Urban" ...
##  $ avg_glucose_level: num  229 202 106 171 174 ...
##  $ stroke           : num  1 1 1 1 1 1 1 1 1 1 ...

Data Cont.

Check missing values

colSums(is.na(stroke_ds))

##    Residence_type avg_glucose_level            stroke 
##                 0                 0                 0

Convert to factors

stroke_ds$Residence_type <- factor(stroke_ds$Residence_type,
                             levels = c("Rural","Urban"))
levels(stroke_ds$Residence_type)

## [1] "Rural" "Urban"

stroke_ds$stroke <- factor(stroke_ds$stroke,
                     levels = c(0,1),labels = c("No","Yes")) 
levels(stroke_ds$stroke)

## [1] "No"  "Yes"

Descriptive Statistics and Visualisation

• cross-tabulation and clustered barchart shows similar stroke/non-stroke proportion of patients live in rural/urban area

tab1 <- table(stroke_ds$stroke,stroke_ds$Residence_type) %>%
  prop.table(margin = 2)
knitr::kable(tab1)

barplot(tab1,
        main = "Stroke History by Residence Type",ylab="Proportion within residence type",
        ylim=c(0,1),legend=rownames(tab1),beside=TRUE,
        args.legend=c(x = "topright",horiz=TRUE, title="Had stroke"),
        xlab="Residence type")

Decsriptive Statistics Cont.

• Summary statistics of the data shows
  • for stroke patients the mean average glucose level is 132.54
  • for non-stroke patients the mean average glucose level is 104.8

stroke_ds %>% group_by(stroke) %>% summarise(Min = min(avg_glucose_level,na.rm = TRUE),
                                      Q1 = quantile(avg_glucose_level,probs = .25,na.rm = TRUE),
                                      Median = median(avg_glucose_level, na.rm = TRUE),
                                      Q3 = quantile(avg_glucose_level,probs = .75,na.rm = TRUE),
                                      Max = max(avg_glucose_level,na.rm = TRUE),
                                      Mean = mean(avg_glucose_level, na.rm = TRUE),
                                      SD = sd(avg_glucose_level, na.rm = TRUE),
                                      n = n(),
                                      Missing = sum(is.na(avg_glucose_level))) -> tab2

knitr::kable(tab2)

Decsriptive Statistics Cont.

• Side-by-side box plot shows average glucose level distributions are right-skewed
• Stroke patients had higher average glucose level compare to non-stroke patients
• outliers observed in average glucose level of non-stroke patients
  • not removed as they are not isolated, and appear plausible

stroke_ds %>% boxplot(avg_glucose_level ~ stroke,data = ., na.rm=TRUE, main="Box Plot of glucose by stroke", 
               ylab="stroke", xlab="glucose", horizontal = TRUE, col = "darkorange2")

Hypothesis Testing and Confidence Interval

• By applying two-sample t-test, we will check if mean difference of average glucose level between stroke and non-stroke patients is statistically significant

• Assumptions: 1) average glucose level is normally distributed 2) Homogeneity of variances

• Before the test, we will check the normality and variance homogeneity assumption

• Check normality using QQ Plot

# QQ plot for stroke = Yes
stroke_yes <- stroke_ds %>% filter(stroke == "Yes")
stroke_yes$avg_glucose_level %>% qqPlot(dist="norm")

## [1] 194 136

Hypothesis Testing and CI Cont.

# QQ plot for stroke = no
stroke_no <- stroke_ds %>% filter(stroke == "No")
stroke_no$avg_glucose_level %>% qqPlot(dist="norm")

## [1]  959 2840

• QQplot shows the average glucose level in both sampling groups fall outside of the 95% CI
  • They do not follow normal distribution
• sample is large enough with n>30 for both groups
  • based on CLT, we can assume they follow normal distribution

Hypothesis Testing and CI Cont.

• By Levene’s Test, check assumption of population variances are homogeneous

leveneTest(avg_glucose_level ~ stroke, data = stroke_ds)

• Null-hypothesis of Levene test H0: \(\sigma_1 = \sigma_2\)
• Alternate hypothesis of Levene test HA: \(\sigma_1 \ne \sigma_2\)
• Since p<0.05, H0 of Levene test rejected.
  • population variances are not homogeneous

Hypothesis Testing and CI Cont.

• Use two-sample Welch test for unequal variances
• H0: Mean average glucose level of stroke patients is not statistically significant different from that of non-stroke patients \[H_0: \mu_1 - \mu_2 = 0\]
• HA: Mean average glucose level of stroke patients is statistically significant from that of non-stroke patients \[H_A: \mu_1 - \mu_2 \ne 0\]

results <- t.test(
  avg_glucose_level ~ stroke,
  data = stroke_ds,
  var.equal = FALSE,
  alternative = "two.sided"
)
results

## 
##  Welch Two Sample t-test
## 
## data:  avg_glucose_level by stroke
## t = -6.9824, df = 260.89, p-value = 2.401e-11
## alternative hypothesis: true difference in means between group No and group Yes is not equal to 0
## 95 percent confidence interval:
##  -35.57474 -19.92371
## sample estimates:
##  mean in group No mean in group Yes 
##          104.7955          132.5447

Hypothesis Testing and CI Cont.

• Use p-value and 95% CI of the mean to make decision about null hypothesis

results$p.value

## [1] 2.401437e-11

results$conf.int

## [1] -35.57474 -19.92371
## attr(,"conf.level")
## [1] 0.95

• Results Summary:
  • Estimated difference between means: 104.8 - 132.54 = -27.74
  • p-value = 2.401e-11, significance level \(\alpha\)=0.05, p<\(\alpha\)
  • t(df=261)=−6.98
  • 95% CI for the difference in means [-35.57 -19.92] cannot capture H0: mean difference = 0
• Reject H0. The two sample t-test results were statistically significant
• Results found stroke patients and non-stroke patients have statistically significant difference in mean average glucose level

Categorical association

• Use Chi-square test of association with hypotheses below

Null Hypothesis H0: residence type and stroke has no statistically significant association

Alternative Hypothesis HA: residence type and stroke has statistically significant association

Assumption: Less than 25% cells with expected counts < 5

chi2 <- chisq.test(table(stroke_ds$stroke,stroke_ds$Residence_type))

• Observed counts

chi2$observed

##      
##       Rural Urban
##   No   2400  2461
##   Yes   114   135

• Expected counts

chi2$expected

##      
##           Rural     Urban
##   No  2391.4978 2469.5022
##   Yes  122.5022  126.4978

expected counts > 5 in all cells

Categorical association Cont.

• Results of Chi-square test

chi2

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  table(stroke_ds$stroke, stroke_ds$Residence_type)
## X-squared = 1.0816, df = 1, p-value = 0.2983

• df = (r-1)(c-1) = (2-1)(2-1) = 1, X-squared = 1.0816

• p-value = 0.2983, \(\alpha\)=0.05, p>\(\alpha\)

• Fail to reject H0. The Chi-square test of association was not statistically significant.

• Results found no association between residence type and stroke

Discussion

• We used the Stroke Prediction Dataset from Kaggle
• primary focus on features average glucose level, residence type and stroke
• Summary statistics shows the mean average glucose level of stroke and non-stroke patients are 132.54 and 104.8
• clustered bar chart shows similar proportion of stroke/non-stroke patients living in both rural and urban areas
• two-sample Welch t-test was used to test mean average glucose level of stroke and non-stroke patients have statistically significant difference
  • The average glucose level for both group of patients exhibited evidence of non-normality upon inspection of the normal Q-Q plot, the central limit theorem ensured that the t-test could be applied due to the large sample size in each group
  • The Levene’s test of homogeneity of variance indicated that assumption of equal variance was violated, with p=4.63e-22 < 0.05
  • Welch’s test assuming unequal variance found a statistically significant difference between the mean average glucose level of stoke and non-stroke patients, with t(df=261)=−6.98, p<0.001, 95% CI for the difference in means [-35.57 -19.92]
  • The results suggest that stroke patients have significantly higher average blood glucose level

Discussion Cont.

• A Chi-square test of association was used to test for a statistically significant association between residency type and stroke
  • Results of the test found no statistically significant association, with χ2=1.0816,p>0.05.
  • This suggest that whether living in rural or urban area have no effect on chance of having stroke
• Limitation:
  • dataset is imbalanced with minority stroke case
  • comparisons with stroke subgroup have higher uncertainty
• Future work
  • use resampling techniques such as SMOTE to make the dataset more balanced before analysis
  • perform regression analysis to investigate any relationship between factors such as bmi, glucose level, age, and their effect on stroke

References

• Feigin, V. L., Brainin, M., Norrving, B., Martins, S. O., Pandian, J., Lindsay, P., F Grupper, M., & Rautalin, I. (2025). World Stroke Organization: Global Stroke Fact Sheet 2025. International journal of stroke : official journal of the International Stroke Society, 20(2), 132–144. https://doi.org/10.1177/17474930241308142
• Grolemund, Y. X. J. J. a. G. (2023, December 30). R Markdown: The Definitive guide. https://bookdown.org/yihui/rmarkdown/
• Stroke Prediction Dataset. (2021, January 26). Kaggle. https://www.kaggle.com/datasets/fedesoriano/stroke-prediction-dataset