RPubs link information

• Rpubs link comes here: https://rpubs.com/mBojczuk/668491

Introduction

• This presentation is to go through patients health statuses and see whether Smoking or levels of Creatinine Phosphokinase (CPK) contribute to the probability of dying to heart failure
• When a patient has gone through a past heart failure or had muscle tissue damage the muscle releases levels of CPK into the blood
• Techniques used in findings:
  • Probability of dying given that the patient was a smoker
  • Levene’s Test to find the probability of dying or surviving heart failure due to CPK homogeneity
  • T-Test to find the critical value, p-value and confidence interval on dying or surving a heart failure due to CPK levels

Problem Statement

• The aim of this investigation is to determine if there is any statistical significance when comparing mean values in patients who have died due to heart failure compared to patients who haven’t died based on patients health status
• The data will be checked for normality using qqplots and historgrams while also determining if the data is suitable for t-testing
• Two-sample t-test will be used to conduct hypothesis testing between Creatinine Phosphokinase levels and if a patient died or survived as a result of heart failure
• Will also be looking at some probabilities of dying and being a smoker and plotting the results in a barplot

Data

• The data was retrieved from user Larxel(2020) from a Kaggle contest called “Heart Failure Prediction”
• The original dataset was collected at the Faisalabad Institute of Cardiology and at the Allied Hospital in Faisalabad which contained the medical records of 299 heart failure patients during April 2015 to December 2015
• It shows 299 obs where patients have either died or are alive after a heart failure and shows underlying health issues and other statuses of the patient
• The variables we will be looking at are:
  • Creatinine Phosphokinase or CPK: Levels of CPK relate to muscle tissue that has been damage and casuses CPK to flow into the blood
  • Smoking: Smoker or Non-Smoker
  • DEATH_EVENT: Whether a patient is deceased or not due to a heart failure

Data Cont.

• CPK is a numerical value measured in mcg/L and higher levels of CPK in the blood may make a patient more prone to death by heart failure
• Smoking is factor with levels 1,0: 1 = Smoker, 0 = Non-SMoker
• DEATH_EVENT is factor with levels 1,0: 1 = Dead, 0 = Alive

#set the factor levels and labels
heart$smoking <- heart$smoking %>% factor(levels = c(1,0), labels = c("Smoker", "Non-Smoker"))
heart$DEATH_EVENT <- heart$DEATH_EVENT %>% factor(levels = c(1,0), labels = c("Dead", "Alive"))

Heart Failure based on Smoking

• Here we take a look at Smoking status based on Heart Failure
• When looking at the probability of heart failure causing death given the patient was a smoker \[PR(Died to Heart Failure|Smoker) = 0.32\]
• with a PR = 0.32 it shows that there is a low probability of heart failure deaths being influenced by the patients smoking status

table(heart$DEATH_EVENT,heart$smoking)  %>% addmargins()

##        
##         Smoker Non-Smoker Sum
##   Dead      30         66  96
##   Alive     66        137 203
##   Sum       96        203 299

#Probability died to heart failure given smoker status 
round((29/292)/(92/292),2)

## [1] 0.32

Heart Failure based on Smoking Cont.

• We then can visualise the proporitions of the status and find that both are fairly equal showing there are no potential signs of death by heart failure being worse in Smokers compared to Non-Smokers

table_1 <- table(heart$DEATH_EVENT,heart$smoking) %>% prop.table(margin = 2)
#barplot with the proportions table that is cross tabulated
table_1 %>% barplot(main = "Patient After Heart Failure Status by Smoking Status", 
                    ylab="Proportion within Smoking Status",
                    xlab="Smoking Status",
                    ylim=c(0,.8), legend=rownames(table_1), beside=TRUE,
                    args.legend=c(x = "top", horiz=TRUE, title="Patient Status"))
grid()

Dealing with Outliers for CPK Levels

• To check for outliers in CPK we create a boxplot and then adjust the data by removing outliers which are extremley high.
• This is to get a better mean as higher outliers increase the mean for both values
• With the boxplot we can see both Alive and Dead Patients have 3-4 values way above 3900 CPK mcg/L and will remove them as potential outliers

#box plot creation
heart %>% boxplot(creatinine_phosphokinase ~ DEATH_EVENT, data = ., 
                  xlab = 'Patient Status', ylab = 'CPK Level per mcg/L')

#after seeing the boxplot we choose to remove CPK values above 3800 mcg/L
heart <- heart %>% filter(creatinine_phosphokinase < 3800)

Descriptive Statistics on CPK Levels

• Based on the summary statistics with such a difference between the Mean and Median we can tell that there are some large values at the upper end of our data set skewing the mean
• Both DEATH_EVENT values also contained a large SD showing that the values are spaced quite far from the mean and the range of values are quite spread
• The data set has no missing values and we have reduced the data to 292 observations after cleaning the data set

table1 <- heart %>% group_by(DEATH_EVENT) %>% summarise(Min = min(creatinine_phosphokinase, na.rm = T),
                                                        Q1 = quantile(creatinine_phosphokinase, probs = 0.25, na.rm = T),
                                                        Median = median(creatinine_phosphokinase, na.rm = T),
                                                        Mean = mean(creatinine_phosphokinase, na.rm = T),
                                                        Q3 = quantile(creatinine_phosphokinase, probs = 0.75, na.rm = T),
                                                        Max = max(creatinine_phosphokinase, na.rm = T),
                                                        SD = sd(creatinine_phosphokinase, na.rm = T),
                                                        Length = n(),
                                                        Missing = sum(is.na(creatinine_phosphokinase)))
kable(table1)

Decsriptive Statistics on CPK Levels Cont.

• Both histograams show a similair right skew
• Both show the large spread of the data that we infered from the SD in the previous slide
• Both also show a high frequency in the lower end of CPK levels

par(mfrow = c(1, 2))
#set filters
deceased <- heart %>% filter(DEATH_EVENT=="Dead")
alive <- heart %>% filter(DEATH_EVENT=="Alive")
#Deceased Plots
hist(deceased$creatinine_phosphokinase, xlab = "Creatinine Phosphokinase Levels", breaks= 10, main = "Deceased Patients from Heart Failure")
abline(v = mean(deceased$creatinine_phosphokinase), col = "red", lw = 2)
text(1500,25, "Mean = 423.15\nSD = 467.52", col = 'black', cex = 0.75)
#Alive Plots
hist(alive$creatinine_phosphokinase, xlab = "Creatinine Phosphokinase Levels", breaks= 10, main = "Alive Patients from Heart Failure")
abline(v = mean(alive$creatinine_phosphokinase), col = "red", lw = 2)
text(1600,56, "Mean = 479.58\nSD = 569.37", col = 'black', cex = 0.75)
#Legend
legend("topright", c('Mean'), fill = c('red'), cex =0.75)

Decsriptive Statistics on CPK Levels Cont

• Using a qqplot to also check for nomality in the data set
• As the values are at the upper end of the dotted line, it shows a more positive skewed data then normal distribution
• In the end as n>30 we can still end up assuming normallity during the t-test as the t-tests is based on the two groups means
• Due to the Central Limit Theorem the distribution is repeated in sampling and converges to a normal distribution irrespective of the current distribution

par(mfrow = c(1, 2))
qqPlot(deceased$creatinine_phosphokinase, dist="norm", ylab = "CPK levels Deceased")

## [1] 74 73

qqPlot(alive$creatinine_phosphokinase, dist="norm", ylab = "CPK levels Alive")

## [1] 133 182

Hypothesis Testing

• Our Hypothesis is that there is no mean difference in people who have died of high CPK levels to those how have not
• Hypothesis for the two-sample t-tests:
  • \(H_0: \mu_1 = \mu_2\)
  • \(H_A: \mu_1 \ne \mu_2\)
• Assumptions:
  • Population homogeneity of variance
  • Large sample of data for both groups as such data normally distributed
• Decision Rules Reject \(H_0\):
  • P-value < 0.05 (significance level)
  • If 95% CI of the mean difference does not capture \(H_0: \mu_1 = \mu_2 = 0\)
  • Otherwise, fail to reject \(H_0\)
• Conclusion:
  • Tests will be statistically signicant if we reject \(H_0\)
  • Otherwise, the test is not statistically significant

Hypthesis Testing Cont.

• Levene’s Test to check Homogeneity of variances

heart %>% leveneTest(creatinine_phosphokinase ~ DEATH_EVENT, data = .)

• As P > 0.05 we fail to reject \(H_0\) and can assume equal variances
• With Equal variances we can apply an equal variance Two-sample t-test

heart %>% t.test(creatinine_phosphokinase ~ DEATH_EVENT, data = ., var.equal = T, alternative = "two.sided")

## 
##  Two Sample t-test
## 
## data:  creatinine_phosphokinase by DEATH_EVENT
## t = -0.83029, df = 290, p-value = 0.4071
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -190.18782   77.33216
## sample estimates:
##  mean in group Dead mean in group Alive 
##            423.1522            479.5800

Hypothesis Testing Conclusion

• Two-Sample t-test result summary:
  • We assumed normality as the data for each variable was greater than 30
  • Leven test showed the variances are homogenous as P > 0.05
  • Estimated Mean difference: \(\bar{x}_1 - \bar{x}_2 = 423.15 - 479.58 = -56.43\)
  • 95% CI of difference between means \([-190.19, 77.33]\)
  • P-value = 0.4071
• Decision:
  • Fail to Reject \(H_0\)
• The results of the study was unable to find statistically significant mean difference between patients who had died from heart failure based on high CPK levels compared patients who have not died, t(df=290)= -0.83,p=0.4, 95% CI for the difference in means [-190.19, 77.33]

Discussion

• For our findings, there were no significance in the probability of you dying to heart failure given that you were a smoker
• No statistically significant mean difference between patients who had died from heart failure due to high CPK as our CI was able to capture our Hypothesis of \(H_0: \mu_1 = \mu_2\) and p-value - 0.4
• Due to a large data set of n>30, the assumption was made of normality, but as the data distribution was highly skewed the result may not give a very good approximation and so the type 1 error rate may have deviated from the 5% level
• A new direction would be trialling nonparametric methods such as the Wilcoxon-Mann-Whitney U test as an alternative as unlike the t-test it doesn’t rely on distributional assumptions
• Our findings were not able to find statistical significances that being a smoker or having higher levels of Creatinine Phosphokinase caused death in patients who had heart failure.

References

• Davide Chicco, Giuseppe Jurman: Machine learning can predict survival of patients with heart failure from serum creatinine and ejection fraction alone. BMC Medical Informatics and Decision Making 20, 16 (2020).
• Larxel 29/06/2020. Heart Failure Prediction. Retrieved from https://www.kaggle.com/andrewmvd/heart-failure-clinical-data