Dimension Reduction in cardiovascular disease dataset
The aim of this article is to use PCA and MCA methods for dimension reduction of medical data. PCA is a statistical method, which is used on highly dimensional continuous data in order to reduce number of dimension (number of variables) in dataset. PCA allows to visualize data on 2-dimensional plot and discover more dependency between sets of variables. MCA corresponds for the same process, but for categorical variables.
Dataset analysis
Data set contains information of group of patients suffering for cardiovascular disease and group of healthy patients. It is taken from kaggle platform. https://www.kaggle.com/sulianova/cardiovascular-disease-dataset
df <- read.csv("cardio.csv", sep = ";")
dim(df)## [1] 70000 13Thera are 13 columns and 7000 rows in the dataset.
colnames(df)## [1] "id" "age" "gender" "height" "weight"
## [6] "ap_hi" "ap_lo" "cholesterol" "gluc" "smoke"
## [11] "alco" "active" "cardio"Names of columns correspond to:
id - id of a patient
age - age of a patient given in days
gender - 1 for women, 2 for men
height - height in cm
weight - weight in kg
ap_hi - systolic blood pressure
ap_lo - diastolic blood pressure
cholesterol - level of cholesterol : 1 - normal 2 - above normal 3 - well above normal
gluc - glucose level: 1 - normal 2 - above normal 3 - well above normal
smoke - 1 - patient smokes, 0 - patient does not smoke
alco - 1 - patient drinks alcoholic beverages, 0 - patient does not drink alcoholic beverages
active - 1 - patient is active, 0 - patient is not active
cardio - 1 - patient suffers for cardiovascular disease, 0 - patient does not suffer for cardiovascular disease
head(df)## id age gender height weight ap_hi ap_lo cholesterol gluc smoke alco active
## 1 0 18393 2 168 62 110 80 1 1 0 0 1
## 2 1 20228 1 156 85 140 90 3 1 0 0 1
## 3 2 18857 1 165 64 130 70 3 1 0 0 0
## 4 3 17623 2 169 82 150 100 1 1 0 0 1
## 5 4 17474 1 156 56 100 60 1 1 0 0 0
## 6 8 21914 1 151 67 120 80 2 2 0 0 0
## cardio
## 1 0
## 2 1
## 3 1
## 4 1
## 5 0
## 6 0Dataset contains numerical as well as categorical variables. To make analysis more accurate, I will separete them and conduct individual analysis for numerical variables (using PCA) and categorical variables (using MCA). I will omit id variable as it does not contain any information.
num_df <-df[, c(2, 4:7)]
cat_df <- df[, c(3,8:13)]Age, height, weight, systolic and diastolic blood pressure are numerical variables and gender, cholesterol, glucose, smoke, alcohol, activity and whether person is healthy or not are categorical variables.
As age is given in days, I will transform it into years, to make it more readable.
num_df$age = num_df$age/365Let’s check the basic statistic for numerical variables
summary(num_df)## age height weight ap_hi
## Min. :29.58 Min. : 55.0 Min. : 10.00 Min. : -150.0
## 1st Qu.:48.39 1st Qu.:159.0 1st Qu.: 65.00 1st Qu.: 120.0
## Median :53.98 Median :165.0 Median : 72.00 Median : 120.0
## Mean :53.34 Mean :164.4 Mean : 74.21 Mean : 128.8
## 3rd Qu.:58.43 3rd Qu.:170.0 3rd Qu.: 82.00 3rd Qu.: 140.0
## Max. :64.97 Max. :250.0 Max. :200.00 Max. :16020.0
## ap_lo
## Min. : -70.00
## 1st Qu.: 80.00
## Median : 80.00
## Mean : 96.63
## 3rd Qu.: 90.00
## Max. :11000.00Average examinated person is 53 years old. The person is 164 cm tall and weights 74kg. Their systolic blood pressure equals 128 and diastolic blood pressure equals 96.
Now, let’s check categorical variables.
library(ggplot2)
library(reshape2)
plot.df <- melt(cat_df, id.vars = NULL)
ggplot(data = plot.df) +
geom_bar(aes(x = value)) +
theme(plot.title = element_text(hjust = 0.5, size = 14)) +
facet_wrap(~ variable, scales = "free", ncol = 4)
Most of the patients are women. Only minority reports high glucose or cholesterol level. Most of participants do not smoke and do not drink alcoholic beverage and are active. However, almost a half of them suffers for cardiovascular disease.
PCA for numerical variables
First, let’s check correlations between variables.
cor<-cor(num_df, method="pearson")
print(cor, digits= 1)## age height weight ap_hi ap_lo
## age 1.00 -0.082 0.05 0.021 0.018
## height -0.08 1.000 0.29 0.005 0.006
## weight 0.05 0.291 1.00 0.031 0.044
## ap_hi 0.02 0.005 0.03 1.000 0.016
## ap_lo 0.02 0.006 0.04 0.016 1.000library(corrplot) ## corrplot 0.84 loadedcorrplot(cor)
The results show there is a positive correlation between height and weight variables.
In order to run PCA, I will use factoextra library
library(factoextra)## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBapca <- prcomp(num_df, center=TRUE, scale=TRUE)
summary(pca)## Importance of components:
## PC1 PC2 PC3 PC4 PC5
## Standard deviation 1.1395 1.0285 0.9919 0.9905 0.8239
## Proportion of Variance 0.2597 0.2115 0.1968 0.1962 0.1358
## Cumulative Proportion 0.2597 0.4713 0.6680 0.8642 1.0000fviz_eig(pca)
Scree plot represents graphically the percentage of variance explained by every component. The results show that PC1 explains about 26% of variation. To explain 86% of variance, there has to be 4 components.
fviz_pca_var(pca, col.var = "darkred")
The plot shows that variables converge into three groups. First, there is weight and height, which confirm the correlation results. The second group is systolic and diastolic blood pressure and the third one is age.
Let’s chech variable contribution in every first 3 dimensions, which explain 66% of variance.
library(pdp)
PC1 <- fviz_contrib(pca, choice = "var", axes = 1)
PC2 <- fviz_contrib(pca, choice = "var", axes = 2)
PC3 <- fviz_contrib(pca, choice = "var", axes = 3)
grid.arrange(PC1, PC2, PC3)
The most important component consist of height and weight. The second one consist only of age. The last one consist of systolic and diastolic blood pressure.
MCA for categorical variables
In order to run MCA, we need to transform data from 0-1 to categories given in character type.
cat_df$gender <- ifelse(cat_df$gender== 1, "female", "male")
cat_df$smoke <- ifelse(cat_df$smoke==0, "Doesn't smoke", "Smoke")
cat_df$alco <- ifelse(cat_df$alco==0, "Doesn't drink", "Drinks")
cat_df$active <- ifelse(cat_df$active==0, "Is not active", "Is active")
cat_df$cholesterol <- ifelse(cat_df$cholesterol==1, "c_normal", ifelse(cat_df$cholesterol==2,
"c_above", "c_well_above"))
cat_df$gluc <- ifelse(cat_df$gluc==1, "g_normal", ifelse(cat_df$gluc==2,
"g_above", "g_well_above"))
cat_df$cardio <- ifelse(cat_df$cardio ==0, "healthy", "sick")
head(cat_df)## gender cholesterol gluc smoke alco active
## 1 male c_normal g_normal Doesn't smoke Doesn't drink Is active
## 2 female c_well_above g_normal Doesn't smoke Doesn't drink Is active
## 3 female c_well_above g_normal Doesn't smoke Doesn't drink Is not active
## 4 male c_normal g_normal Doesn't smoke Doesn't drink Is active
## 5 female c_normal g_normal Doesn't smoke Doesn't drink Is not active
## 6 female c_above g_above Doesn't smoke Doesn't drink Is not active
## cardio
## 1 healthy
## 2 sick
## 3 sick
## 4 sick
## 5 healthy
## 6 healthyNow, we can run MCA on categorical data.
library(FactoMineR)
mca<-MCA(cat_df, graph = FALSE)
fviz_screeplot(mca, addlabels = TRUE)
Scree plot represent graphically the percentage of explained variance, just like in PCA.
Let’s have a look at the contribution plot, which shows variables contribution to the results in 2 dimensional space.
fviz_contrib(mca, choice = "var", axes = 1:2)
High level of cholesterol, glucose, smoking, drinking alcohol and being a man has the biggest contribution to the result.
fviz_mca_var(mca, col.var = "contrib",
gradient.cols = c("darkgreen", "yellow", "darkred"),
repel = TRUE,
ggtheme = theme_minimal()
)
The plot shows the results of MCA. Variables with the biggest contribution are represented in red colour, green represents variables with the lowest contribution. We can observe 2 groups of variables which stand out from the others. It’s high level of glucose and cholesterol as the first group, drinking and smoking as the second group. Opposite categories are set out on the opposite sides of the plots eg. “healthy” is on the opposite of “sick”.
Conclusions
Although the percantege of explained variance in 2- dimensional space is not high enough to assume that all points have been assigned correctly, the results seems to be reasonable in both analysis. Height is related to weight in most cases, as well as diastolic/systolic blood pressure. High level of glucose and cholesterol may corresponds to people with health issues. Alcohol and smoking also very often occurs together.