Exercise 4.4: Exploring the FEV dataset - solution

1 Aims of this exercise

In this exercise, you will learn how data exploration and plots can help you to discover confounding in a real datasets.

You will also improve your data wrangling skills by importing, tidying, wrangling and visualizing data yourself.

2 The FEV dataset

The forced expiratory volume (FEV) is a measure of how much air a person can exhale (in liters) during a forced breath. In this dataset, the FEV of 606 children, between the ages of 6 and 17, were measured. The dataset also provides additional information on these children: their age, their height, their gender and, most importantly, whether the child is a smoker or a non-smoker.

The goal of this experiment was to find out whether or not smoking has an effect on the FEV of children.

Note: to analyse this dataset properly, we will need some relatively advanced modeling techniques. At the end of this week, you will have seen all three required steps to analyse such a dataset! For now, we will limit ourselves to exploring the data.

3 Load libraries

If you do not have these libraries installed, make sure to install them first by using the install.packages() function with missing the package name inside the parentheses (and using quotation marks, like install.packages("car"))

library(readr)
library(dplyr)
library(tidyverse)
library(ggplot2)
library(car)

4 Import the data

Note: fev.txt is a tab-separated file: make sure to select the correct readr function!

fev <- read_tsv("https://raw.githubusercontent.com/statOmics/PSLSData/main/fev.txt")

## Rows: 606 Columns: 5
## ── Column specification ──────────────────────────────────────────────
## Delimiter: "\t"
## chr (1): gender
## dbl (4): age, fev, height, smoking
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

head(fev)

5 Data wrangling

There are a few things in the formatting of the data that can be improved:

1. Both gender and smoking can be transformed to factors.

2. The height variable is written in inches. Assuming that this audience is mainly Portuguese/Belgian, inches are hard to interpret. Let’s add a new column, height_cm, with the values converted to centimeters.

fev <- fev %>%
  mutate(gender = as.factor(gender)) %>%
  mutate(smoking = as.factor(smoking)) %>%
  mutate(height_cm = height * 2.54)

head(fev)

That’s better!

6 Data exploration

Now, let’s make a first explorative plot, showing only the FEV for both smoking categories.

Which type of plot do you suggest?

fev %>%
  ggplot(aes(x = smoking, y = fev, fill = smoking)) +
  scale_fill_manual(values = c("dimgrey", "firebrick")) +
  theme_bw() +
  geom_boxplot(outlier.shape = NA) +
  geom_jitter(width = 0.2, size = 0.1) +
  ggtitle("Boxplot of FEV versus smoking") +
  ylab("FEV (l)") +
  xlab("smoking status")

Did you expect these results?

It appears that children that smoke have a higher median FEV than children that do not smoke.

fev %>%
  ggplot(aes(x = age, y = fev, color = smoking)) +
    geom_point() +
    geom_smooth()

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

The trends in the plot seems to match much more with our expectations.

First, it seems that we do not have any smoking children of ages 6, 7 or 8. Second, it no longer seems that smokers have a higher FEV than non-smokers; on the contrary smoking seems to lead to a lower lung capacity for the elder pupils.

This shows that accounting for important confounders (in this case age) is crucial! If we simply analysed based on the smoking status and FEV values only, we would have made wrong conclusions.

Can we provide additional insights in the data, e.g. by accounting for other useful explanatory variables?

fev %>%
  ggplot(aes(x = age, y = fev, color = smoking)) +
    geom_point() +
    geom_smooth() +
    facet_grid(cols = vars(gender))

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

This plot holds one extra level of information, the gender of the child. Especially for higher ages, the FEV is higher for males as compared to females.

The only source of information that is lacking is height. We could simply make a scatterplot displaying the FEV in function of a child’s height (in cm). Additionally, we could color the dots based on gender and making two plots according to the smoking status.

fev %>%
  ggplot(aes(x = height_cm, y = fev, color = gender)) +
  geom_point() +
  scale_color_manual(values = c("darkorchid", "olivedrab4")) +
  theme_bw() +
  ggtitle("Boxplot of FEV versus height") +
  ylab("FEV (l)") +
  xlab("Height (cm)") +
  facet_grid(cols = vars(smoking))

There is a clear relationship between height and FEV. In addition, we see that for the large height values (>175cm), we mainly find male subjects.

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This work is licensed under the CC BY-NC-SA 4.0 licence.