UK Lung Deaths Data Analysis

Introduction

This notebook analyzes the built-in UK Lung Deaths dataset. The dataset consists of monthly deaths from bronchitis, emphysema, and asthma in the UK, categorized by sex (male and female).

Loading the Data

# Load the data
data("ldeaths")

Warning: data set ‘ldeaths’ not found

data("mdeaths")

Warning: data set ‘mdeaths’ not found

data("fdeaths")

Warning: data set ‘fdeaths’ not found

# Create a data frame
ldeaths_df <- data.frame(
  date = time(ldeaths),
  total_deaths = as.numeric(ldeaths),
  male_deaths = as.numeric(mdeaths),
  female_deaths = as.numeric(fdeaths)
)

# Display the first few rows of the dataset
head(ldeaths_df)

Basic Exploration

# Summary statistics
summary(ldeaths_df)

      date       total_deaths   male_deaths   female_deaths   
 Min.   :1974   Min.   :1300   Min.   : 940   Min.   : 330.0  
 1st Qu.:1975   1st Qu.:1552   1st Qu.:1138   1st Qu.: 411.0  
 Median :1977   Median :1870   Median :1344   Median : 512.0  
 Mean   :1977   Mean   :2057   Mean   :1496   Mean   : 560.7  
 3rd Qu.:1978   3rd Qu.:2552   3rd Qu.:1846   3rd Qu.: 681.5  
 Max.   :1980   Max.   :3891   Max.   :2750   Max.   :1141.0  

# Check for missing values
sum(is.na(ldeaths_df))

[1] 0

Visualization

Total Deaths Over Time

ggplot(ldeaths_df, aes(x = date, y = total_deaths)) +
  geom_line(color = "blue") +
  labs(title = "Total Lung Deaths Over Time", x = "Year", y = "Total Deaths")

Male and Female Deaths Over Time

ggplot(ldeaths_df) +
  geom_line(aes(x = date, y = male_deaths, color = "Male Deaths")) +
  geom_line(aes(x = date, y = female_deaths, color = "Female Deaths")) +
  labs(title = "Male and Female Lung Deaths Over Time", x = "Year", y = "Deaths") +
  scale_color_manual("", breaks = c("Male Deaths", "Female Deaths"), values = c("blue", "red"))

Seasonal Decomposition

# Decompose the time series
ldeaths_decomp <- decompose(ts(ldeaths, frequency = 12))
mdeaths_decomp <- decompose(ts(mdeaths, frequency = 12))
fdeaths_decomp <- decompose(ts(fdeaths, frequency = 12))

# Plot the decompositions
plot(ldeaths_decomp)

plot(mdeaths_decomp)

plot(fdeaths_decomp)

Statistical Analysis

Correlation Between Male and Female Deaths

# Calculate correlation
correlation <- cor(ldeaths_df$male_deaths, ldeaths_df$female_deaths)
correlation

[1] 0.9762413

Seasonal Autoregressive Integrated Moving Average (SARIMA) Model

# Fit SARIMA model for total deaths
sarima_model <- auto.arima(ldeaths)
summary(sarima_model)

Series: ldeaths 
ARIMA(0,0,2)(2,1,0)[12] with drift 

Coefficients:
         ma1      ma2     sar1     sar2    drift
      0.1844  -0.2477  -0.9533  -0.5024  -5.5270
s.e.  0.1487   0.1469   0.1325   0.1305   1.1477

sigma^2 = 56263:  log likelihood = -417.34
AIC=846.67   AICc=848.26   BIC=859.24

Training set error measures:
                   ME     RMSE      MAE       MPE     MAPE
Training set 10.67715 207.3123 126.0795 0.0532634 6.068906
                  MASE       ACF1
Training set 0.5372706 0.01905913

# Forecast next 12 months
forecast_sarima <- forecast(sarima_model, h = 12)
plot(forecast_sarima, main = "SARIMA Forecast for Total Deaths")

Conclusion

This analysis provided an overview of the UK Lung Deaths dataset, including visualizations and a simple SARIMA model for forecasting future deaths. The dataset shows clear seasonal patterns and a strong correlation between male and female deaths due to lung diseases. ```

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