• Real cancer patient data from medical studies
• Survival analysis using actual patient outcomes
• How tumor characteristics relate to diagnosis
• Statistical methods used in cancer research

Using data from the North Central Cancer Treatment Group study:

• 228 patients with advanced lung cancer
• Variables include survival time, age, sex, and performance scores
• This is real clinical trial data used in research

Let’s explore what affects patient survival

In cancer research, survival probability over time is often calculated using the formula:

\[S(t) = P(T > t)\]

Where \(S(t)\) is the probability of surviving beyond time \(t\).

The hazard function represents instantaneous risk:

\[h(t) = \lim_{\Delta t \to 0} \frac{P(t \leq T < t + \Delta t | T \geq t)}{\Delta t}\]

Hazard function (in simple terms):: If you’ve survived until day \(t\), what’s your risk of dying right now?

Research Question: Do males and females have different survival rates?

\[H_0: S_{male}(t) = S_{female}(t)\] \[H_1: S_{male}(t) \neq S_{female}(t)\]

We use the log-rank test to compare survival curves:

Result: p-value = 0.0013

At α = 0.05, we reject the null hypothesis.

Here’s the code for the survival analysis plot (slide 6):

library(survival)

# Load lung cancer data
data(cancer)
lung <- cancer

# Create survival object and fit
surv_obj <- Surv(lung$time, lung$status == 2)
fit <- survfit(surv_obj ~ 1, data = lung)

# Extract survival data for plotting
surv_data <- data.frame(
  time = fit$time,
  surv = fit$surv,
  upper = fit$upper,
  lower = fit$lower
)

ggplot(surv_data, aes(x = time, y = surv)) +
  geom_line(color = "#8C1D40", size = 1.2) +
  geom_ribbon(aes(ymin = lower, ymax = upper), alpha = 0.2, fill = "#8C1D40") +
  labs(title = "Overall Survival Curve for Lung Cancer Patients",
       x = "Time (days)",
       y = "Survival Probability") +
  theme_minimal() +
  ylim(0, 1)

• Patient age and performance status strongly affect survival
• The median survival time in this study was about 10 months
• Early detection and treatment remain critical
• Statistical models help identify risk factors and evaluate treatments

Important: These analyses use real patient data to advance cancer research and improve care.

Datasets Used:

• Lung cancer: survival::cancer (Loprinzi et al., 1994)
• Breast biopsy: MASS::biopsy (Wisconsin Diagnostic Breast Cancer)