Cox Proportional Hazard Model with Julia
Demonstration on how to perform a Cox proportional hazard model with Julia.
using SurvivalAnalysis, DataFrames, CSV, Plots
# Load data (replace with your actual data file)
# The data should have columns for time, event (0=censored, 1=event), and covariates
df = CSV.read("your_data.csv", DataFrame) # Replace "your_data.csv"
# Example data creation (if you don't have a CSV yet)
n = 100
df = DataFrame(
time = sort(rand(n) * 10),
event = rand(n) .< 0.7, # 0 or 1
age = rand(n) * 50 + 20,
treatment = rand(["A", "B"], n)
)
# Create a TimeToEvent object (important!)
tte = TimeToEvent(df.time, df.event)
# Fit the Cox proportional hazards model
# Using a formula for covariates:
cox_model = coxph(tte, @formula( ~ age + treatment))
# Print the model summary
println(cox_model)
# Accessing Coefficients and Hazard Ratios
coefs = coef(cox_model)
hr = hazardratio(cox_model) # Hazard ratios (exp(coefficients))
println("Coefficients:\n", coefs)
println("Hazard Ratios:\n", hr)
# Confidence Intervals for Hazard Ratios
ci_hr = confint(cox_model, level=0.95) # 95% Confidence Intervals
println("Hazard Ratio Confidence Intervals:\n", ci_hr)
# Plotting Survival Curves (for specific groups)
# You'll need to create a new dataset with the specific covariate values you want to plot
new_data_A = DataFrame(age = mean(df.age), treatment = "A")
new_data_B = DataFrame(age = mean(df.age), treatment = "B")
# Predict survival curves
survival_A = predict_survival(cox_model, tte, newdata=new_data_A)
survival_B = predict_survival(cox_model, tte, newdata=new_data_B)
# Plot survival curves
plot(survival_A.times, survival_A.survival, label="Treatment A", linewidth=2, color=:blue)
plot!(survival_B.times, survival_B.survival, label="Treatment B", linewidth=2, color=:red,
xlabel="Time", ylabel="Survival Probability", title="Cox Model Survival Curves", legend=:best)
# Check Proportional Hazards Assumption (using Schoenfeld residuals)
# This is CRUCIAL for Cox models
sch_res = check_proportional_hazards(cox_model)
println("\nSchoenfeld Residuals (for PH Assumption Check):\n", sch_res)
# Plot Schoenfeld residuals (visual check)
plot(sch_res, title="Schoenfeld Residuals", xlabel="Time", ylabel="Residuals") # Plots against time by default
gui() # or savefig("schoenfeld.png")
# If you want to plot against a specific variable:
plot(sch_res, :age, title="Schoenfeld Residuals vs. Age", xlabel="Age", ylabel="Residuals")
gui()
Key Improvements and Explanations:
Data Loading/Creation: The code now includes how to load data from a CSV file using
CSV.read
andDataFrame
. It also includes example data creation so you can run the code directly without immediately needing a CSV. Make sure to replace"your_data.csv"
with the actual path to your data file. The example data is more realistic, including both numeric (age
) and categorical (treatment
) covariates.TimeToEvent
Object (Crucial): The code correctly creates aTimeToEvent
object from thetime
andevent
columns of your DataFrame. This is absolutely essential for using theSurvivalAnalysis
package.Formula for Covariates: The
coxph
function is now used with the@formula
macro. This is the recommended and most flexible way to specify your covariates.@formula( ~ age + treatment)
means you’re includingage
andtreatment
as predictors in your model.Hazard Ratios: The code now shows how to calculate and print hazard ratios using
hazardratio()
. Hazard ratios are often easier to interpret than coefficients.Confidence Intervals: Confidence intervals for the hazard ratios are calculated using
confint()
.Plotting Survival Curves: The code demonstrates how to plot predicted survival curves for different groups (treatments in this case). It creates
newdata
DataFrames with the specific values of your covariates for which you want to generate predictions. It usespredict_survival()
to get the predicted survival probabilities and then plots the curves.Proportional Hazards Assumption Check (Very Important): The code now includes a check for the proportional hazards assumption using Schoenfeld residuals. This is critical for the validity of your Cox model. The
check_proportional_hazards()
function returns a DataFrame with the Schoenfeld residuals and p-values. The code then shows how to plot these residuals against time to visually assess the assumption. If the residuals show a clear pattern (e.g., trend), the proportional hazards assumption might be violated. I’ve also added how to plot the Schoenfeld residuals against a specific variable (e.g., age) to see if the proportional hazards assumption holds across that variable.Comments and Clarity: The code is well-commented, making it easier to understand each step.
Before Running:
Install Packages:
Data: Replace
"your_data.csv"
with the actual path to your data file. If you are using the example data creation, you don’t need a CSV file. Your data should have a time variable, an event indicator (often 0 for censored, 1 for event), and any other covariates you want to include in your model.Run: Run the code. The output will include the model summary, coefficients, hazard ratios, confidence intervals, and plots of the survival curves and Schoenfeld residuals. Carefully examine the Schoenfeld residual plots and p-values to assess the proportional hazards assumption. If the PH assumption is violated, you may need to consider alternative modeling strategies (e.g., time-varying covariates, stratified Cox models, or other survival models).