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 Survival Analysis and How to Run it in Stata and R

Introduction to Survival Analysis Survival analysis is a statistical method used to analyze and model time-to-event data. It focuses on estimating the time until an event of interest occurs, such as death, recovery from illness, equipment failure, or customer churn. The unique aspect of survival data is its ability to handle censored observations—instances where the event has not yet occurred by the end of the study.

Key Concepts in Survival Analysis:

• Time-to-Event: The time duration until the occurrence of an event.
• Censoring: When the event has not occurred for some subjects during the observation period.
• Hazard Function: Describes the instantaneous rate of the event occurring at a given time.
• Survival Function: Represents the probability of an individual surviving past a certain time.

Steps to Perform Survival Analysis in Stata

1. Import and Prepare Data: Ensure your dataset includes:

• Time variable indicating the duration of follow-up.
• Event variable (1 for event occurrence, 0 for censoring).

use dataset.dta, clear

2. Declare Survival Data (stset): Stata requires data to be declared as survival data using the stset command.

stset time_variable, failure(event_variable)

3. Kaplan-Meier Estimator (Non-Parametric Analysis): To generate the Kaplan-Meier survival curve and estimate survival probabilities:

sts list
sts graph

4. Log-Rank Test (Comparing Survival Curves): Used to compare survival distributions between groups.

sts test group_variable

5. Cox Proportional Hazards Model: A semi-parametric model that estimates the effect of covariates on survival.

stcox age gender treatment

6. Parametric Survival Models: For parametric models like Weibull or Exponential distributions:

streg age gender, distribution(weibull)

7. Checking Proportional Hazards Assumption: Test for the proportional hazards assumption with Schoenfeld residuals:

stphplot, by(group_variable)

8. Exporting Results: Export results and tables for reporting:

outreg2 using results.doc, replace

Running Survival Analysis in R

1. Load Sample Data:

library(survival)
data <- data.frame(
  time = c(5, 8, 12, 6, 15, 9, 11),
  status = c(1, 1, 0, 1, 0, 1, 0),
  age = c(45, 60, 50, 70, 65, 55, 80)
)

2. Fit a Kaplan-Meier Survival Curve:

km_fit <- survfit(Surv(time, status) ~ 1, data = data)
plot(km_fit, main = "Kaplan-Meier Curve")

3. Fit a Cox Proportional Hazards Model:

cox_fit <- coxph(Surv(time, status) ~ age, data = data)
summary(cox_fit)

Survival analysis is a powerful tool for time-to-event data, allowing for both non-parametric and parametric modeling. Stata and R provide comprehensive sets of commands for conducting these analyses efficiently. Proper data preparation and interpretation of results are crucial for drawing meaningful conclusions.