Survival analysis is a powerful statistical tool for analyzing the time until an event occurs, such as death, failure, or churn. For actuarial students, mastering survival analysis in R opens up a world of possibilities—from assessing insurance risk to predicting policyholder longevity. This tutorial walks you through using survival analysis in R step by step, blending theory, practical examples, and insider tips to help you confidently apply these methods in your studies and future work.
To begin, let’s clarify what survival analysis involves. Unlike typical regression that predicts an outcome, survival analysis focuses on time-to-event data. This means we’re interested in how long it takes for an event to happen and accounting for incomplete observations, known as censoring. For example, if you’re analyzing time until a policyholder passes away, some data points might be censored because the event hasn’t happened yet or the person left the study early. Handling this properly is what makes survival analysis unique and essential in actuarial science.
The R ecosystem offers excellent packages for survival analysis, primarily the survival package developed by Terry Therneau, a pioneer in the field, and survminer which helps visualize results beautifully. If you’re new to R, open RStudio and install these packages with:
install.packages(c("survival", "survminer"))Load them into your session using:
library(survival)
library(survminer)Next, we need data. The survival package includes built-in datasets like lung, which contains survival times and patient information for lung cancer patients—ideal for practice.
data("lung")
head(lung)This gives you a glimpse of variables such as survival time (time), status (censored or event occurred), age, sex, and performance scores. Understanding your data structure is crucial before diving into modeling.
The first step in survival analysis is creating a survival object using the Surv() function. This object combines survival time and event status. Here’s how to create it with the lung dataset:
surv_obj <- Surv(time = lung$time, event = lung$status == 2)
head(surv_obj)Notice the event argument is lung$status == 2 because in this dataset, status 2 means the event (death) occurred, while 1 means censored.
With the survival object ready, you can estimate survival probabilities over time using the Kaplan-Meier estimator, which gives a stepwise survival curve showing the probability of surviving past certain times.
km_fit <- survfit(surv_obj ~ 1)
summary(km_fit)
plot(km_fit, xlab = "Days", ylab = "Survival Probability", main = "Kaplan-Meier Survival Curve")This basic plot shows survival probability decreasing over time. To make it more interpretable and visually appealing, the survminer package’s ggsurvplot() function is your friend:
ggsurvplot(km_fit, conf.int = TRUE, surv.median.line = "hv")This plot includes confidence intervals and marks the median survival time with horizontal and vertical lines, which is incredibly helpful for actuarial interpretations.
One practical tip: Kaplan-Meier curves also allow comparison between groups. Suppose you want to compare survival between male and female patients:
km_sex_fit <- survfit(surv_obj ~ sex, data = lung)
ggsurvplot(km_sex_fit, conf.int = TRUE, pval = TRUE, legend.labs = c("Male", "Female"))The pval = TRUE option adds a p-value from the log-rank test, assessing if survival differs significantly between groups. This is key for actuarial decisions, such as pricing policies differently based on gender.
While Kaplan-Meier is excellent for visualization and univariate analysis, it doesn’t adjust for multiple risk factors simultaneously. That’s where the Cox proportional hazards model shines. It’s a semi-parametric regression model that estimates the effect of several variables on survival time.
Here’s how to fit a Cox model with age and sex as predictors:
cox_model <- coxph(surv_obj ~ age + sex, data = lung)
summary(cox_model)The output provides hazard ratios (HRs) for each variable. For example, an HR greater than 1 for age means older patients have a higher risk of the event occurring sooner. Understanding these hazard ratios is crucial for actuarial risk modeling.
You can also visualize the Cox model’s survival curves for different risk profiles using:
ggsurvplot(survfit(cox_model), data = lung)An important assumption of the Cox model is proportional hazards, meaning the hazard ratios remain constant over time. To check this, use the cox.zph() function:
cox.zph(cox_model)If the test shows significant violations, you might need to adjust your model or use time-varying covariates.
Speaking of time-varying covariates, they’re useful when risk factors change over the study period—think of a policyholder’s health status or lifestyle changes. Including them requires more advanced coding but is supported in R’s survival package.
From my experience, the best way to master survival analysis in R is to experiment with your own datasets or publicly available ones. Try building Kaplan-Meier curves, compare groups, fit Cox models, and validate assumptions. The hands-on approach solidifies understanding and reveals nuances beyond textbooks.
Actuarial work often demands interpreting these models into actionable insights—like estimating expected future lifetimes or pricing insurance products. R’s flexibility means you can automate these calculations once you’ve set up your models, saving time and reducing errors.
Remember, survival analysis is not just about running code but understanding the story behind the data: why some observations are censored, what factors truly impact survival, and how to communicate findings clearly. For actuarial students, blending statistical rigor with real-world context is what sets you apart.
Finally, as a bit of encouragement: survival analysis is a skill that grows with practice. Don’t get discouraged if the first few models feel complex. With each analysis, you’ll gain intuition for the data and confidence in your interpretations. And when you can tell a compelling, data-driven story about risk and time, that’s when actuarial magic happens.
In summary, start with loading your data and packages, create survival objects, plot Kaplan-Meier curves, test group differences, then build and validate Cox models. Use visualization tools like survminer to make your results clear and compelling. Keep exploring, ask questions, and soon survival analysis in R will be one of your go-to tools in the actuarial toolkit.