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Survival Analysis
gtregression supports a complete survival workflow:
describe the cohort, draw Kaplan-Meier curves, summarise observed
survival, compare groups, fit Cox or parametric survival models, check
assumptions, predict survival probabilities, visualise estimates, and
export publication-ready tables.
library(gtregression)
library(dplyr)
data("data_lungcancer", package = "gtregression")
lung_data <- data_lungcancer |>
mutate(
trt = factor(trt, levels = c(1, 2),
labels = c("Standard treatment", "Test treatment")),
prior = factor(prior, levels = c(0, 10), labels = c("No", "Yes")),
celltype = factor(
celltype,
levels = c("squamous", "smallcell", "adeno", "large"),
labels = c("Squamous", "Small cell", "Adenocarcinoma", "Large cell")
)
)
attr(lung_data$time, "label") <- "Survival time"
attr(lung_data$status, "label") <- "Death status"
attr(lung_data$trt, "label") <- "Treatment group"
attr(lung_data$celltype, "label") <- "Cancer cell type"
attr(lung_data$karno, "label") <- "Karnofsky performance score"
attr(lung_data$age, "label") <- "Age"
attr(lung_data$prior, "label") <- "Prior therapy"
surv_exposures <- c("trt", "celltype", "karno", "age", "prior")
1. Describe The Cohort
Start with a baseline table. This helps readers understand the
treatment groups before looking at survival curves or models.
lung_summary <- descriptive_table(
data = lung_data,
exposures = c("time", "status", "celltype", "karno", "age", "prior"),
by = trt,
statistic = c(time = "median", karno = "mean", age = "mean"),
percent = column,
show_overall = last
)
lung_summary$table
Characteristic | Standard treatment, N=69 | Test treatment, N=68 | Overall, N=137 |
|---|
Survival time | 97.0 (25.0-153.0) | 52.5 (24.8-117.2) | 80.0 (25.0-144.0) |
Death status |
|
|
|
0 | 5 (7.2%) | 4 (5.9%) | 9 (6.6%) |
1 | 64 (92.8%) | 64 (94.1%) | 128 (93.4%) |
Cancer cell type |
|
|
|
Squamous | 15 (21.7%) | 20 (29.4%) | 35 (25.5%) |
Small cell | 30 (43.5%) | 18 (26.5%) | 48 (35.0%) |
Adenocarcinoma | 9 (13.0%) | 18 (26.5%) | 27 (19.7%) |
Large cell | 15 (21.7%) | 12 (17.6%) | 27 (19.7%) |
Karnofsky performance score | 59.2 (18.7) | 57.9 (21.4) | 58.6 (20.0) |
Age | 57.5 (10.8) | 59.1 (10.3) | 58.3 (10.5) |
Prior therapy |
|
|
|
No | 48 (69.6%) | 49 (72.1%) | 97 (70.8%) |
Yes | 21 (30.4%) | 19 (27.9%) | 40 (29.2%) |
Categorical variables shown as n (%); percentages are by column. |
Continuous summaries: time = Median (IQR); karno = Mean (SD); age = Mean (SD). |
2. Show Observed Survival
Use km_plot() for the Kaplan-Meier curve. Add
risk_table = TRUE when the number at risk should appear
under the curve. When survival remains high, use ylim to
focus the y-axis, for example ylim = c(50, 100) with the
default percentage scale. Confidence intervals are shown as shaded bands
when conf.int = TRUE.
km_curve <- km_plot(
data = lung_data,
time = time,
event = status,
by = trt,
break_time_by = 200,
ylim = c(50, 100),
title = "Kaplan-Meier Survival by Treatment"
)
km_curve
For multi-panel publication figures, make each Kaplan-Meier plot
lighter and let patchwork arrange the panels. A common
pattern is to remove the risk table, use short panel titles, reduce
title_size, and collect legends across panels.
km_trt_panel <- km_plot(
data = lung_data,
time = time,
event = status,
by = trt,
risk_table = FALSE,
break_time_by = 200,
ylim = c(50, 100),
title = "A. Treatment group",
title_size = 10,
title_face = plain,
legend_position = bottom,
base_size = 10
)
km_prior_panel <- km_plot(
data = lung_data,
time = time,
event = status,
by = prior,
risk_table = FALSE,
break_time_by = 200,
ylim = c(50, 100),
title = "B. Prior therapy",
title_size = 10,
title_face = plain,
legend_position = bottom,
base_size = 10
)
patchwork::wrap_plots(km_trt_panel, km_prior_panel, ncol = 2) +
patchwork::plot_layout(guides = "collect") &
ggplot2::theme(legend.position = "bottom")
Use table summaries when readers need exact survival values.
survival_summary(
data = lung_data,
time = time,
event = status,
by = trt
)$table
Kaplan-Meier survival summaryGroup | N | Events | Censored | Median survival (95% CI) |
|---|
Standard treatment | 69 | 64 | 5 | 103.0 (59.0-132.0) |
Test treatment | 68 | 64 | 4 | 52.5 (44.0-95.0) |
Median survival is estimated using Kaplan-Meier methods. Not reached means survival did not fall to 50% during observed follow-up. |
survival_prob(
data = lung_data,
time = time,
event = status,
by = trt,
times = c(90, 180, 365)
)$table
Kaplan-Meier survival probabilitiesGroup | Time | At risk | Events | Censored | Survival probability (95% CI) |
|---|
Standard treatment | 90.0 | 37 | 31 | 1 | 54.7% (44.0%-67.9%) |
Standard treatment | 180.0 | 13 | 21 | 3 | 21.2% (13.2%-34.1%) |
Standard treatment | 365.0 | 4 | 8 | 1 | 7.1% (2.8%-18.0%) |
Test treatment | 90.0 | 25 | 42 | 2 | 38.0% (28.0%-51.6%) |
Test treatment | 180.0 | 14 | 9 | 1 | 23.3% (14.9%-36.3%) |
Test treatment | 365.0 | 6 | 7 | 1 | 11.0% (5.3%-22.7%) |
Survival probabilities are estimated using Kaplan-Meier methods. Events and censored counts are interval counts up to each requested time point. |
rmst_table() reports restricted mean survival time up to
a chosen follow-up time. This is useful when an absolute survival-time
summary is easier to explain than a ratio measure.
rmst_table(
data = lung_data,
time = time,
event = status,
by = trt,
tau = 365
)$table
Restricted mean survival timeGroup | Tau | N | Events | RMST (95% CI) | RMST difference (95% CI) | p-value |
|---|
Standard treatment | 365.0 | 69 | 64 | 119.0 (93.5-144.5) |
|
|
Test treatment | 365.0 | 68 | 64 | 112.4 (83.3-141.6) |
|
|
Difference (Test treatment - Standard treatment) | 365.0 |
|
|
| -6.6 (-45.3-32.2) | 0.740 |
RMST is restricted mean survival time up to tau. For two groups, the difference is the second group minus the first group. |
3. Compare Survival Curves
logrank_test() compares Kaplan-Meier curves. It is a
group comparison test, not an effect-size model.
logrank_test(
data = lung_data,
time = time,
event = status,
by = trt
)$table
Log-rank testGroup | N | Observed events | Expected events |
|---|
Standard treatment | 69 | 64 | 64.50 |
Test treatment | 68 | 64 | 63.50 |
Log-rank test: chi-square = 0.01, df = 1, p-value = 0.928. This compares survival curves; use cox_reg() when a hazard ratio is needed. |
4. Fit Cox Regression
cox_reg() reports hazard ratios. Use
adjust_for to produce adjusted hazard ratios while keeping
the syntax aligned with multi_reg().
cox_crude <- cox_reg(
data = lung_data,
time = time,
event = status,
exposures = surv_exposures
)
cox_adjusted <- cox_reg(
data = lung_data,
time = time,
event = status,
exposures = c(trt, celltype, prior),
adjust_for = c(age, karno)
)
cox_adjusted$table
Characteristic | Adjusted HR (95% CI) | p-value |
|---|
Treatment group |
|
|
Standard treatment | Ref. |
|
Test treatment | 1.21 (0.84–1.74) | 0.307 |
Cancer cell type |
|
|
Squamous | Ref. |
|
Small cell | 2.06 (1.26–3.39) | 0.004 |
Adenocarcinoma | 3.23 (1.82–5.74) | <0.001 |
Large cell | 1.38 (0.80–2.37) | 0.244 |
Prior therapy |
|
|
No | Ref. |
|
Yes | 0.96 (0.64–1.42) | 0.820 |
Abbreviations: HR = Hazard Ratio; CI = Confidence Interval. |
Ref. = reference category. |
Adjusted for Age and Karnofsky performance score |
Planned interactions use the same
interaction = exposure*modifier grammar as
multi_reg(). In the default exposure-by-exposure workflow,
supply the single exposure you want to interpret.
cox_interaction <- cox_reg(
data = lung_data,
time = time,
event = status,
exposures = trt,
adjust_for = c(age, karno),
interaction = trt*prior
)
cox_interaction$table
Characteristic | Adjusted HR (95% CI) | p-value |
|---|
Treatment group |
|
|
Standard treatment | Ref. |
|
Test treatment | 1.52 (0.98–2.36) | 0.061 |
Treatment group: Test treatment x Prior therapy: Yes | 0.47 (0.21–1.06) | 0.070 |
Abbreviations: HR = Hazard Ratio; CI = Confidence Interval. |
Ref. = reference category. |
Adjusted for Age and Karnofsky performance score |
Model includes interaction term: trt*prior |
Check the proportional hazards assumption before treating Cox hazard
ratios as final.
check_ph(cox_adjusted)$table
## NULL
5. Fit Parametric Survival Regression
surv_reg() fits accelerated failure time style
parametric survival models and reports time ratios. A time ratio above 1
suggests longer survival time; below 1 suggests shorter survival time,
conditional on the selected distribution.
Before choosing the final distribution, compare candidate parametric
models numerically and visually. Lower AIC/BIC is useful for screening;
the fitted curve should also look reasonable against the Kaplan-Meier
curve.
surv_model_compare(
data = lung_data,
time = time,
event = status,
exposures = c(trt, celltype, prior),
adjust_for = c(age, karno),
distributions = c(weibull, exponential, "log-normal", "log-logistic")
)$table
Parametric survival model comparisonDistribution | AIC | BIC | Log-likelihood | Scale | N | Events | Best AIC | Best BIC |
|---|
loglogistic | 1,441.93 | 1,468.21 | -711.96 | 0.58 | 137 | 128 | Yes | Yes |
lognormal | 1,447.29 | 1,473.57 | -714.64 | 1.06 | 137 | 128 | No | No |
exponential | 1,448.32 | 1,471.68 | -716.16 | 1.00 | 137 | 128 | No | No |
weibull | 1,449.11 | 1,475.39 | -715.55 | 0.93 | 137 | 128 | No | No |
Lower AIC or BIC indicates better relative fit among the compared distributions. Use model fit statistics with clinical judgment and visual checks. |
plot_surv_fit(
data = lung_data,
time = time,
event = status,
by = trt,
adjust_for = c(age, karno),
distributions = c(weibull, "log-logistic"),
break_time_by = 200
)
After selecting a distribution, fit crude and adjusted
publication-ready tables.
surv_crude <- surv_reg(
data = lung_data,
time = time,
event = status,
exposures = surv_exposures,
distribution = loglogistic
)
surv_adjusted <- surv_reg(
data = lung_data,
time = time,
event = status,
exposures = c(trt, celltype, prior),
adjust_for = c(age, karno),
distribution = loglogistic,
model_stats = TRUE
)
surv_adjusted$table
Characteristic | Adjusted Time Ratio (95% CI) | p-value |
|---|
Treatment group |
|
|
Standard treatment | Ref. |
|
Test treatment | 0.95 (0.66–1.37) | 0.771 |
Cancer cell type |
|
|
Squamous | Ref. |
|
Small cell | 0.51 (0.31–0.81) | 0.005 |
Adenocarcinoma | 0.48 (0.28–0.80) | 0.005 |
Large cell | 1.01 (0.60–1.71) | 0.968 |
Prior therapy |
|
|
No | Ref. |
|
Yes | 1.07 (0.71–1.62) | 0.740 |
Abbreviations: Time Ratio = exponentiated accelerated failure time coefficient; CI = Confidence Interval. |
Distribution: loglogistic. |
Ref. = reference category. |
Adjusted for Age and Karnofsky performance score |
surv_adjusted$model_stats
## model distribution AIC BIC logLik scale events n
## 1 trt loglogistic 1449.511 1464.111 -719.7554 0.6186080 128 137
## 2 celltype loglogistic 1438.331 1458.771 -712.1656 0.5796411 128 137
## 3 prior loglogistic 1449.486 1464.086 -719.7429 0.6178590 128 137
Parametric survival models use the same interaction grammar and
display Adjusted Time Ratio (95% CI) when adjustment or multivariable
modelling is used.
surv_interaction <- surv_reg(
data = lung_data,
time = time,
event = status,
exposures = trt,
adjust_for = c(age, karno),
interaction = trt*prior,
distribution = loglogistic
)
surv_interaction$table
Characteristic | Adjusted Time Ratio (95% CI) | p-value |
|---|
Treatment group |
|
|
Standard treatment | Ref. |
|
Test treatment | 0.84 (0.55–1.30) | 0.444 |
Treatment group: Test treatment x Prior therapy: Yes | 1.52 (0.66–3.47) | 0.323 |
Abbreviations: Time Ratio = exponentiated accelerated failure time coefficient; CI = Confidence Interval. |
Distribution: loglogistic. |
Ref. = reference category. |
Adjusted for Age and Karnofsky performance score |
Model includes interaction term: trt*prior |
6. Predict Survival Probabilities
surv_predict() turns a fitted parametric survival model
into predicted survival probabilities at selected follow-up times for a
profile.
surv_predict(
model = surv_adjusted$models$trt,
newdata = data.frame(
trt = factor("Test treatment", levels = levels(lung_data$trt)),
age = 60,
karno = 70
),
times = c(90, 180, 365)
)$table
Predicted survival probabilitiesProfile | trt | age | karno | Time | Predicted survival | Model distribution |
|---|
1 | Test treatment | 60 | 70 | 90.0 | 54.5% | loglogistic |
1 | Test treatment | 60 | 70 | 180.0 | 28.1% | loglogistic |
1 | Test treatment | 60 | 70 | 365.0 | 11.1% | loglogistic |
Model-based predictions from a parametric survival regression model. Distribution: loglogistic. Predictions depend on the supplied profile and model specification. |
7. Visualise And Export Model Results
The survival model outputs work with the same downstream tools used
for other regression tables.
plot_reg_combine(
cox_crude,
cox_adjusted,
show_ref = FALSE,
title_uni = "Crude HR",
title_multi = "Adjusted HR"
)
surv_forest_data <- forest_df(cox_crude, cox_adjusted, desc = lung_summary)
forest_reg(
surv_forest_data,
xlim = list(c(0.25, 8), c(0.25, 8)),
ticks_at = list(c(0.5, 1, 2, 4, 8), c(0.5, 1, 2, 4, 8)),
quiet = TRUE
)
If forest plot x-axis labels overlap, set xlim and
ticks_at. If the confidence-interval plot panel is too
narrow or too wide, tune ci_col_width. For very wide
descriptive-plus-crude-plus-adjusted tables, export using a wider
graphics device or Word canvas.
Survival Workflow Map
| Kaplan-Meier curve |
km_plot() |
| Number at risk |
km_risk_table() |
| Median survival |
survival_summary() |
| Survival quantiles |
survival_quantiles() |
| Fixed-time survival probability |
survival_prob() |
| Restricted mean survival time |
rmst_table() |
| Compare KM curves |
logrank_test() |
| Cox hazard ratios |
cox_reg() |
| Cox PH check |
check_ph() |
| Parametric time ratios |
surv_reg() |
| Compare parametric distributions |
surv_model_compare() |
| Plot fitted parametric curves |
plot_surv_fit() |
| Predict survival probabilities |
surv_predict() |
| Model plots and forest tables |
plot_reg(), plot_reg_combine(),
forest_df(), forest_reg() |
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
Health stats visible at Monitor.