When a subject can fail in more than one way – relapse or death, one cancer or another – the events compete: the first one to happen removes the subject from being at risk for the others. In that setting the ordinary Kaplan-Meier estimate of “probability of event X” is biased upward, because it treats the competing events as if they were merely censored. The right summary is the cumulative incidence function (CIF), and survminer draws it with ggcompetingrisks().

library(survminer)
library(survival)

We use the mgus2 data (monoclonal gammopathy): the competing events are progression to a plasma-cell malignancy (PCM) and death without progression. The standard construction records, for each subject, the time to the first event and which event it was:

mgus2$etime <- with(mgus2, ifelse(pstat == 1, ptime, futime))
mgus2$event <- with(mgus2, ifelse(pstat == 1, 1, 2 * death))
mgus2$event <- factor(mgus2$event, 0:2, labels = c("censor", "PCM", "death"))
mgus2$sex   <- factor(mgus2$sex,   labels = c("Female", "Male"))

table(mgus2$event)
#> 
#> censor    PCM  death 
#>    409    115    860

Why not 1 − Kaplan-Meier?

A subject who dies without progressing can never progress afterwards. The Kaplan-Meier estimate for PCM ignores that – it censors the deaths and lets the remaining subjects stand in for them, which inflates the estimated probability of PCM to a value the data cannot support (in the limit, 1 − KM for every cause can sum to more than 1). The cumulative incidence function counts a competing event as leaving the risk set, so the incidences of all causes add up correctly.

Cumulative incidence, the right way

ggcompetingrisks() accepts a tidycmprsk::cuminc() fit, which carries proper pointwise confidence intervals. Fit the cumulative incidence by group and plot one panel per cause:

cif <- tidycmprsk::cuminc(Surv(etime, event) ~ sex, data = mgus2)

ggcompetingrisks(cif, conf.int = TRUE, palette = "jco")

Each curve rises to the fraction of the cohort that has experienced that cause by time t, with a shaded pointwise confidence band. Death (without progression) is far more common than progression to PCM and accumulates faster in men; progression to PCM is uncommon in either sex and, as Gray’s test below shows, not significantly different by sex.

The naive-KM trap, made visible

The clearest way to see the bias is to overlay the naive 1 − KM estimate for one cause on its cumulative incidence. add.naive.km = TRUE draws that contrast for the chosen cause:

ggcompetingrisks(cif, add.naive.km = TRUE, cause = "PCM", palette = "jco")

The dashed line is 1 − KM for PCM; the solid line is its cumulative incidence. The dashed curve sits well above the solid one and climbs steeply late in follow-up: in women it reaches about 0.75 by the end of follow-up, against a true cumulative incidence near 0.20 – more than triple. That gap is the bias the CIF avoids; reporting the dashed value would materially overstate a patient’s risk of progression.

Testing between groups: Gray’s test

Gray’s test compares the cumulative incidence of a cause across groups (the competing-risks analogue of the log-rank test). pval = TRUE annotates it per cause:

ggcompetingrisks(cif, pval = TRUE, palette = "jco")

Here the incidence of death differs by sex (p = 0.00064) while progression to PCM does not (p = 0.27). Gray’s test is available on the cmprsk / tidycmprsk path; an Aalen-Johansen (survfit) object carries no Gray’s test.

A number-at-risk table

risk.table = TRUE adds a per-group number-at-risk table beneath the plot, locked to the same time axis. Note the layout changes: to share one time axis with the table, the causes are drawn in a single overlaid panel – each cause is a colour and each group a linetype (solid Female, dashed Male) – rather than the separate panels above. (So here a dashed line marks the male group, not the naive estimate of the earlier figure.) A subject who has had a competing event counts as having left the risk set, matching the Kaplan-Meier convention used elsewhere in survminer:

ggcompetingrisks(cif, risk.table = TRUE, break.time.by = 60, palette = "jco")

Where to next

Get started – presets, themes, and the composable curve.
Absolute effect measures – RMST, milestone, and landmark analysis.
Interrogating a Cox model – forest plots and proportional-hazards diagnostics.