Example using dummy data

We generate the dataset \(S1\) in Stegherr, Beyersmann, et al. (2021) using the parameter values for Arm A. First we define the sample size and a range of censoring times. Then we set the hazard of the three event types (adverse event, death/hard competing event and soft competing event). After the dataset has been generated, we set \(\tau\) as the maximum event time.

n <- 200

min_cens <- 0
max_cens <- 1000

set.seed(2020)
dat1 <- generate_data(
  n,
  cens = c(min_cens, max_cens),
  haz_ae = 0.00265,
  haz_death = 0.00151,
  haz_soft = 0.00227
)

tau <- max(dat1[, "time_to_event"])

The structure of the dataset looks as follows:

kable(head(dat1, 10), align = c("crcr"))

For this dataset we then compute all the estimators used in the comparisons in Stegherr, Schmoor, Beyersmann, et al. (2021) and Stegherr, Schmoor, Lübbert, et al. (2021). We start with the estimators that do not account for competing events (incidence proportion, incidence density, Inverse Kaplan Meier), then incidence proportion accounting for competing events and Aalen-Johansen (both first with death only as hard competing event, then using all competing events):

ip <- inc_prop(dat1, tau)
id <- prop_trans_inc_dens(dat1, tau)
km <- one_minus_kaplan_meier(dat1, tau)

idce_2 <- prop_trans_inc_dens_ce(dat1, ce = 2, tau)
aj_2 <- aalen_johansen(dat1, ce = 2, tau)

idce_3 <- prop_trans_inc_dens_ce(dat1, ce = 3, tau)
aj_3 <- aalen_johansen(dat1, ce = 3, tau)

The AE risks look as follows:

tab <- rbind(ip, id, km, idce_2, aj_2[1:2], idce_3, aj_3[1:2])
colnames(tab) <- c(
  "estimated AE probability",
  "variance of estimation"
)
rownames(tab) <- c(
  "incidence proportion",
  "probability transform incidence density ignoring competing event",
  "1 - Kaplan-Meier", "probability transform incidence density (death only)",
  "Aalen-Johansen (death only), AE risk", "probability transform incidence density (all CEs)",
  "Aalen-Johansen (all CEs), AE risk"
)

kable(tab, digits = c(3, 5))

Finally, the estimated probabilities of competing events based on the Aalen-Johansen estimators:

tab <- rbind(aj_2[3:4], aj_3[3:4])
colnames(tab) <- c(
  "estimated probability",
  "variance of estimation"
)
rownames(tab) <- c(
  "Aalen-Johansen (death only), CE risk",
  "Aalen-Johansen (all CEs), CE risk"
)

kable(tab, digits = c(3, 5))