estimate_rmtl: Estimate Restricted Mean Time Lost (RMTL) and its Difference

In stopsack/khsmisc: Miscellaneous functions for epidemiology research

Estimate Restricted Mean Time Lost (RMTL) and its Difference

Description

The method of Connor and Trinquart (Stat Med 2021) estimates the RMTL in the presence of competing risks. This function is a modification of their R code. Estimation functions are identical; input handling and output have been adapted.

Usage

estimate_rmtl(
  data,
  exposure = NULL,
  time,
  time2 = NULL,
  event,
  event_of_interest = 1,
  weight = NULL,
  tau = NULL,
  reach_tau = c("warn", "stop", "ignore"),
  conf.level = 0.95
)

Arguments

data	Data frame (tibble).
exposure	Optional. Name of exposure variable within the data. If omitted, will return unstratified RMTL.
time	Name of time variable within the data. By default, this is the event time. If time2 is also given, this is the entry time, as per Surv standard.
time2	Optional. Name of the variable within the data indicating the exit (event) time. If omitted, time is the event time, as per Surv standard.
event	Name of event variable within the data. Can be integer, factor, character, or logical. The reference level indicates censoring and is taken as the first level of the factor, the lowest numeric value (usually 0), or FALSE for a logical variables. Other levels are events of different types. If no competing risks, the alternative level, e.g. 1, indicates the event (e.g., death).
event_of_interest	Optional. Indicator for which of the non-censoring events is of main interest. Others are treated as competing. Defaults to 1, i.e., the first non-censoring event.
weight	Optional. Weights, such as inverse-probability weights or survey weights. The default (NULL) uses equal weights for all observations.
tau	Optional. Time horizon to restrict event times. By default, the latest time in the group with the shortest follow-up. Prefer a user-defined, interpretable time horizon.
reach_tau	Optional. How to handle provided tau values that are not reached in one of the exposure categories. "warn" Default. Display a warning and estimate RMTL and its difference in those exposure categories where tau is reached. "stop" Stop with an error if tau not reached in one or more of the exposure categories. "ignore" Ignore exposure categories where tau is not reached; estimate RMTL and its difference in those exposure categories where tau is reached. If tau is not reached in any of the exposure categories, the function always stops with an error.
conf.level	Optional. Confidence level. Defaults to 0.95.

Details

Differences to the original function rmtl::rmtl():

• Convert print for errors to stop or warning.

• Pass data as a data frame/tibble and select variables from it.

• Allow for different variable types in the event variable.

• Use Surv conventions for entry/exit times (time, time2).

• Allow for exposure groups where tau is not reached.

• Return contrasts in restricted mean time lost as comparisons to the reference level instead of all pairwise comparisons.

• Add origin (time 0, cumulative incidence 0) to the returned cumulative incidence function for proper plotting.

• Return results as a list of tibbles. Do not print or plot.

Value

List:

• tau Time horizon.

• rmtl Tibble with absolute estimates of RMTL, per exposure group if given.

• rmtdiff Tibble with contrasts of RMTL between exposure groups, compared to a common reference (the first level). Empty tibble if no exposure variable given.

• cif Tibble with cumulative incidence function for the event of interest:

  • exposure Exposure group.

  • time Event time.

  • estimate Aalen-Johansen estimate of cumulative incidence function with se, conf.low, and conf.high.

References

Conner SC, Trinquart L. Estimation and modeling of the restricted mean time lost in the presence of competing risks. Stat Med 2021;40:2177–96. https://doi.org/10.1002/sim.8896.

Examples

data(cancer, package = "survival")
cancer <- cancer %>% dplyr::mutate(
  status = status - 1,   # make 0/1
  sex    = factor(sex, levels = 1:2, labels = c("Men", "Women")))

result <- estimate_rmtl(
  data = cancer,
  exposure = sex,
  time = time,
  event = status,
  tau = 365.25)  # time horizon: one year
result

# Make simple plot
library(ggplot2)
library(dplyr)
library(tidyr)

result$cif %>%
  ggplot(mapping = aes(x = time, y = estimate, color = exposure)) +
  geom_step() +
  scale_x_continuous(breaks = seq(from = 0, to = 365, by = 60)) +
  labs(x = "Time since start of follow-up in days",
       y = "Cumulative incidence")

# Make fancier plot with a shaded area for the RMTL difference
df_ribbon <- result$cif %>%
  select(exposure, time, estimate) %>%
  pivot_wider(names_from = exposure,
              values_from = estimate,
              names_repair = ~c("time", "surv", "surv2")) %>%
  filter(time < 365.25) %>%  # tau for RMST
  arrange(time) %>%  # carry forward survival values per stratum
  fill(surv) %>%
  fill(surv2)

result$cif %>%
  ggplot() +
  geom_step(mapping = aes(x = time, y = estimate, color = exposure)) +
  scale_x_continuous(breaks = seq(from = 0, to = 365, by = 60)) +
  scale_y_continuous(expand = expansion()) +
  labs(x = "Time since start of follow-up in days",
       y = "Cumulative incidence") +
  cowplot::theme_minimal_hgrid() +
  geom_stepribbon(data = df_ribbon,
                  mapping = aes(x = time, ymin = surv, ymax = surv2),
                  fill = "gray80", alpha = 0.5)

stopsack/khsmisc documentation built on Sept. 22, 2023, 12:26 p.m.