Differences and ratios of survival at a time point

rift_survival_difference() and rift_survival_ratio() compare the Kaplan-Meier survival probability, or the cumulative incidence, at a time point between the levels of a stratifying variable, each level against the first, with a confidence interval. They are the estimators behind the "survdiff", "cumincdiff", "survratio" and "cumincratio" rows of tbl_rift(), exported so they can be called on their own or wrapped in a custom method of add_difference() or a stat_fns function of tbl_custom_summary(). The survival package must be installed.

The per-level estimates and their limits are those of summary(survival::survfit(), times = time, extend = TRUE): Greenwood standard errors and, by default, log-transformed limits. With competing events (a factor status in Surv()), the curves are Aalen-Johansen cumulative incidences of state. The limits of a difference come from the MOVER method of Zou and Donner (2008), which recovers the interval of a difference from the two levels' own intervals and so keeps their asymmetry: for the difference d = e_i - e_1 with limits (l, u) around each estimate e, the lower limit is d - sqrt((e_i - l_i)^2 + (u_1 - e_1)^2) and the upper limit is d + sqrt((u_i - e_i)^2 + (e_1 - l_1)^2). approach = "squareadd" instead adds the squared standard errors (Altman and Andersen, 1999), the Z-test difference cardx computes. Ratios always use MOVER on the log scale. The standard error, statistic and p-value are derived from the limits.

Usage

rift_survival_difference(
  x,
  data = NULL,
  time,
  estimand = c("survival", "cuminc"),
  approach = c("mover", "squareadd"),
  conf.level = 0.95,
  state = NULL,
  ...
)

rift_survival_ratio(
  x,
  data = NULL,
  time,
  estimand = c("survival", "cuminc"),
  conf.level = 0.95,
  state = NULL,
  ...
)

Arguments

x: (formula or survfit)
A formula Surv(time, event) ~ group evaluated in data, or a fitted survival::survfit() object stratified by one variable. A survfit object keeps its own confidence level.
data: (data.frame)
The data frame the formula refers to.
time: (scalar numeric)
The time point.
estimand: (string)
"survival" (the default) or "cuminc", the cumulative incidence 1 - survival. Only "cuminc" is available with competing events.
approach: (string)
For differences, "mover" (the default) or "squareadd".
conf.level: (scalar numeric)
Confidence level. Default is 0.95.
state: (string)
With competing events, the state whose cumulative incidence is compared. Default is the first state after censoring, with a message.
...: Not used. Accepted so that the functions can be wrapped in custom methods that receive more arguments.

Value

A data frame with one row per level other than the first: level, reference (the first level), estimate, std.error (on the log scale for a ratio), statistic, p.value, conf.low, conf.high and method.

References

Zou GY, Donner A. Construction of confidence limits about effect measures: a general approach. Stat Med 2008;27:1693-702.

Altman DG, Andersen PK. Calculating the number needed to treat for trials where the outcome is time to an event. BMJ 1999;319:1492-5.

Stopsack KH. rifttable: Results tables to bridge the rift between epidemiologists and their data. R package, https://stopsack.github.io/rifttable/.

Examples

library(survival)

# Example 1 ----------------------------------
# the difference in 12-month survival, Drug B against Drug A
rift_survival_difference(Surv(ttdeath, death) ~ trt, trial, time = 12)
#>    level reference  estimate  std.error statistic    p.value     conf.low
#> 1 Drug B    Drug A 0.0962406 0.05221127  1.843292 0.06528644 -0.008266038
#>   conf.high                      method
#> 1 0.1963984 Survival difference (MOVER)

# Example 2 ----------------------------------
# the ratio of the 12-month risk of death, from a survfit object
fit <- survfit(Surv(ttdeath, death) ~ grade, trial)
rift_survival_ratio(fit, time = 12, estimand = "cuminc")
#>   level reference estimate std.error   statistic   p.value  conf.low conf.high
#> 1    II         I 0.560241 0.5107325 -1.13442611 0.2566159 0.1873319  1.387025
#> 2   III         I 1.033333 0.4579234  0.07160548 0.9429159 0.4118896  2.479425
#>                               method
#> 1 Cumulative incidence ratio (MOVER)
#> 2 Cumulative incidence ratio (MOVER)