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Estimate Difference in Survival or Cumulative Incidence and Confidence Interval

Source: R/survdiff_ci.R
survdiff_ci.Rd

This function estimates the unadjusted difference or ratio in survival or cumulative incidence (risk) at a given time point based on the difference between per-group Kaplan-Meier estimates or, if competing events are prevent, Aalen-Johansen estimates of the cumulative incidence.

For constructing confidence limits, the MOVER approach described by Zou and Donner (2008) is used, with estimation on the log scale for ratios.

Usage

survdiff_ci(
  formula,
  data,
  time,
  estimand = c("survival", "cuminc"),
  type = c("diff", "ratio"),
  approach = c("mover", "squareadd"),
  conf.level = 0.95,
  event_type = NULL,
  id_variable = NULL,
  weighted = FALSE
)

Arguments

formula

Formula of a survival object using Surv of the form, Surv(time, event) ~ group. The exposure variable (here, group) must be categorical with at least 2 categories.

data

Data set.

time

Time point to estimate survival difference at.

estimand

Optional. Estimate difference in survival ("survival") or cumulative incidence ("cuminc")? This parameter affects the sign of the differences. Only "cuminc" is available if competing events are present, i.e., event_type is not NULL. Defaults to "survival".

type

Optional. Estimate differences ("diff") or ratio ("ratio") of survival or cumulative incidence? Defaults to "diff".

approach

Optional. For estimating confidence limits of differences, use the MOVER approach based on upper and lower confidence limits of each group ("mover"), or square-and-add standard errors ("squareadd")? Defaults to "mover".

conf.level

Optional. Confidence level. Defaults to 0.95.

event_type

Optional. Event type (level) for event variable with competing events. Defaults to NULL.

id_variable

Optional. Identifiers for individual oberversations, required if data are clustered, or if competing events and time/time2 notation are used concomitantly.

weighted

Optional. Weigh survival curves, e.g. for inverse-probability weighting, before estating differences or ratios? If TRUE, the data must contain a variable called .weights. Defaults to FALSE.

Value

Tibble in tidy format:

  • term Name of the exposure stratum.

  • estimate Difference or ratio.

  • std.error Large-sample standard error of the difference in survival functions (see References). For each survival function, Greenwood standard errors with log transformation are used, the default of the survival package/survfit).

  • statistic z statistic.

  • p.value From the z statistic.

  • conf.low Lower confidence limit

  • conf.high Upper confidence limit

References

Com-Nougue C, Rodary C, Patte C. How to establish equivalence when data are censored: a randomized trial of treatments for B non-Hodgkin lymphoma. Stat Med 1993;12:1353–64. https://doi.org/10.1002/sim.4780121407.

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. https://doi.org/10.1136/bmj.319.7223.14929.

Zou GY, Donner A. Construction of confidence limits about effect measures: A general approach. Statist Med 2008;27:1693–1702. https://doi.org/10.1002/sim.3095

Examples

# Load 'cancer' dataset from survival package (Used in all examples)
data(cancer, package = "survival")

cancer <- cancer %>%
  dplyr::mutate(
    sex = factor(
      sex,
      levels = 1:2,
      labels = c("Male", "Female")
    ),
    status = status - 1
  )

survdiff_ci(
  formula = survival::Surv(time = time, event = status) ~ sex,
  data = cancer,
  time = 365.25)
#> # A tibble: 1 × 7
#>   term   estimate std.error statistic p.value conf.low conf.high
#>   <chr>     <dbl>     <dbl>     <dbl>   <dbl>    <dbl>     <dbl>
#> 1 Female    0.190    0.0750      2.54 0.00557   0.0475     0.342
# Females have 19 percentage points higher one-year survival than males
# (95% CI, 5 to 34 percentage points).