wlr: Weighted logrank test

In Merck/simtrial: Clinical Trial Simulation

Weighted logrank test

Description

Weighted logrank test

Usage

wlr(data, weight, return_variance = FALSE, ratio = NULL)

## Default S3 method:
wlr(data, weight, return_variance = FALSE, ratio = NULL)

## S3 method for class 'tte_data'
wlr(data, weight, return_variance = FALSE, ratio = NULL)

## S3 method for class 'counting_process'
wlr(data, weight, return_variance = FALSE, ratio = NULL)

Arguments

data	Dataset (generated by sim_pw_surv()) that has been cut by counting_process(), cut_data_by_date(), or cut_data_by_event().
weight	Weighting functions, such as fh(), mb(), and early_zero().
return_variance	A logical flag that, if TRUE, adds columns estimated variance for weighted sum of observed minus expected; see details; Default: FALSE.
ratio	randomization ratio (experimental:control). If the data is generated by simtrial, such as data = sim_pw_surv(...) |> cut_data_by_date(...) data = sim_pw_surv(...) |> cut_data_by_event(...) data = sim_pw_surv(...) |> cut_data_by_date(...) |> counting_process(...) data = sim_pw_surv(...) |> cut_data_by_event(...) |> counting_process(...) there is no need to input the ratio, as simtrial gets the ratio via the block arguments in sim_pw_surv(). If the data is a custom dataset (see Example 2) below, Users are suggested to input the planned randomization ratio to ratio; If not, simtrial takes the empirical randomization ratio.

Details

• z - Standardized normal Fleming-Harrington weighted logrank test.

• i - Stratum index.

• d_i - Number of distinct times at which events occurred in stratum i.

• t_{ij} - Ordered times at which events in stratum i, j = 1, 2, \ldots, d_i were observed; for each observation, t_{ij} represents the time post study entry.

• O_{ij.} - Total number of events in stratum i that occurred at time t_{ij}.

• O_{ije} - Total number of events in stratum i in the experimental treatment group that occurred at time t_{ij}.

• N_{ij.} - Total number of study subjects in stratum i who were followed for at least duration.

• E_{ije} - Expected observations in experimental treatment group given random selection of O_{ij.} from those in stratum i at risk at time t_{ij}.

• V_{ije} - Hypergeometric variance for E_{ije} as produced in Var from counting_process().

• N_{ije} - Total number of study subjects in stratum i in the experimental treatment group who were followed for at least duration t_{ij}.

• E_{ije} - Expected observations in experimental group in stratum i at time t_{ij} conditioning on the overall number of events and at risk populations at that time and sampling at risk observations without replacement:

  E_{ije} = O_{ij.} N_{ije}/N_{ij.}

• S_{ij} - Kaplan-Meier estimate of survival in combined treatment groups immediately prior to time t_{ij}.

• \rho, \gamma - Real parameters for Fleming-Harrington test.

• X_i - Numerator for signed logrank test in stratum i

  X_i = \sum_{j=1}^{d_{i}} S_{ij}^\rho(1-S_{ij}^\gamma)(O_{ije}-E_{ije})

• V_{ij} - Variance used in denominator for Fleming-Harrington weighted logrank tests

  V_i = \sum_{j=1}^{d_{i}} (S_{ij}^\rho(1-S_{ij}^\gamma))^2V_{ij})

  The stratified Fleming-Harrington weighted logrank test is then computed as:

  z = \sum_i X_i/\sqrt{\sum_i V_i}.

Value

A list containing the test method (method), parameters of this test method (parameter), point estimate of the treatment effect (estimate), standardized error of the treatment effect (se), Z-score (z), p-values (p_value).

Examples

# ---------------------- #
#      Example 1         #
#  Use dataset generated #
#     by simtrial        #
# ---------------------- #
x <- sim_pw_surv(n = 200) |> cut_data_by_event(100)

# Example 1A: WLR test with FH wights
x |> wlr(weight = fh(rho = 0, gamma = 0.5))
x |> wlr(weight = fh(rho = 0, gamma = 0.5), return_variance = TRUE)

# Example 1B: WLR test with MB wights
x |> wlr(weight = mb(delay = 4, w_max = 2))

# Example 1C: WLR test with early zero wights
x |> wlr(weight = early_zero(early_period = 4))

# Example 1D
# For increased computational speed when running many WLR tests, you can
# pre-compute the counting_process() step first, and then pass the result of
# counting_process() directly to wlr()
x <- x |> counting_process(arm = "experimental")
x |> wlr(weight = fh(rho = 0, gamma = 1))
x |> wlr(weight = mb(delay = 4, w_max = 2))
x |> wlr(weight = early_zero(early_period = 4))

# ---------------------- #
#      Example 2         #
#  Use cumsum dataset    #
# ---------------------- #
x <- data.frame(treatment = ifelse(ex1_delayed_effect$trt == 1, "experimental", "control"),
                stratum = rep("All", nrow(ex1_delayed_effect)),
                tte = ex1_delayed_effect$month,
                event = ex1_delayed_effect$evntd)

# Users can specify the randomization ratio to calculate the statistical information under H0
x |> wlr(weight = fh(rho = 0, gamma = 0.5), ratio = 2)

x |>
  counting_process(arm = "experimental") |>
  wlr(weight = fh(rho = 0, gamma = 0.5), ratio = 2)

# If users don't provide the randomization ratio, we will calculate the emperical ratio
x |> wlr(weight = fh(rho = 0, gamma = 0.5))

x |>
  counting_process(arm = "experimental") |>
  wlr(weight = fh(rho = 0, gamma = 0.5))

Merck/simtrial documentation built on April 14, 2025, 5:37 a.m.