wlr {simtrial}

Weighted logrank test

Description

Weighted logrank test

Usage

wlr(data, weight, return_variance = FALSE)

Arguments

data

Dataset that has been cut, generated by sim_pw_surv().

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.

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 estimation of the treatment effect (estimation), standardized error of the treatment effect (se), Z-score (z), p-values (p_value).

Examples

x <- sim_pw_surv(n = 200) |> cut_data_by_event(100)

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

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

# Example 3: WLR test with early zero wights
x |> wlr(weight = early_zero(early_period = 4))