wlr | R Documentation |
With output from the function counting_process
wlr(
x = sim_pw_surv(n = 200) %>% cut_data_by_event(150) %>% counting_process(arm =
"Experimental"),
rg = tibble(rho = c(0, 0, 1, 1), gamma = c(0, 1, 0, 1)),
returnVariance = FALSE
)
x |
a |
rg |
a |
returnVariance |
a logical flag that, if true, adds columns estimated variance for weighted sum of observed minus expected; see details; Default: FALSE |
The input value x
produced by counting_process()
produces a counting process dataset
grouped by strata and sorted within strata by increasing times where events occur.
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 the counting_process()
routine
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}
a tibble
with rg
as input and the FH test statistic
for the data in x
(Z
, a directional square root of the usual weighted logrank test);
if variance calculations are specified (e.g., to be used for covariances in a combination test),
the this will be returned in the column Var
library(tidyr)
# Use default enrollment and event rates at cut at 100 events
x <- sim_pw_surv(n = 200) %>%
cut_data_by_event(100) %>%
counting_process(arm ="Experimental")
# compute logrank (FH(0,0)) and FH(0,1)
wlr(x, rg = tibble(rho = c(0, 0), gamma = c(0, 1)))
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