Produces a data frame that is sorted by stratum and time. Included in this is only the times at which one or more event occurs. The output dataset contains stratum, TTE (time-to-event), at risk count, and count of events at the specified TTE sorted by stratum and TTE.
Arguments
- x
A data frame with no missing values and contain variables:
stratum
: Stratum.treatment
: Treatment group.tte
: Observed time.event
: Binary event indicator,1
represents event,0
represents censoring.
- arm
Value in the input
treatment
column that indicates treatment group value.
Value
A data frame grouped by stratum
and sorted within stratum by tte
.
Remain rows with at least one event in the population, at least one subject
is at risk in both treatment group and control group.
Other variables in this represent the following within each stratum at
each time at which one or more events are observed:
events
: Total number of eventsn_event_tol
: Total number of events at treatment groupn_risk_tol
: Number of subjects at riskn_risk_trt
: Number of subjects at risk in treatment groupS
: Left-continuous Kaplan-Meier survival estimateo_minus_e
: In treatment group, observed number of events minus expected number of events. The expected number of events is estimated by assuming no treatment effect with hypergeometric distribution with parameters total number of events, total number of events at treatment group and number of events at a time. (Same assumption of log-rank test under the null hypothesis)var_o_minus_e
: Variance ofo_minus_e
under the same assumption.
Details
The function only considered two group situation.
The tie is handled by the Breslow's Method.
The output produced by counting_process()
produces a
counting process dataset grouped by stratum and sorted within stratum
by increasing times where events occur.
Examples
# Example 1
x <- data.frame(
stratum = c(rep(1, 10), rep(2, 6)),
treatment = rep(c(1, 1, 0, 0), 4),
tte = 1:16,
event = rep(c(0, 1), 8)
)
counting_process(x, arm = 1)
#> stratum events n_event_tol tte n_risk_tol n_risk_trt s o_minus_e
#> 1 1 1 1 2 9 5 1.0000000 0.4444444
#> 2 1 1 0 4 7 4 0.8888889 -0.5714286
#> 3 1 1 1 6 5 3 0.7619048 0.4000000
#> 4 1 1 0 8 3 2 0.6095238 -0.6666667
#> 5 2 1 0 12 5 2 1.0000000 -0.4000000
#> 6 2 1 1 14 3 1 0.8000000 0.6666667
#> var_o_minus_e
#> 1 0.2469136
#> 2 0.2448980
#> 3 0.2400000
#> 4 0.2222222
#> 5 0.2400000
#> 6 0.2222222
# Example 2
x <- sim_pw_surv(n = 400)
y <- cut_data_by_event(x, 150) |> counting_process(arm = "experimental")
# Weighted logrank test (Z-value and 1-sided p-value)
z <- sum(y$o_minus_e) / sqrt(sum(y$var_o_minus_e))
c(z, pnorm(z))
#> [1] -2.14606589 0.01593386