Step 1: Define design parameters

To run simulations for a fixed design, several design characteristics may be used. Depending on the data cutoff for analysis option, different inputs may be required. The following lines of code specify an unstratified 2-arm trial with equal randomization. The simulation is repeated 2 times. Enrollment is targeted to last for 12 months at a constant enrollment rate. The median for the control arm is 10 months, with a delayed effect during the first 3 months followed by a hazard ratio of 0.7 thereafter. There is an exponential dropout rate of 0.001 over time.

n_sim <- 100
total_duration <- 36
stratum <- data.frame(stratum = "All", p = 1)
block <- rep(c("experimental", "control"), 2)

enroll_rate <- data.frame(stratum = "All", rate = 12, duration = 500 / 12)
fail_rate <- data.frame(stratum = "All",
                        duration = c(3, Inf), fail_rate = log(2) / 10, 
                        hr = c(1, 0.6), dropout_rate = 0.001)

We specify sample size and targeted event count based on the fixed_design_ahr() function and the above options. The following design computes the sample size and targeted event counts for 85% power. In this approach, users can obtain the sample size and targeted events from the output of x, specifically by using sample_size <- x$analysis$n and target_event <- x$analysis$event.

x <- fixed_design_ahr(enroll_rate = enroll_rate, fail_rate = fail_rate, 
                      alpha = 0.025, power = 0.85, ratio = 1, 
                      study_duration = total_duration) |> to_integer()
x |> summary() |> gt() |> 
  tab_header(title = "Sample Size and Targeted Events Based on AHR Method", 
             subtitle = "Fixed Design with 85% Power, One-sided 2.5% Type I error") |>
  fmt_number(columns = c(4, 5, 7), decimals = 2)

Now we set the derived targeted sample size, enrollment rate, and event count from the above.

sample_size <- x$analysis$n
target_event <- x$analysis$event
enroll_rate <- x$enroll_rate

Step 2: Run sim_fixed_n()

Now that we have set up the design characteristics in Step 1, we can proceed to run sim_fix_n() for our simulations. This function automatically utilizes a parallel computing backend, which helps reduce the running time.

The timing_type specifies one or more of the following cutoffs for setting the time for analysis:

• timing_type = 1: The planned study duration.
• timing_type = 2: The time until target event count has been observed.
• timing_type = 3: The planned minimum follow-up period after enrollment completion.
• timing_type = 4: The maximum of planned study duration and time to observe the targeted event count (i.e., using timing_type = 1 and timing_type = 2 together).
• timing_type = 5: The maximum of time to observe the targeted event count and minimum follow-up following enrollment completion (i.e., using timing_type = 2 and timing_type = 3 together).

The rho_gamma argument is a data frame containing the variables rho and gamma, both of which should be greater than or equal to zero, to specify one Fleming-Harrington weighted log-rank test per row. For instance, setting rho = 0 and gamma = 0 yields the standard unweighted log-rank test, while rho = 0 and gamma = 0.5 provides the weighted Fleming-Harrington (0, 0.5) log-rank test. If you are interested in tests other than the Fleming-Harrington weighted log-rank test, please refer to the vignette Custom Fixed Design Simulations: A Tutorial on Writing Code from the Ground Up.

sim_res <- sim_fixed_n(
  n_sim = 2, # only use 2 simulations for initial run
  sample_size = sample_size, 
  block = block, 
  stratum = stratum,
  target_event = target_event, 
  total_duration = total_duration,
  enroll_rate = enroll_rate, 
  fail_rate = fail_rate,
  timing_type = 1:5, 
  rho_gamma = data.frame(rho = 0, gamma = 0))

The output of sim_fixed_n is a data frame with one row per simulated dataset per cutoff specified in timing_type, per test statistic specified in rho_gamma. Here we have just run 2 simulated trials and see how the different cutoffs vary for the 2 trial instances.

sim_res |>
  gt() |>
  tab_header("Tests for Each Simulation Result", subtitle = "Logrank Test for Different Analysis Cutoffs") |>
  fmt_number(columns = c(4, 5, 7), decimals = 2)

Step 3: Summarize simulations

Now we run 100 simulated trials and summarize the results by how data is cutoff for analysis.

sim_res <- sim_fixed_n(
  n_sim = n_sim,
  sample_size = sample_size, 
  block = block, stratum = stratum,
  target_event = target_event, 
  total_duration = total_duration,
  enroll_rate = enroll_rate, 
  fail_rate = fail_rate,
  timing_type = 1:5, 
  rho_gamma = data.frame(rho = 0, gamma = 0))

With the 100 simulations provided, users can summarize the simulated power and compare it to the targeted 85% power. All cutoff methods approximate the targeted power well and have a similar average duration and mean number of events.

sim_res |>
  group_by(cut) |>
  summarize(`Simulated Power` = mean(z > qnorm(1 - 0.025)), 
            `Mean events` = mean(event),
            `Mean duration` = mean(duration)) |>
  mutate(`Sample size` = sample_size,
         `Targeted events` = target_event) |>
  gt() |>
  tab_header(title = "Summary of 100 simulations by 5 different analysis cutoff methods",
             subtitle = "Tested by logrank") |>
  fmt_number(columns = c(2:4), decimals = 2)

We can also do things like summarize distribution of event counts at the planned study duration. We can see the event count varies a fair amount.

hist(sim_res$event[sim_res$cut == "Planned duration"], 
     breaks = 10,
     main = "Distribution of Event Counts at Planned Study Duration",
     xlab = "Event Count at Targeted Trial Duration")

We also evaluate the distribution of the trial duration when analysis is performed when the targeted events are achieved.

plot(density(sim_res$duration[sim_res$cut == "Targeted events"]), 
     main = "Trial Duration Smoothed Density",
     xlab = "Trial duration when Targeted Event Count is Observed")