Fast Treatment Switching in Simulated Trial Data

Applies a treatment-switching rule to simulated trial data, such as the output of simdata_fast, by changing only the outcomes that occur after each subject's switch. Subjects of the selected groups switch either at their intermediate event (for example disease progression), at an opening time after an interim analysis (crossover at a milestone), or at the later of the two, and the remaining time to the terminal event after the switch is either multiplied by an acceleration factor or redrawn from a new (piecewise) exponential hazard. All simulated trials are processed at once with vectorized operations. Because the outcomes observed before the switch are kept exactly, an analysis at or before the opening time gives the same result before and after switching, so a crossover that depends on an interim result can be simulated by analyzing the interim, deciding per simulated trial, and switching afterward.

Usage

switch_fast(
  data,
  group,
  prob = 1,
  when = c("intermediate", "cutoff", "later"),
  cutoff = NULL,
  delay = 0,
  sims = NULL,
  aft.factor = NULL,
  hazard = NULL,
  median = NULL,
  time = NULL,
  seed = NULL,
  stream = NULL
)

Arguments

data: A data frame from simdata_fast (single-endpoint, multi-arm, or illness-death), containing at least sim, group, accrual_time, and the latent columns described in Details.
group: A vector of group labels whose subjects may switch, for example the control group 1.
prob: A single probability in [0, 1] that an eligible subject switches. Defaults to 1.
when: A character string, one of "intermediate", "cutoff", and "later", giving the switch time (see Details).
cutoff: Per-simulation calendar times at which switching opens, used with when = "cutoff" or "later". Either a numeric vector with one element per simulated trial or a one-column matrix from cutoff_fast. As in the cutoff.looks argument of analysis_fast, the names of a vector (or the row names of a matrix) are matched to the values of data$sim; without names the elements are taken in the order of the sorted distinct values of data$sim. NA disables switching in that simulated trial.
delay: A single non-negative number added to cutoff, for example the time needed to implement the crossover after an interim analysis. Defaults to 0.
sims: An optional logical vector with one element per simulated trial (in the order of the sorted distinct values of data$sim). Switching is applied only in the simulated trials with TRUE. Requires when = "cutoff" or "later".
aft.factor: A single positive acceleration factor applied to the remaining time after the switch. Exactly one of aft.factor, hazard, and median must be supplied.
hazard: Post-switch hazard, a single value or a vector for a piecewise exponential distribution with breakpoints time, measured from the switch.
median: A single post-switch median; an alternative to a single hazard.
time: Breakpoints for a piecewise hazard, starting at 0 and ending with Inf, measured from the switch.
seed: Optional integer seed for the dqrng generator. If NULL (default), the draws come from the current state of that generator, which set.seed() does not control; supply seed for reproducible results (see simdata_fast).
stream: Optional non-negative whole number selecting a dqrng stream; requires seed. See simdata_fast.

Value

The data frame data with the latent and observed columns of the switched subjects updated, and the columns switched (0 or 1) and switch_time (time from accrual to the switch, NA for subjects who did not switch) added or updated.

Details

The function works on the latent columns of simdata_fast. For a single-endpoint simulation these are surv_time and dropout_time; for an illness-death simulation they are e1_surv_time (time to the first event, such as progression-free survival), e2_surv_time (time to the terminal event, such as overall survival), dropout_time, and intermediate. The observed columns (tte, event, and calendar_time, or their e1_ and e2_ counterparts) are recomputed from the modified latent times, and the columns switched and switch_time (time from accrual to the switch) record the switches. The columns sim, group, accrual_time, and the subgroup columns are unchanged.

The switch time s, measured from accrual, is

when = "intermediate": the intermediate event time e1_surv_time of a subject whose intermediate event occurred (intermediate == 1); illness-death data only;
when = "cutoff": the opening time cutoff + delay of the subject's simulated trial minus the accrual time (zero for a subject accrued after the opening);
when = "later": the later of the intermediate event time and the opening time, for a subject whose intermediate event occurred; illness-death data only.

A subject of the selected group switches with probability prob when the switch occurs before the terminal event and before dropout (s < e2_surv_time, or s < surv_time for single-endpoint data, and s < dropout_time) and the subject has not already switched (switched == 1, for example at progression through the switch.prop argument of simdata_fast). With when = "cutoff" or "later", the switch never occurs before the opening time, so every outcome observed by calendar time cutoff + delay is left unchanged; subjects accrued after the opening are also eligible, as in a protocol that opens crossover from that time on.

The effect of switching on the terminal time T > s is

aft.factor = f: T_new = s + f * (T - s), the causal accelerated failure time model of the rank-preserving structural failure time (RPSFT) method, under which f > 1 prolongs the remaining survival;
hazard (or median): T_new = s + R, where the remaining time R is drawn from the (piecewise) exponential distribution with hazard hazard and breakpoints time measured from the switch.

In illness-death data with when = "cutoff", a switch can occur before the intermediate event. The acceleration factor is then applied in the same way to the first-event time when it lies after the switch, which keeps the first event no later than the terminal event; a redrawn hazard is not available in this case because the latent time to the intermediate event after the terminal event is not stored.

sims restricts the switching to some simulated trials, for example those in which the interim analysis crossed an efficacy boundary. It is available with when = "cutoff" or "later" only, so that the decision cannot change outcomes observed before it is made.

The random numbers (one uniform per row when prob < 1, and one exponential per row when hazard or median is used) are drawn with dqrng, in row order, so the result is reproducible from seed and stream, or from the state left by a seeded simdata_fast call.

References

Robins, J. M., & Tsiatis, A. A. (1991). Correcting for non-compliance in randomized trials using rank preserving structural failure time models. Communications in Statistics - Theory and Methods, 20(8), 2609-2631.

Examples

# Crossover at an interim analysis: control subjects still on study at the
# 150th event switch to the experimental treatment, which multiplies their
# remaining survival time by 1.5.
df <- simdata_fast(nsim = 50, n = c(150, 150), a.time = c(0, 12),
                   a.rate = 300 / 12, e.median = list(12, 18),
                   d.hazard = 0.01, seed = 1)
ia <- cutoff_fast(df, event.looks = 150)
dfs <- switch_fast(df, group = 1, when = "cutoff", cutoff = ia,
                   aft.factor = 1.5)
mean(dfs$switched[dfs$group == 1])
#> [1] 0.3404

# The interim analysis is unchanged; the final analysis is diluted.
r0 <- analysis_fast(df,  control = 1, cutoff.looks = ia)
r1 <- analysis_fast(dfs, control = 1, cutoff.looks = ia)
all.equal(r0$logrank.z, r1$logrank.z)
#> [1] TRUE
fa0 <- analysis_fast(df,  control = 1, event.looks = 220)
fa1 <- analysis_fast(dfs, control = 1, event.looks = 220)
c(mean(fa0$logrank.z), mean(fa1$logrank.z))
#> [1] -3.078266 -2.112271

# Switching at progression in an illness-death simulation: 50 percent of
# the control subjects who progress switch, with a post-progression median
# of 15 instead of 10.
id <- simdata_fast(nsim = 50, n = c(150, 150), a.time = c(0, 12),
                   a.rate = 300 / 12, h01.median = list(6, 9),
                   h02.median = list(20, 24), h12.median = list(10, 10),
                   seed = 2)
ids <- switch_fast(id, group = 1, prob = 0.5, when = "intermediate",
                   median = 15)
table(ids$group, ids$switched)
#>    
#>        0    1
#>   1 4587 2913
#>   2 7500    0