Censoring and Realistic Assessment Schedules

Choosing the censoring rate for a target censoring fraction

censoring_rate_for() solves for a dist parameter (rate, scale, meanlog, or gamma rate) that would give a target independent-censoring fraction, estimated from the event times of an already-run, uncensored simulation. It is an approximation, not an exact calculation – the estimate depends on the particular uncensored run it is given, so always redraw on a larger cohort afterward and check the realized fraction landed close to the target, the way this example does:

# 1. Solve: what rate gives ~20% independently censored, given this
#    model's own event-time scale?
event_times <- sim_uncensored$events$sim_time[
  sim_uncensored$events$sim_status == 1]
rate_20pct <- censoring_rate_for(event_times, target = 0.2)
rate_20pct
#> [1] 0.0205978

# 2. Redraw: apply that rate to a larger cohort.
check <- sim_tte_ode(model = "exponential", param = list(H0 = 0.09),
  n = 2000, end = 30, delta = 2,
  censoring = list(dist = "exponential", rate = rate_20pct), seed = 1)
#> Loading model from cache.

# 3. Check: did it land close to 20%?
mean(check$events$sim_reason == "censored")
#> [1] 0.1895

If the realized fraction in step 3 is not close enough, re-solve with a larger or different uncensored sample rather than trusting the first answer – the check is the point, not an optional extra.

Left censoring

An event with sim_time_left == 0 – one that happened before the first post-baseline visit – is a left-censored observation: the event is known to have occurred before sim_time_right, with the exact time unknown. add_interval_censoring() already produces this with no separate mechanism:

ev <- data.frame(ID = 1:3, sim_time = c(5, 15, 25),
  sim_status = c(1L, 1L, 0L))
add_interval_censoring(ev, visits = c(0, 10))
#>   ID sim_time sim_status sim_time_left sim_time_right
#> 1  1        5          1             0             10
#> 2  2       15          1            10            Inf
#> 3  3       25          0            10            Inf

Subject 1’s row (sim_time_left = 0, sim_time_right = 10) is left censoring – “no lower bound” is exactly what sim_time_left == 0 means. There is no dedicated left_censor_at = option: it would only ever rebuild, less completely, what a plain add_interval_censoring() call already gives for the whole cohort at once.

Delayed entry (not implemented)

A genuinely different concept, easy to confuse with left censoring: delayed entry / left truncation, where a subject is only observed from some entry time entry > 0 onward (e.g. enrollment after treatment already started), and a subject whose event already happened before entry is excluded from the risk set entirely rather than bounded by an interval. This changes the analysis dataset’s shape – a counting-process survival::Surv(start, stop, event) rather than a single time column – not just how one event is bounded, and nothing in this package currently represents it.

Missed visits and assessment dropout

thin_visits() reads no simulated outcome at all – it only thins a schedule, so it can never bias an interval-censored analysis (the visit process stays independent of the outcome, the assumption most such analyses make). Each non-baseline visit is independently missed with probability p_miss; independently of that, a subject may also start dropping out at a random visit and never return, with probability p_dropout:

realized <- thin_visits(sched, p_miss = 0.1, p_dropout = 0.05, seed = 2)
nrow(sched) - nrow(realized) # visits lost to missed/dropout
#> [1] 156
out <- add_interval_censoring(sim_censored$events, visits = realized)
head(out[, c("sim_time", "sim_status", "sim_time_left", "sim_time_right")])
#>    sim_time sim_status sim_time_left sim_time_right
#> 1 14.734534          1     12.145707      16.816416
#> 2 10.983644          1      8.321596      12.258228
#> 3  6.190283          1      4.374046       7.768207
#> 4  1.069800          1      0.000000       3.760070
#> 5  6.278294          0      3.534441            Inf
#> 6  1.190571          1      0.000000       3.964160

thin_visits() also accepts a plain vector schedule directly, given the subject IDs to expand it across (ids =), and composes with add_censoring() in either relative order – it only ever touches the visit schedule, never events.

Informative assessment schedules

visit_schedule_informative() is different in kind: it reads $events and lets the visit process react to the simulated outcome – a visit shortly before a subject’s event may be missed at an elevated rate (miss_near_event, e.g. “too unwell to attend”), and an unscheduled extra visit may be added shortly after it (extra_visit_after_event, e.g. “brought in for follow-up after a reported symptom”). This makes the resulting schedule informative by construction – whether/when a subject is assessed now depends on whether/when they had the event – which every function in this package says loudly, on every call, because it breaks the assumption most interval-censored analyses (including the Turnbull fit above) make about assessment timing. Use it to study that bias, not as a general visit generator:

rate <- 0.08
sim_small <- sim_tte_ode(model = "exponential", param = list(H0 = rate),
  n = 800, end = 24, delta = 2, seed = 1)
base_sched <- visit_schedule(n = 800, every = 3, end = 24, seed = 1)
base_sched$ID <- sim_small$events$ID[base_sched$ID]
visit_times <- seq(0, 24, by = 3)
analytical_surv <- exp(-rate * visit_times)

fit_surv <- function(schedule) {
  out <- add_interval_censoring(sim_small$events, visits = schedule)
  right <- ifelse(is.infinite(out$sim_time_right), NA, out$sim_time_right)
  fit <- survival::survfit(survival::Surv(time = sim_time_left, time2 = right,
    type = "interval2") ~ 1,
    data = data.frame(sim_time_left = out$sim_time_left, right = right))
  summary(fit, times = visit_times, extend = TRUE)$surv
}

c1_sched <- thin_visits(base_sched, p_miss = 0.3, seed = 2)
c2_sched <- visit_schedule_informative(base_sched, sim_small$events,
  end = 24, p_miss_base = 0.1, miss_near_event = list(window = 3, p = 0.9),
  seed = 2)

data.frame(time = visit_times,
  truth = round(analytical_surv, 3),
  c1_non_informative = round(fit_surv(c1_sched), 3),
  c2_informative = round(fit_surv(c2_sched), 3))
#>   time truth c1_non_informative c2_informative
#> 1    0 1.000              1.000          1.000
#> 2    3 0.787              0.796          0.666
#> 3    6 0.619              0.623          0.576
#> 4    9 0.487              0.509          0.443
#> 5   12 0.383              0.372          0.332
#> 6   15 0.301              0.282          0.237
#> 7   18 0.237              0.220          0.209
#> 8   21 0.186              0.173          0.143
#> 9   24 0.147              0.132          0.140

At the same nominal miss rate (0.3 for C1’s uniform miss; 0.1 background + 0.9 near an event for C2 – additive, not overriding: a near-window visit for an event subject is missed with probability 1 - (1 - p_miss_base) * (1 - p), so the two mechanisms compete rather than one replacing the other), C2’s estimate strays further from the analytical curve than C1’s – missing visits specifically because a subject is about to have the event pulls the estimated survival away from the truth in a way a uniform miss rate does not. A visit-process generator reacting to a subject’s own PK/PD trajectory, rather than the exact event time, is out of scope for this release – it would need keep_trajectory = TRUE and interpolation between reported times, the same complexity class this package has consistently declined to add.