Conduct of a study with a time-to-event endpoint

Specifies how subjects are enrolled, how they drop out and when the analysis takes place. The operating characteristics of a design with a time-to-event endpoint (design_tte) are computed by simulating studies conducted in this way, and the posterior predictive probabilities by simulating future studies.

Usage

conduct_tte(
  accrual_time,
  accrual_rate = rep(1, length(accrual_time) - 1L),
  dropout_time = 0,
  dropout_hazard = 0,
  cut_time = NULL,
  cut_events = NULL
)

Arguments

accrual_time

Boundaries of the enrollment intervals: an increasing numeric vector that starts at 0, of length at least 2.

accrual_rate

Non-negative relative enrollment rates of the intervals, one fewer than accrual_time, with a positive sum. The default is a constant rate (uniform enrollment).

dropout_time

Start times of the pieces of the dropout hazard: an increasing numeric vector that starts at 0.

dropout_hazard

Non-negative dropout hazards of the pieces, of the same length as dropout_time. The default 0 means no dropout.

cut_time

Calendar time of the analysis after the start of enrollment (positive), or NULL.

cut_events

Number of events that triggers the analysis (a whole number of at least 1), or NULL. Exactly one of cut_time and cut_events must be given.

Value

An object of class "qdm_conduct" with the arguments and the element accrual_cum, the cumulative probabilities of enrollment at the ends of the intervals.

Details

The subjects of all groups are enrolled at independent times with a piecewise uniform distribution: the enrollment period is divided by accrual_time, and the probability of an interval is proportional to its rate in accrual_rate times its length (only the relative rates matter). The dropout time of a subject, measured from enrollment, has a piecewise exponential distribution with hazard dropout_hazard[j] from time dropout_time[j] (the last hazard applies until infinity), independently of the event time. The analysis takes place at the calendar time cut_time after the start of enrollment, or at the calendar time of the cut_events-th event among all subjects of the study (if fewer events occur, all subjects are followed until their event or dropout). A subject enrolled at time \(e\) with event time \(T\) and dropout time \(C\) contributes the observed time \(\min(T, C, \textrm{cut} - e)\) (0 if enrolled after the analysis) and an event if \(T \le C\) and \(e + T \le \textrm{cut}\).

See also

design_tte

Examples

# Enrollment over 15 months with increasing rates, dropout hazard 0.00226
# per month, analysis 15.44 months after the start of enrollment
conduct_tte(accrual_time = c(0, 5, 10, 15), accrual_rate = c(0.4, 2, 4.5),
            dropout_hazard = 0.00226, cut_time = 15.44)
#> Enrollment: piecewise uniform on (0, 5, 10, 15) with rates (0.4, 2.0, 4.5)
#> Dropout: hazard 0.00226
#> Analysis: at time 15.44

# Uniform enrollment over 12 months, analysis at the 20th event
conduct_tte(accrual_time = c(0, 12), cut_events = 20)
#> Enrollment: uniform from 0 to 12
#> Dropout: none
#> Analysis: at event 20