stoppingrule (version 0.6)

OC.rule.tite: Operating Characteristics Function (TITE Method)

Description

Compute operating characteristics for a stopping rule at a set of toxicity rates. Characteristics calculated include the overall rejection probability, the expected number of patients evaluated, and the expected number of events.

Usage

OC.rule.tite(rule, ps, ps.compt = NULL, MC, tau, A, family = "power", s = 1)

Value

A matrix with columns containing the toxicity probabilities ps, competing risk probability (0 for survival outcome), the corresponding rejection probabilities, and the corresponding expected number of events. If tau and A are also specified, the expected numbers of enrolled patients and the expected calendar time at the point of stopping/study end are also included.

Arguments

rule

A rule.tite object with the safety stopping rule for evaluation

ps

Vector of cumulative incidence probabilities for toxicity at time tau

ps.compt

Vector of cumulative incidence probabilities for competing risks at time tau if competing risks are involved. Set to NULL if no competing risks exist.

MC

Number of Monte Carlo replicated datasets to simulate

tau

Length of observation period

A

Length of accrual period

family

Event time distribution, choices including power distribution ('power') and Weibull distribution ('weibull')

s

Shape parameter for Weibull distribution or power parameter for power distribution

Details

Times are generated for each event cause so that its marginal distribution follows a Weibull or power family distribution as specified by the user.

For the Weibull distribution, the cumulative distribution function is \(1- \exp(- \lambda t^s), t \ge 0\), where \(\lambda\) is the rate parameter and s is the shape parameter.

The power distribution has the cumulative distribution function \(k (t /\tau)^s, 0 \le t \le \tau k^{-1/s}\), where s is the power parameter and \(k\) is the value at \(t=\tau\).

For the toxicity event distribution, the Weibull rate parameter is \(\lambda = - \log(1-p) / \tau\) and the power parameter is \(k = p\), where \(p\) is the cumulative incidence of toxicity at \(t=\tau\). For competing risk events' distribution, \(\lambda = - 1 / \tau \log(1-p_c)\) and \(k = p_c\), where \(p_c\) is the cumulative incidence of competing events at \(t=\tau\).

Examples

if (FALSE) {
# Bayesian beta-extended binomial method in 50 patient cohort at 10% level,
# expected toxicity probability of 20%
bb_rule = calc.rule.tite(n=50,p0=0.20,alpha=0.10,type="BB",param=c(2,8))

# Compute operating characteristics at toxicity probabilities of 20%, 25%, 30%, 35%, and 40%
OC.rule.tite(rule=bb_rule,ps=seq(0.2,0.4,0.05), MC =1000, tau=30,A=730, family = 'weibull', s = 2)
}