Generate operating characteristics for drug combination trials

Description

Obtain the operating characteristics of the BOIN design or waterfall design for drug combination trials. The BOIN design is to find a MTD, and the waterfall design is to find the MTD contour (i.e., multple MTDs in the dose matrix)

Usage

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get.oc.comb(target, p.true, ncohort, cohortsize, n.earlystop=NULL, startdose=c(1, 1),
                   p.saf=0.6*target, p.tox=1.4*target, cutoff.eli=0.95, extrasafe=FALSE,
                   offset=0.05, ntrial=1000, MTD.contour=FALSE)

Arguments

target

the target toxicity rate

p.true

a J*K matrix (J<=K) containing the true toxicity probabilities of combinations with J dose levels of agent A and K dose levels of agent B

ncohort

a 1*J vector specifying the number of cohorts for each of J subtrials if MTD.contour=TRUE; Otherwise, a scalar specifying the total number of cohorts for the trial.

cohortsize

the cohort size

n.earlystop

the early stopping parameter. If the number of patients treated at the current dose reaches n.earlystop, stop the trial or subtrial and select the MTD based on the observed data. When the waterfall design is used to find the MTD contour, n.earlystop=12 by default.

startdose

the starting dose combination level for drug combination trial

p.saf

the highest toxicity probability that is deemed subtherapeutic (i.e. below the MTD) such that dose escalation should be undertaken. The default value is p.saf=0.6*target.

p.tox

the lowest toxicity probability that is deemed overly toxic such that deescalation is required. The default value is p.tox=1.4*target.

cutoff.eli

the cutoff to eliminate an overly toxic dose for safety. We recommend the default value of (cutoff.eli=0.95) for general use.

extrasafe

set extrasafe=TRUE to impose a more stringent stopping rule

offset

a small positive number (between 0 and 0.5) to control how strict the stopping rule is when extrasafe=TRUE. A larger value leads to a more strict stopping rule. The default value offset=0.05 generally works well.

ntrial

the total number of trials to be simulated

MTD.contour

set MTD.contour=TRUE to select the MTD contour (claiming multiple MTDs). Otherwise, BOIN design is used to search for a single MTD.

Details

The operating characteristics of the BOIN design or waterfall design are generated by simulating trials under the prespecified true toxicity probabilities of the investigational dose combinations. The BOIN and waterfall designs have two built-in stopping rules: (1) stop the trial/subtrial if the lowest dose is eliminated due to toxicity, and no dose should be selected as the MTD; and (2) stop the trial/subtrial and select the MTD if the number of patients treated at the current dose reaches n.earlystop. The first stopping rule is a safety rule to protect patients from the case in which all doses are overly toxic. The rationale for the second stopping rule is that when there is a large number (i.e., n.earlystop) of patients assigned to a dose, it means that the dose-finding algorithm has approximately converged. Thus, we can stop the trial/subtrial early and select the MTD to save sample size and reduce the trial duration.

For some applications, investigators may prefer a more strict safety stopping rule than rule (1) for extra safety when the lowest dose is overly toxic. This can be achieved by setting extrasafe=TRUE, which imposes the following more strict safety stopping rule: stop the trial if (i) the number of patients treated at the lowest dose >=3, and (ii) Pr(toxicity rate of the lowest dose > target | data) > cutoff.eli-offset. As a tradeoff, the strong stopping rule will decrease the MTD selection percentage when the lowest dose actually is the MTD.

Value

get.oc.comb() returns the operating characteristics of the BOIN or waterfall design as a list, including (1) selection percentage at each dose level, (2) the number of patients treated at each dose level, (3) the number of toxicities observed at each dose level, (4) the total correct selection of the MTD, (5) the total percentage of patients treated at the MTD.

Note

We should avoid setting the values of p.saf and p.tox very close to the target. This is because the small sample sizes of typical phase I trials prevent us from differentiating the target toxicity rate from the rates close to it. In addition, in most clinical applications, the target toxicity rate is often a rough guess, and finding a dose level with a toxicity rate reasonably close to the target rate will still be of interest to the investigator. The default values provided by get.oc.comb() are generally reasonable for most clinical applications.

Author(s)

Suyu Liu and Ying Yuan

References

Liu S. and Yuan, Y. (2015). Bayesian Optimal Interval Designs for Phase I Clinical Trials, Journal of the Royal Statistical Society: Series C, 64, 507-523.

Lin R. and Yin, G. (2016). Bayesian Optimal Interval Designs for Dose Finding in Drug-combination Trials, Statistical Methods in Medical Research, to appear.

Zhang L. and Yuan, Y. (2016). A Simple Bayesian Design to Identify the Maximum Tolerated Dose Contour for Drug Combination Trials, under review.

See Also

Tutorial: http://odin.mdacc.tmc.edu/~yyuan/Software/BOIN/BOIN2.4_tutorial.pdf

Paper: http://odin.mdacc.tmc.edu/~yyuan/Software/BOIN/paper.pdf

Examples

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p.true<-matrix(c(0.01,0.03,0.15,0.20,0.30,
                 0.03,0.05,0.10,0.30,0.60,
                 0.08,0.10,0.30,0.60,0.75), byrow=TRUE, ncol=5)
## find the MTD contour using waterfall design
get.oc.comb(target=0.3, p.true, ncohort=c(10,5,5), cohortsize=3, n.earlystop=12, startdose=c(1,1),
  		       ntrial=10, MTD.contour=TRUE)

## find a single MTD using BOIN design
get.oc.comb(target=0.3, p.true, ncohort=20, cohortsize=3, n.earlystop=12, startdose=c(1,1),
			       ntrial=10, MTD.contour=FALSE)