get.oc.comb {BOIN} | R Documentation |

## 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

```
get.oc.comb(target, p.true, ncohort, cohortsize, n.earlystop=NULL, startdose=c(1, 1),
titration=FALSE,p.saf=0.6*target, p.tox=1.4*target, cutoff.eli=0.95,
extrasafe=FALSE,offset=0.05, ntrial=1000, mtd.contour=FALSE,
boundMTD=FALSE, seed=6)
```

### Arguments

`target` |
the target DLT rate |

`p.true` |
a |

`ncohort` |
a |

`cohortsize` |
the cohort size |

`n.earlystop` |
the early stopping parameter. If the number of patients treated at the current
dose reaches |

`startdose` |
the starting dose combination level for drug combination trial |

`titration` |
set |

`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.tox` |
the lowest toxicity probability that is deemed overly toxic such that deescalation
is required. The default value is |

`cutoff.eli` |
the cutoff to eliminate an overly toxic dose for safety. We recommend the
default value of ( |

`extrasafe` |
set |

`offset` |
a small positive number (between 0 and 0.5) to control how strict the stopping
rule is when |

`ntrial` |
the total number of trials to be simulated |

`mtd.contour` |
set |

`boundMTD` |
set |

`seed` |
the random seed for simulation |

### 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. If `titration=TRUE`

, we perform dose escalation with cohort size = 1 at the begining of the trial:
starting from `startdose`

, if no toxicity is observed, we escalate the dose;
otherwise, the titration is completed and we switch to cohort size = `cohortsize`

.
Titration accelerates the dose escalation and is useful when low doses are believed to be safe.

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 > \code{target} | data) > \code{cutoff.eli}-\code{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 combination or
waterfall design as a list. For the BOIN combination design, including:
(1) true toxicity probability at each dose level (`$p.true`

),
(2) selection percentage at each dose level (`$selpercent`

),
(3) the number of patients treated at each dose level (`$npatients`

)
(4) the number of toxicities observed at each dose level (`$ntox`

),
(5) the total number of patients in the trial (`$totaln`

),
(6) the total number of toxicities observed for the trial (`$totaltox`

)
(7) the pecentage of correct selection (`$pcs`

),
(8) the total percentage of patients treated at the MTD (`$npercent`

).
(9) the percentage of early stopping without selecting the MTD (`$percentstop`

)
For the the waterfall design, including:
(1) true toxicity probability at each dose level (`$p.true`

),
(2) selection percentage of dose combinations (`$selpercent`

),
(3) the number of patients treated at each dose combination (`$npatients`

)
(4) the number of toxicities observed at each dose combination (`$ntox`

),
(5) the total number of patients in the trial (`$totaln`

),
(6) the total number of toxicities observed for the trial (`$totaltox`

)
(7) the total percentage of correct selection at the MTD contour (`$pcs.contour`

),
(8) the total percentage of patients treated at MTD contour
(`$npercent.contour`

)
(9) the total percentage of patients treated above MTD contour
(`$npercent.above.contour`

)
(10) the total percentage of patients treated below MTD contour
(`$npercent.below.contour`

)

### 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 DLT rate from the rates close to it. The default values provided by
`get.oc()`

are strongly recommended, and generally yield excellent operating characteristics.

### Author(s)

Suyu Liu, Liangcai Zhang, Yanhong Zhou, 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. (2017). Bayesian Optimal Interval Designs for Dose Finding in
Drug-combination Trials, *Statistical Methods in Medical Research*, 26, 2155-2167.

Yan, F., Zhang, L., Zhou, Y., Pan, H., Liu, S. and Yuan, Y. (2020).BOIN: An R Package
for Designing Single-Agent and Drug-Combination Dose-Finding Trials Using Bayesian Optimal
Interval Designs. *Journal of Statistical Software*, 94(13),1-32.<doi:10.18637/jss.v094.i13>.

Zhang L. and Yuan, Y. (2016). A Simple Bayesian Design to Identify the Maximum
Tolerated Dose Contour for Drug Combination Trials, *Statistics in Medicine*, 35, 4924-4936.

### See Also

Tutorial: http://odin.mdacc.tmc.edu/~yyuan/Software/BOIN/BOIN2.6_tutorial.pdf

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

### Examples

```
###### drug-combination trial ######
##### combination trial to find a single MTD ######
## get the operating characteristics for BOIN design
p.true <- matrix(c(0.01,0.03,0.10,0.20,0.30,
0.03,0.05,0.15,0.30,0.60,
0.08,0.10,0.30,0.60,0.75), byrow=TRUE, ncol=5)
oc.comb <- get.oc.comb(target=0.3, p.true, ncohort=20, cohortsize=3,
n.earlystop=12, startdose=c(1,1), ntrial=100)
summary(oc.comb)
plot(oc.comb)
## get the operating characteristics with titration for BOIN design
oc.comb <- get.oc.comb(target=0.3, p.true, ncohort=20, cohortsize=3,
n.earlystop=12, startdose=c(1,1), titration=TRUE, ntrial=100)
summary(oc.comb)
plot(oc.comb)
##### combination trial to find the MTD contour ######
## find the MTD contour using waterfall design
oc.comb <- get.oc.comb(target=0.3, p.true, ncohort=c(10,5,5), cohortsize=3,
n.earlystop=12, startdose=c(1,1), ntrial=100, mtd.contour=TRUE)
summary(oc.comb)
plot(oc.comb)
```

*BOIN*version 2.7.2 Index]