# Calculate all possible trial pathways for the standard 3+3 design, together with their probability of occurring

### Description

All possible pathways of a standard 3+3 design are calculated and assigned a probability of occurring. This facilitates the calculation of operating characteristics, using `print.threep3`

and `plot.threep3`

.

### Usage

1 |

### Arguments

`truep` |
A vector of length |

`start` |
Starting dose level. Defaults to 1, i.e. the lowest dose level |

`dose` |
Optional vector of length |

### Details

The dose-escalation schema used here relates to that defined by Chang et al. (2006), which incorporates dose de-escalation also. Variations of this design exist in the literature (see Storer 1989, Reiner et al. 1999).

The first cohort of three patients are administered the starting dose (usually the lowest dose). The trial then proceeds as follows:

If none of the three patients experience a DLT, then dose the next three patients at the next highest dose level;

If one of the three patients last treated experiences a DLT, then dose the next three patients at the current dose level;

If at least two patients in the first dose level experience a DLT the trial is stopped for safety and no dose is recommended;

Escalation / de-escalation rules to the next dose level for subsequent cohorts proceed as follows:

Escalate: If 0/3 or at most 1/6 DLTs are observed in the current cohort AND the next highest dose has not yet been tested;

Stay at current dose level: If 1/3 DLTs have been observed at this level. Dose a further three patients at the same level;

De-Escalate: If at least two out of three to six patients experience DLTs at the current dose level AND fewer than six patients have been dosed at the next lowest level

If none of the rules above are satisfied then the trial stops. If the current dose level has at most one DLT observed then this is claimed to be the MTD, otherwise the dose level below is deemed to be the MTD.

If dose-escalation extends to doses outside of that defined by `dose`

, the MTD is determined to be the largest dose in `dose`

.

### Value

`threep3`

returns an object of class "threep3".
The function `print`

(i.e. `print.threep3`

) can be used to obtain operating characteristics of the design used.

An object of class "threep3" is a list with the following components:

`prob` |
A vector with the probabilities of each design occurring. As all possible designs are calculated, this vector sums to one |

`ssize` |
A vector with the sample size of each design |

`mtd` |
A vector of dose levels giving the recommended maximum tolerated dose (MTD) at the end of the trial |

`exp` |
A vector of length |

`dlt.no` |
A vector with the number of toxicities (DLTs) that occur in each trial |

`truep` |
The true probabilities of toxicity at each dose level, specified by the user |

`dose` |
The actual doses as supplied in the function arguments |

`n.average` |
The average number of patients dosed at each level |

`dlt.average` |
The average number of DLTs experienced at each dose level |

`all.designs` |
A matrix containing all possible 3+3 designs, with each row representing a different design. Columns labelled "d k" and "tox k" represent the dose level and number of toxicities for the kth cohort, respectively. |

### Author(s)

Graham Wheeler graham.wheeler@mrc-bsu.cam.ac.uk (MRC Biostatistics Unit, Cambridge, UK) and

Michael Sweeting mjs212@medschl.cam.ac.uk (University of Cambridge, UK)

### References

Sweeting M., Mander A., Sabin T. bcrm: Bayesian Continual Reassessment Method Designs for Phase I Dose-Finding Trials. *Journal of Statistical Software* (2013) 54: 1–26. http://www.jstatsoft.org/article/view/v054i13

Chang A., Ganz P., Hayes D., Kinsella T., Pass H., Schiller J., Stone R., Strecher V. *Oncology: An Evidence-Based Approach*. Springer (2006).

Storer B. Design and Analysis of Phase I Clinical Trials. *Biometrics* (1989) 45: 925–937.

Reiner E., Paoletti X., O'Quigley J. Operating characteristics of the standard phase I clinical trial design. *Computational Statistics & Data Analysis* (1999) 30: 303–315.

Neuenschwander B., Branson M., Gsponer T. Critical aspects of the Bayesian approach to phase I cancer trials. *Statistics in Medicine* (2008) 27: 2420–2439.

### See Also

`threep3`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 | ```
## What are the operating characteristics of a standard 3+3 design if we conside only the first
## 12 doses of the dose-escalation cancer trial example as described in Neuenschwander et al 2008.
## Pre-defined doses
dose<-c(1,2.5,5,10,15,20,25,30,40,50,75,100)
## Pre-specified probabilities of toxicity
p.tox0<-c(0.010,0.015,0.020,0.025,0.030,0.040,0.050,0.100,0.170,0.300,0.400,0.500)
## Not run:
design.threep3<-threep3(p.tox0,dose)
print(design.threep3)
plot(design.threep3)
## End(Not run)
``` |

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