get_oc_BAR {BAR} | R Documentation |

Randomization is the established method for obtaining scientifically valid comparisons of competing treatments in clinical trials and other experiments. Bayesian adaptive randomization (BAR) allows changes to be made to the randomization probabilities to treatments during the trial. The aim of the procedure is to allocate a greater proportion of patients to treatments that have so far demonstrated evidence of a better performance than other arms. Binary outcomes are considered in this package

```
get_oc_BAR(success_prob, n_burn_in, tot_num, block_size,
power_c = "n/2N", lower_bound = .05, reptime,
control_arm = "", output = "", seed = 100)
```

`success_prob` |
the successful probability for each arm (the first slot refers to the control arm) |

`n_burn_in` |
the number of burn-in for each arm |

`tot_num` |
the total number of patients enrolled for the trial |

`block_size` |
the block size |

`power_c` |
the power correction of allocation probability. The default value is power_c = "n/2N" and can also be numeric, e.g., power_c = .5 |

`lower_bound` |
the lower bound of the allocation probability. It must between 0 and |

`reptime` |
the number of simulated trials |

`control_arm` |
if this argument is "fixed", then allocation probability of control arm (the first slot)
will be fixed to |

`output` |
if this argument is "raw", then the function will return updated allocation probability path after burn-in for each arm for each simulated trial. The default of this argument will return the average allocation probability and the average number of patients assigned to each arm |

`seed` |
the seed. The default value is seed = 100 |

We show how the updated allocation probabilities for each arm are calculated.

Treatments are denoted by `k = 1,\ldots,K`

.`\;N`

is the total sample size. If no burn-in(s), the BAR will be initiated start of a study, that is, for each enrolled patient, `n = 1,\ldots,N,`

the BAR will be used to assign each patient. Denoting the true unknown response rates of `K`

treatments by `\pi_{1},\ldots,\pi_{K},\;`

we can compute `K`

posterior probabilities: `r_{k,n} = Pr(\pi_{k} = max\{\pi_{1},\ldots,\pi_{K}\}\;|\;Data_{n})`

, here, `n`

refers to the `n`

-th patient and `k`

refers to the `k`

-th arm. We calculate the updated probabilities of the BAR algorithm according to the following steps.

`\;`

Step 1: (Normalization) Normalize `r_{k,n}`

as `r_{k,n}^{(c)} = \frac{(r_{k,n})^{c}}{\sum_{j=1}^{K}(r_{j,n})^{c}}`

, here `\;c = \frac{n}{2N}`

.

Step 2: (Restriction) To avoid the BAR sticking to very low/high probabilities, a restriction rule to the posterior probability `r_{k,n}^{(c)}`

will be applied:

`Lower\;Bound \le r_{k,n}^{(c)} \le 1 - (K - 1) \times Lower\;Bound,`

`0 \le Lower\;Bound \le \frac{1}{K}`

After restriction, the posterior probability is denoted as `r_{k,n}^{(c,re)}`

.

Step 3: (Re-normalization) Then, we can have the updated allocation probabilities by the BAR denoted as:

`r_{k,n}^{(f)} = \frac{r_{k,n}^{(c,re)}\times(\frac{r_{k,n}^{(c,re)}}{\frac{n_{k}}{n}})^{2}}{\sum_{j=1}^{K}\{r_{j,n}^{(c,re)}\times(\frac{r_{j,n}^{(c,re)}}{\frac{n_{j}}{n}})^{2}\}}`

where `n_{k}`

is the number of patients enrolled on arm `k`

up-to-now.

Step 4: (Re-restriction) Finally, restricts again by using

`Lower\;Bound \le r_{k,n}^{(f)} \le 1 - (K-1) \times Lower\;Bound,`

`0 \le Lower\;Bound \le \frac{1}{K}`

and denote `r_{k,n}^{(ff)}`

as the allocation probability used in the BAR package.

`get_oc_BAR()`

depending on the argument "output", it returns:

default: (1) the average allocation probability (2) the average number of patients assigned to each arm

raw: (1) updated allocation probability path after burn-in for each arm for each simulated trial

Chia-Wei Hsu, Haitao Pan

Wathen JK, Thall PF. A simulation study of outcome adaptive randomization in multi-arm clinical trials. Clin Trials. 2017 Oct; 14(5): 432-440. doi: 10.1177/1740774517692302.

Xiao, Y., Liu, Z. & Hu, F. Bayesian doubly adaptive randomization in clinical trials. Sci. China Math. 60, 2503-2514 (2017). doi: 10.1007/s11425-016-0056-1.

Hu F, Zhang L X. Asymptotic properties of doubly adaptive biased coin designs for multi-treatment clinical trials. Ann Statist, 2004, 30: 268–301.

```
## power_c = "n/2N"
get_oc_BAR(success_prob = c(.1, .5, .8), n_burn_in = 10,
tot_num = 150, block_size = 1, reptime = 5)
## power_c = .5
get_oc_BAR(success_prob = c(.1, .5, .8), n_burn_in = 10,
tot_num = 150, block_size = 1, power_c = .5,
reptime = 5)
```

[Package *BAR* version 0.1.1 Index]