Description Usage Arguments Details Value Note Author(s) References See Also Examples

The function `propdiff.mblacc`

returns the required sample sizes to reach a given coverage probability on average for a posterior credible interval of fixed length using a mixed Bayesian/likelihood approach for the difference between two binomial proportions.

1 | ```
propdiff.mblacc(len, c1, d1, c2, d2, level = 0.95, m = 10000, mcs = 3)
``` |

`len` |
The fixed length of the posterior credible interval for the difference between the two unknown proportions |

`c1` |
First prior parameter of the Beta density for the binomial proportion for the first population |

`d1` |
Second prior parameter of the Beta density for the binomial proportion for the first population |

`c2` |
First prior parameter of the Beta density for the binomial proportion for the second population |

`d2` |
Second prior parameter of the Beta density for the binomial proportion for the second population |

`level` |
The desired average coverage probability of the posterior credible interval (e.g., 0.95) |

`m` |
The number of points simulated from the preposterior distribution of the data. For each point, the probability coverage of the highest posterior density interval of fixed length |

`mcs` |
The Maximum number of Consecutive Steps allowed in the same direction in the march towards the optimal sample size, before the result for the next upper/lower bound is cross-checked. In our experience, mcs = 3 is a good choice. |

Assume that a sample from each of two populations will be
collected in order to estimate the difference between two independent binomial proportions.
Assume that the proportions have prior information in the form of
Beta(*c1*, *d1*) and Beta(*c2*, *d2*) densities in each population, respectively.
The function `propdiff.mblacc`

returns the required sample sizes to attain the
desired average coverage probability *level* for the posterior credible interval of fixed length *len*
for the difference between the two unknown proportions.

This function uses a Mixed Bayesian/Likelihood (MBL) approach.
MBL approaches use the prior information to derive the predictive distribution of the data, but use only the likelihood function for final inferences.
This approach is intended to satisfy investigators who recognize that prior information is important for planning purposes but prefer to base final inferences only on the data.

The required sample sizes (n1, n2) for each group given the inputs to the function.

The sample sizes are calculated via Monte Carlo simulations, and therefore may vary from one call to the next.

Lawrence Joseph lawrence.joseph@mcgill.ca, Patrick Belisle and Roxane du Berger

Joseph L, du Berger R, and Belisle P.

Bayesian and mixed Bayesian/likelihood criteria for sample size determination

Statistics in Medicine 1997;16(7):769-781.

`propdiff.mblalc`

, `propdiff.mblmodwoc`

, `propdiff.mblwoc`

, `propdiff.acc`

, `propdiff.alc`

, `propdiff.modwoc`

, `propdiff.woc`

1 | ```
propdiff.mblacc(len=0.05, c1=3, d1=11, c2=11, d2=54)
``` |

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