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

The function `propdiff.alc`

returns the required sample sizes to reach a given posterior credible interval length on average for a fixed coverage probability for the difference between two binomial proportions.

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

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

`equal` |
logical. Whether or not the final group sizes (n1, n2) are forced to be equal:
| |||||||||

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

`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.alc`

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

This function uses a fully Bayesian approach to sample size determination.
Therefore, the desired coverages and lengths are only realized if the prior distributions input to the function
are used for final inferences. Researchers preferring to use the data only for final inferences are encouraged
to use the Mixed Bayesian/Likelihood version of the function.

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.acc`

, `propdiff.modwoc`

, `propdiff.woc`

, `propdiff.mblacc`

, `propdiff.mblalc`

, `propdiff.mblmodwoc`

, `propdiff.mblwoc`

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

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