propdiff.mblacc {SampleSizeProportions}

Bayesian sample size determination for the difference between two binomial proportions using the Mixed Bayesian/Likelihood Average Coverage Criterion

Description

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.

Usage

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

Arguments

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 len is estimated, in order to approximate the average coverage probability. Usually 10000 is sufficient, but one can increase this number at the expense of program running time.

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.

Details

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.

Value

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

Note

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

Author(s)

Lawrence Joseph [e-mail], Patrick Bélisle and Roxane du Berger

References

Joseph L, du Berger R, and Bélisle P.
Bayesian and mixed Bayesian/likelihood criteria for sample size determination
Statistics in Medicine 1997;16(7):769-781.

See Also

propdiff.mblalc, propdiff.mblmodwoc, propdiff.mblwoc, propdiff.acc, propdiff.alc, propdiff.modwoc, propdiff.woc

Examples

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