mudiff.mblacc {SampleSizeMeans}

Bayesian sample size determination for differences in normal means using the mixed Bayesian/likelihood Average Coverage Criterion

Description

The function mudiff.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 normal means.

Usage

mudiff.mblacc(len, alpha1, beta1, alpha2, beta2, level = 0.95, m = 10000, mcs = 3)

Arguments

len

The desired fixed length of the posterior credible interval for the difference between the two unknown means

alpha1

First prior parameter of the Gamma density for the precision (reciprocal of the variance) for the first population

beta1

Second prior parameter of the Gamma density for the precision (reciprocal of the variance) for the first population

alpha2

First prior parameter of the Gamma density for the precision (reciprocal of the variance) for the second population

beta2

Second prior parameter of the Gamma density for the precision (reciprocal of the variance) 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 normal means. Assume that the precision within each of the two the populations are unknown, but have prior information in the form of Gamma(alpha1, beta1) and Gamma(alpha2, beta2) densities, respectively. The function mudiff.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 means.

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] and Patrick Bélisle

References

Joseph L, Bélisle P.
Bayesian sample size determination for Normal means and differences between Normal means
The Statistician 1997;46(2):209-226.

See Also

mudiff.mblalc, mudiff.mblmodwoc, mudiff.mblacc.equalvar, mudiff.mblalc.equalvar, mudiff.mblmodwoc.equalvar, mudiff.mbl.varknown, mudiff.acc, mudiff.alc, mudiff.modwoc, mudiff.acc.equalvar, mudiff.alc.equalvar, mudiff.modwoc.equalvar, mudiff.varknown, mudiff.freq, mu.mblacc, mu.mblalc, mu.mblmodwoc, mu.mbl.varknown, mu.acc, mu.alc, mu.modwoc, mu.varknown, mu.freq

Examples

mudiff.mblacc(len=0.2, alpha1=2, beta1=2, alpha2=3, beta2=3)