Description Usage Arguments Details Value Note Author(s) References See Also Examples
The function propdiff.woc
calculates conservative sample sizes for the difference between two binomial proportions, in the
sense that the desired posterior credible interval coverage and length are guaranteed over all possible data sets.
1  propdiff.woc(len, c1, d1, c2, d2, level = 0.95, equal = TRUE)

len 
The desired total length of the posterior credible interval for the difference between the two unknown proportions  
c1 
First parameter of the Beta prior density for the binomial proportion for the first population  
d1 
Second parameter of the Beta prior density for the binomial proportion for the first population  
c2 
First parameter of the Beta prior density for the binomial proportion for the second population  
d2 
Second parameter of the Beta prior 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:

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.woc
returns the required sample sizes to attain the desired length len
for the posterior credible interval of fixed coverage probability level
for the difference between the two unknown proportions.
The Worst Outcome Criterion used is conservative,
in the sense that the posterior credible interval length len
is guaranteed over all possible data sets that can arise, for a fixed coverage probability level.
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 returned by this function are exact.
It is also correct to state that the coverage probability of the posterior credible interval of fixed length len will be at least level with the sample sizes returned.
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):769781.
propdiff.acc
, propdiff.alc
, propdiff.modwoc
, propdiff.mblacc
, propdiff.mblalc
, propdiff.mblmodwoc
, propdiff.mblwoc
1  propdiff.woc(len=0.05, c1=3, d1=11, c2=11, d2=54)

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