| Title: | Calculating Sample Size Requirements when Estimating the Difference Between Two Binomial Proportions |
|---|---|
| Description: | Sample size requirements calculation using three different Bayesian criteria in the context of designing an experiment to estimate the difference between two binomial proportions. Functions for calculation of required sample sizes for the Average Length Criterion, the Average Coverage Criterion and the Worst Outcome Criterion in the context of binomial observations are provided. In all cases, estimation of the difference between two binomial proportions is considered. Functions for both the fully Bayesian and the mixed Bayesian/likelihood approaches are provided. For reference see Joseph L., du Berger R. and Bélisle P. (1997) <doi:10.1002/(sici)1097-0258(19970415)16:7%3C769::aid-sim495%3E3.0.co;2-v>. |
| Authors: | Lawrence Joseph [aut], Patrick Bélisle [aut, cre], Roxane du Berger [aut] |
| Maintainer: | Patrick Bélisle <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 1.1.3 |
| Built: | 2024-12-16 06:37:02 UTC |
| Source: | CRAN |
Calculate sample sizes based on highest posterior density intervals when comparing two binomial proportions using three different Bayesian approaches.
| Package: | SampleSizeProportions |
| Type: | Package |
| Version: | 1.1.3 |
| Date: | 2023-08-22 |
| License: | GLP (version 2 or later) |
| URL: | http://www.medicine.mcgill.ca/epidemiology/Joseph/Methodological-Publications-Bayesian-Sample-Size.html |
A set of R functions for calculating sample size requirements using three different Bayesian criteria in the context of designing an experiment
to estimate the difference between two binomial proportions.
Functions for calculation of required sample sizes for the Average Length Criterion,
the Average Coverage Criterion and the Worst Outcome Criterion
in the context of binomial observations are provided.
In all cases, estimation of the difference between two binomial proportions is considered.
Functions for both the fully Bayesian and the mixed Bayesian/likelihood approaches are provided.
See the related package SampleSizeMeans for Bayesian sample sizes calculations based on highest posterior density intervals for normal means
https://CRAN.R-project.org/package=SampleSizeMeans
Lawrence Joseph, Roxane du Berger and Patrick Bélisle
Maintainer: Patrick Bélisle [email protected]
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.
propdiff.acc, propdiff.alc, propdiff.modwoc, propdiff.woc, propdiff.mblacc, propdiff.mblalc, propdiff.mblmodwoc, propdiff.mblwoc
The function propdiff.acc returns the required sample sizes to reach a given coverage probability on average for a posterior credible interval of fixed length for the difference between two binomial proportions.
propdiff.acc(len, c1, d1, c2, d2, level = 0.95, equal = TRUE, m = 10000, mcs = 3)propdiff.acc(len, c1, d1, c2, d2, level = 0.95, equal = TRUE, 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) |
|||||||||
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 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. |
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.acc 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 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 [email protected], 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.alc, propdiff.modwoc, propdiff.woc, propdiff.mblacc, propdiff.mblalc, propdiff.mblmodwoc, propdiff.mblwoc
propdiff.acc(len=0.05, c1=3, d1=11, c2=11, d2=54)propdiff.acc(len=0.05, c1=3, d1=11, c2=11, d2=54)
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.
propdiff.alc(len, c1, d1, c2, d2, level = 0.95, equal = TRUE, m = 10000, mcs = 3)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 level is estimated, in order to approximate the average length. 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. |
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 [email protected], Patrick Bélisle and Roxane du Berger
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.
propdiff.acc, propdiff.modwoc, propdiff.woc, propdiff.mblacc, propdiff.mblalc, propdiff.mblmodwoc, propdiff.mblwoc
propdiff.alc(len=0.05, c1=3, d1=11, c2=11, d2=54)propdiff.alc(len=0.05, c1=3, d1=11, c2=11, d2=54)
The function propdiff.freq returns the required sample sizes to obtain a confidence interval of given length and confidence level for the difference between two binomial proportions.
propdiff.freq(len, p1.estimate, p2.estimate, level = 0.95)propdiff.freq(len, p1.estimate, p2.estimate, level = 0.95)
len |
The desired total length of the confidence interval for the proportion |
p1.estimate |
A point estimate for the binomial proportion for the first population |
p2.estimate |
A point estimate for the binomial proportion for the second population |
level |
The desired level of the confidence interval (e.g., 0.95) |
Assume that a random sample from each of two populations will be
collected in order to estimate the difference between two independent binomial proportions.
Assume that the best point estimates for the unknown binomial proportions in the two populations are (p1.estimate, p2.estimate), respectively.
The function propdiff.freq returns the required sample sizes to attain the
desired length len and confidence level level for the confidence interval
for the difference between the two unknown proportions from a frequentist point of view, using a normal approximation.
The required sample sizes (n1, n2) for each group given the inputs to the function.
Lawrence Joseph [email protected], Patrick Bélisle and Roxane du Berger
Lemeshow S, Hosmer Jr DW, Klar J, Lwanga SK.
Adequacy of Sample Size in Health Studies. Wiley and Sons, New York, 1990.
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.
propdiff.acc, propdiff.modwoc, propdiff.woc, propdiff.mblacc, propdiff.mblalc, propdiff.mblmodwoc, propdiff.mblwoc
propdiff.freq(len=0.01, p1.estimate=0.15, p2.estimate=0.20)propdiff.freq(len=0.01, p1.estimate=0.15, p2.estimate=0.20)
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.
propdiff.mblacc(len, c1, d1, c2, d2, level = 0.95, m = 10000, mcs = 3)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 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. |
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 [email protected], Patrick Bélisle and Roxane du Berger
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.
propdiff.mblalc, propdiff.mblmodwoc, propdiff.mblwoc, propdiff.acc, propdiff.alc, propdiff.modwoc, propdiff.woc
propdiff.mblacc(len=0.05, c1=3, d1=11, c2=11, d2=54)propdiff.mblacc(len=0.05, c1=3, d1=11, c2=11, d2=54)
The function propdiff.mblalc returns the required sample sizes to reach a given posterior credible interval length on average for a fixed coverage probability using a mixed Bayesian/likelihood approach for the difference between two binomial proportions.
propdiff.mblalc(len, c1, d1, c2, d2, level = 0.95, m = 10000, mcs = 3)propdiff.mblalc(len, c1, d1, c2, d2, level = 0.95, 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) |
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 level is estimated, in order to approximate the average length. 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. |
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.mblalc 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 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 [email protected], Patrick Bélisle and Roxane du Berger
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.
propdiff.mblacc, propdiff.mblmodwoc, propdiff.mblwoc, propdiff.acc, propdiff.alc, propdiff.modwoc, propdiff.woc
propdiff.mblalc(len=0.05, c1=3, d1=11, c2=11, d2=54)propdiff.mblalc(len=0.05, c1=3, d1=11, c2=11, d2=54)
The function propdiff.mblmodwoc uses a mixed Bayesian/likelihood approach to
determine 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 a given proportion of data sets that can arise according to the prior information.
propdiff.mblmodwoc(len, c1, d1, c2, d2, level = 0.95, worst.level = 0.95)propdiff.mblmodwoc(len, c1, d1, c2, d2, level = 0.95, worst.level = 0.95)
len |
The desired total 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) |
worst.level |
The probability that the length of the posterior credible interval of fixed coverage probability level will be at most len |
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.mblmodwoc
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 Modified Worst Outcome Criterion used is conservative, in the sense that the posterior credible interval
length len is guaranteed over the worst.level proportion of all
possible data sets that can arise according to the prior information, for a fixed coverage probability level.
This function uses a Mixed Bayesian/Likelihood (MBL) approach.
MBL approaches use the prior information to derive the predictive distribution
of the data, but uses 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 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 probability worst.level with the sample sizes returned.
Lawrence Joseph [email protected], Patrick Bélisle and Roxane du Berger
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.
propdiff.mblacc, propdiff.mblalc, propdiff.mblwoc, propdiff.acc, propdiff.alc, propdiff.modwoc, propdiff.woc
propdiff.mblmodwoc(len=0.05, c1=3, d1=11, c2=11, d2=54, worst.level=0.95)propdiff.mblmodwoc(len=0.05, c1=3, d1=11, c2=11, d2=54, worst.level=0.95)
The function propdiff.mblwoc uses a mixed Bayesian/likelihood approach to determine 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.
propdiff.mblwoc(len, c1, d1, c2, d2, level = 0.95)propdiff.mblwoc(len, c1, d1, c2, d2, level = 0.95)
len |
The desired 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) |
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.mblwoc
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 Mixed Bayesian/Likelihood (MBL) approach.
MBL approaches use the prior information to derive the predictive distribution
of the data, but uses 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 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 [email protected], Patrick Bélisle and Roxane du Berger
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.
propdiff.mblacc, propdiff.mblalc, propdiff.mblmodwoc, propdiff.acc, propdiff.alc, propdiff.modwoc, propdiff.woc
propdiff.mblwoc(len=0.05, c1=3, d1=11, c2=11, d2=54)propdiff.mblwoc(len=0.05, c1=3, d1=11, c2=11, d2=54)
The function propdiff.modwoc 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 a given proportion of data sets that can arise according to the prior information.
propdiff.modwoc(len, c1, d1, c2, d2, level = 0.95, worst.level = 0.95, equal = TRUE)propdiff.modwoc(len, c1, d1, c2, d2, level = 0.95, worst.level = 0.95, equal = TRUE)
len |
The desired 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) |
|||||||||
worst.level |
The probability that the length of the posterior credible interval of fixed coverage probability level will be at most len |
|||||||||
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.modwoc
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 Modified Worst Outcome Criterion used is conservative, in the sense that the posterior credible interval
length len is guaranteed over the worst.level proportion of all
possible data sets that can arise according to the prior information, 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 probability worst.level with the sample sizes returned.
Lawrence Joseph [email protected], Patrick Bélisle and Roxane du Berger
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.
propdiff.acc, propdiff.alc, propdiff.woc, propdiff.mblacc, propdiff.mblalc, propdiff.mblmodwoc, propdiff.mblwoc
propdiff.modwoc(len=0.05, c1=3, d1=11, c2=11, d2=54, worst.level=0.95)propdiff.modwoc(len=0.05, c1=3, d1=11, c2=11, d2=54, worst.level=0.95)
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.
propdiff.woc(len, c1, d1, c2, d2, level = 0.95, equal = TRUE)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 [email protected], Patrick Bélisle and Roxane du Berger
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.
propdiff.acc, propdiff.alc, propdiff.modwoc, propdiff.mblacc, propdiff.mblalc, propdiff.mblmodwoc, propdiff.mblwoc
propdiff.woc(len=0.05, c1=3, d1=11, c2=11, d2=54)propdiff.woc(len=0.05, c1=3, d1=11, c2=11, d2=54)