TY - JOUR
T1 - Comparison of Bayesian sample size criteria
T2 - ACC, ALC, and WOC
AU - Cao, Jing
AU - Lee, J. Jack
AU - Alber, Susan
N1 - Funding Information:
The authors thank Dr. Peter Mueller and Dr. Peter Thall for their constructive suggestions and Ms. LeeAnn Chastain for editorial assistance. This work was supported in part by grants from the National Cancer Institute CA16672, CA97007, and the Department of Defense W81XWH-06-1-0303.
PY - 2009/12/1
Y1 - 2009/12/1
N2 - A challenge for implementing performance-based Bayesian sample size determination is selecting which of several methods to use. We compare three Bayesian sample size criteria: the average coverage criterion (ACC) which controls the coverage rate of fixed length credible intervals over the predictive distribution of the data, the average length criterion (ALC) which controls the length of credible intervals with a fixed coverage rate, and the worst outcome criterion (WOC) which ensures the desired coverage rate and interval length over all (or a subset of) possible datasets. For most models, the WOC produces the largest sample size among the three criteria, and sample sizes obtained by the ACC and the ALC are not the same. For Bayesian sample size determination for normal means and differences between normal means, we investigate, for the first time, the direction and magnitude of differences between the ACC and ALC sample sizes. For fixed hyperparameter values, we show that the difference of the ACC and ALC sample size depends on the nominal coverage, and not on the nominal interval length. There exists a threshold value of the nominal coverage level such that below the threshold the ALC sample size is larger than the ACC sample size, and above the threshold the ACC sample size is larger. Furthermore, the ACC sample size is more sensitive to changes in the nominal coverage. We also show that for fixed hyperparameter values, there exists an asymptotic constant ratio between the WOC sample size and the ALC (ACC) sample size. Simulation studies are conducted to show that similar relationships among the ACC, ALC, and WOC may hold for estimating binomial proportions. We provide a heuristic argument that the results can be generalized to a larger class of models.
AB - A challenge for implementing performance-based Bayesian sample size determination is selecting which of several methods to use. We compare three Bayesian sample size criteria: the average coverage criterion (ACC) which controls the coverage rate of fixed length credible intervals over the predictive distribution of the data, the average length criterion (ALC) which controls the length of credible intervals with a fixed coverage rate, and the worst outcome criterion (WOC) which ensures the desired coverage rate and interval length over all (or a subset of) possible datasets. For most models, the WOC produces the largest sample size among the three criteria, and sample sizes obtained by the ACC and the ALC are not the same. For Bayesian sample size determination for normal means and differences between normal means, we investigate, for the first time, the direction and magnitude of differences between the ACC and ALC sample sizes. For fixed hyperparameter values, we show that the difference of the ACC and ALC sample size depends on the nominal coverage, and not on the nominal interval length. There exists a threshold value of the nominal coverage level such that below the threshold the ALC sample size is larger than the ACC sample size, and above the threshold the ACC sample size is larger. Furthermore, the ACC sample size is more sensitive to changes in the nominal coverage. We also show that for fixed hyperparameter values, there exists an asymptotic constant ratio between the WOC sample size and the ALC (ACC) sample size. Simulation studies are conducted to show that similar relationships among the ACC, ALC, and WOC may hold for estimating binomial proportions. We provide a heuristic argument that the results can be generalized to a larger class of models.
KW - Average coverage criterion
KW - Average length criterion
KW - Coverage rate
KW - Credible interval
KW - Interval length
KW - Worst outcome criterion
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U2 - 10.1016/j.jspi.2009.05.041
DO - 10.1016/j.jspi.2009.05.041
M3 - Article
C2 - 25554718
AN - SCOPUS:69249220077
SN - 0378-3758
VL - 139
SP - 4111
EP - 4122
JO - Journal of Statistical Planning and Inference
JF - Journal of Statistical Planning and Inference
IS - 12
ER -