关于两个独立二项总体推断的Bayes样本容量的确定

Bayesian Sample Size Determination for Inference of Independent Two Binomial Populations

样本容量的确定在现代生物医学研究以及在对两个独立的二项实验进行统计分析时,是经常遇到的一个问题。在实验设计阶段,往往需要计算最佳样本容量,目的是为了保证两个二项参数差的估计值与真实值的误差在所要求的范围内概率最大。巧妙地利用先验信息是实验设计的一个关键环节,目前正在广泛应用的样本量的计算公式在利用先验信息时通常采用点估计的形式。本文提出了确定样本容量的Bayes风险准则,给出了样本容量计算的Monte Carlo方法,并把这些方法应用到估计两个二项比例差的实验设计上。最后考虑了0-1损失函数和平方损失函数下计算样本容量的Bayes方法。

Sample Size Determination is commonly encountered in modern medical studies and statistical analysis for two independent binomial experiments. During experimental design for estimating the difference between two binomial proportions, sample size is often calculated to ensure that the estimation will be within a desired distance from the true value with sufficiently high probability. Prudent use of the prior information is a crucial step of experimental planning. Most of sample size formulae in current use employ this information only in the form of point estimates, even though it is usually more accurately expressed as a distribution over a range of values. In this paper, Bayesian posterior risk criteria and Monte carlo method to determine sample size were proposed and these approaches to the design of an experiment to estimate the difference between two binomial proportions were applied. Finally, Bayesian methods for sample size calculation under 0 - 1 loss function and quadratic loss function were considered.