Altham P M E
Statistical Laboratory, University of Cambridge, UK.
Dev Biol (Basel). 2002;107:77-83.
Statistical analysis for discrete data, particularly for probability models such as the binomial, Poisson and multinomial, is by now very well understood, with a wealth of suitable software. It can happen that the standard generalized linear modelling (glm) software is not completely appropriate, since over-dispersion is present, relative to the standard distributions such as the Poisson or the binomial. Failure to take account of this over-dispersion, for example in fitting a model such as log(p/(1 - p)) = alpha + beta x (where the covariate x is the dose) will mean that our estimates of beta will be less precise than the binomial-based formula gives us. Thus for example we will be quoting confidence intervals for beta that are too narrow. One way of coping with this problem is to use a probability model which is more general than the binomial, and one such model is the beta-binomial. This paper discusses beta-binomial modelling (in S-Plus) in relation to the interesting data set given in the 1998 BMJ paper by Spiegelhalter and Marshall on success rates of 52 in vitro fertilisation clinics in the UK.
对于离散数据的统计分析，尤其是对于二项式、泊松和多项分布等概率模型，目前已经有了很好的理解，并且有大量合适的软件。可能会出现这样的情况，即标准的广义线性建模（glm）软件并不完全适用，因为相对于泊松或二项式等标准分布而言，存在过度离散的情况。如果没有考虑到这种过度离散，例如在拟合诸如log(p/(1 - p)) = alpha + beta x（其中协变量x是剂量）这样的模型时，这将意味着我们对beta的估计不如基于二项式的公式所给出的那样精确。因此，例如我们给出的beta的置信区间会过窄。解决这个问题的一种方法是使用比二项式更通用的概率模型，其中一种这样的模型就是贝塔 - 二项式模型。本文结合Spiegelhalter和Marshall在1998年《英国医学杂志》上发表的关于英国52家体外受精诊所成功率的有趣数据集，讨论了（在S - Plus中）贝塔 - 二项式建模。
