Burton P R, Gurrin L C, Campbell M J
Division of Biostatistics and Genetic Epidemiology, TVW Telethon Institute for Child Health Research, West Perth, Australia.
J Epidemiol Community Health. 1998 May;52(5):318-23. doi: 10.1136/jech.52.5.318.
To take the common "Bayesian" interpretation of conventional confidence intervals to its logical conclusion, and hence to derive a simple, intuitive way to interpret the results of public health and clinical studies.
The theoretical basis and practicalities of the approach advocated is at first explained and then its use is illustrated by referring to the interpretation of a real historical cohort study. The study considered compared survival on haemodialysis (HD) with that on continuous ambulatory peritoneal dialysis (CAPD) in 389 patients dialysed for end stage renal disease in Leicestershire between 1974 and 1985. Careful interpretation of the study was essential. This was because although it had relatively low statistical power, it represented all of the data that were available at the time and it had to inform a critical clinical policy decision: whether or not to continue putting the majority of new patients onto CAPD.
Conventional confidence intervals are often interpreted using subjective probability. For example, 95% confidence intervals are commonly understood to represent a range of values within which one may be 95% certain that the true value of whatever one is estimating really lies. Such an interpretation is fundamentally incorrect within the framework of conventional, frequency-based, statistics. However, it is valid as a statement of Bayesian posterior probability, provided that the prior distribution that represents pre-existing beliefs is uniform, which means flat, on the scale of the main outcome variable. This means that there is a limited equivalence between conventional and Bayesian statistics, which can be used to draw simple Bayesian style statistical inferences from a standard analysis. The advantage of such an approach is that it permits intuitive inferential statements to be made that cannot be made within a conventional framework and this can help to ensure that logical decisions are taken on the basis of study results. In the particular practical example described, this approach is applied in the context of an analysis based upon proportional hazards (Cox) regression.
The approach proposed expresses conclusions in a manner that is believed to be a helpful adjunct to more conventional inferential statements. It is of greatest value in those situations in which statistical significance may bear little relation to clinical significance and a conventional analysis using p values is liable to be misleading. Perhaps most importantly, this includes circumstances in which an important public health or clinical decision must be based upon a study that has unavoidably low statistical power. However, it is also useful in situations in which a decision must be based upon a large study that indicates that an effect that is highly statistically significant seems too small to be of practical relevance. In the illustrative example described, the approach helped in making a decision regarding the use of CAPD in Leicestershire during the latter half of the 1980s.
将传统置信区间的常见“贝叶斯”解释推导至其逻辑结论，从而得出一种简单、直观的方式来解读公共卫生和临床研究的结果。
首先解释所倡导方法的理论基础和实际应用，然后通过参考一项真实历史队列研究的解读来说明其用法。该研究比较了1974年至1985年期间在莱斯特郡接受终末期肾病透析的389例患者中血液透析（HD）和持续性非卧床腹膜透析（CAPD）的生存率。对该研究进行仔细解读至关重要。这是因为尽管其统计效力相对较低，但它代表了当时所有可用的数据，并且它必须为一项关键的临床政策决策提供依据：是否继续让大多数新患者接受CAPD治疗。
传统置信区间常使用主观概率来解读。例如，95%置信区间通常被理解为代表一系列值，在这些值范围内，人们可以有95%的把握确定所估计的任何真实值确实在其中。在传统的基于频率的统计框架内，这种解读从根本上说是不正确的。然而，只要代表先验信念的先验分布在主要结局变量的尺度上是均匀的（即平坦的），它作为贝叶斯后验概率的陈述就是有效的。这意味着传统统计和贝叶斯统计之间存在有限的等效性，可用于从标准分析中得出简单的贝叶斯式统计推断。这种方法的优点是它允许做出在传统框架内无法做出的直观推断陈述，这有助于确保根据研究结果做出合理的决策。在所描述的具体实际例子中，这种方法应用于基于比例风险（Cox）回归的分析中。
所提出的方法以一种被认为是对更传统推断陈述有帮助的辅助方式来表达结论。在统计显著性可能与临床显著性关系不大且使用p值的传统分析可能产生误导的情况下，它具有最大价值。也许最重要的是，这包括重要的公共卫生或临床决策必须基于一项统计效力不可避免地较低的研究的情况。然而，在必须基于一项大型研究做出决策的情况下，即该研究表明一个在统计上高度显著的效应似乎太小而不具有实际相关性时，它也很有用。在所描述的示例中，该方法有助于做出关于20世纪80年代后半期莱斯特郡CAPD使用的决策。
