3 - 贝叶斯与频率论方法

The analytical methods provided on this site all fall into one of two broad categories of statistical methods: frequentist or Bayesian.

Frequentist methods use conventional statistical techniques to calculate maximum-likelihood estimates of true prevalence and confidence limits, in a similar manner to standard techniques used to analyse conventional survey data. Frequentist methods are conceptually simpler to understand and are usually computationally easier to implement (and take less computer time to run). They do not take account of any existing knowledge of the likely prevalence, although some methods do allow for adjustment of estimates for imperfect sensitivity and specificity of the tests used.

On the other hand, Bayesian analysis uses simulation (using a Gibbs sampler) to derive a posterior probability distribution(s) for the parameter(s) of interest - usually true prevalence but distributions for sensitivity, specificity and other parameters are also generated.

贝叶斯方法也具有以下优点:

• 可以将预先存在的患病率估计值纳入分析中，以增加对结果的信心;
• 测试的不敏感性和特异性以及不确定性;和
• 流行的可能性较低，不能为负.

Briefly, a Bayesian approach allows the combination of any prior information available on test sensitivity and specificity and estimated prevalence of disease with the results of testing, to produce a posterior probability distribution of the estimated true prevalence (and other measures such as test sensitivity and specificity) that best fits the combination of prior distributions and observed testing results. Bayesian methods were initially developed for estimating prevalence from individual testing and were subsequently extended for use with pooled testing strategies.

However, Bayesian estimates can be seriously affected by the use of inappropriate prior distributions (inaccurate estimates and/or overconfidence in the values) for prevalence, sensitivity or specificity and therefore must be used with care. Wherever possible prior estimates should be based on real data and should be appropriately weighted (wide probability limits) to ensure that any errors do not dominate the data, causing inaccurate results. See the Glossary for more details on Bayesian methods and the Beta distribution and its parameters.

Bayesian also rely on simulation rather than analytical methods, and therefore can take some time to run, depending on the number of iterations used. It is also that sufficient iterations are run to allow convergence of the Bayesian model and to support inference from the results.

Outputs from the Gibbs sampler are revised estimates of prevalence, test sensitivity, test specificity and other parameters as posterior probability distributions.