使用成本调整的BIC的贝叶斯变量选择及其在医疗质量成本效益测量中的应用
Bayesian variable selection using cost-adjusted BIC, with application to cost-effective measurement of quality of health care
摘要：
在保健质量衡量领域，评估病人入院时病情的一种方法是，对入院后30天内的死亡率进行逻辑斯谛回归，对相当多的疾病指标（大约100个）进行回归，以建立一个疾病量表，采用经典的变量选择方法找到10- 20个指标的"最佳“子集。这种“只考虑效益”的方法忽略了疾病指标在数据收集成本方面的巨大差异，当入院疾病被用来推动计划时，这一问题至关重要（目前在包括美国和英国在内的几个国家实施或正在考虑）。通过比较观察到的死亡率和预期的死亡率（考虑到入院时的疾病）来确定不合格的医院。当同时考虑数据收集成本和30天死亡率预测的准确性时，出现了一个很大的变量选择问题，即在最终量表中应忽略那些预测效果不佳的昂贵变量。在本文中，（a）我们开发了一种方法来解决这个问题的基础上后验模型的赔率，从一个先验分布，（1）占每个变量的成本和（2）在一组后验模型概率，对应于一个广义的成本调整版本的贝叶斯信息准则（BIC）的结果，以及（b）将该方法与基于期望效用最大化的决策理论成本收益方法进行比较。我们使用可逆跳马尔可夫链蒙特卡罗（RJMCMC）方法来搜索模型空间，我们检查我们的研究结果的稳定性与MCMC模型组合（$\mathit{MC}^3$）算法的两个变体。
英文摘要：
In the field of quality of health care measurement, one approach to assessing patient sickness at admission involves a logistic regression of mortality within 30 days of admission on a fairly large number of sickness indicators (on the order of 100) to construct a sickness scale, employing classical variable selection methods to find an ``optimal'' subset of 10--20 indicators. Such ``benefit-only'' methods ignore the considerable differences among the sickness indicators in cost of data collection, an issue that is crucial when admission sickness is used to drive programs (now implemented or under consideration in several countries, including the U.S. and U.K.) that attempt to identify substandard hospitals by comparing observed and expected mortality rates (given admission sickness). When both data-collection cost and accuracy of prediction of 30-day mortality are considered, a large variable-selection problem arises in which costly variables that do not predict well enough should be omitted from the final scale. In this paper (a) we develop a method for solving this problem based on posterior model odds, arising from a prior distribution that (1) accounts for the cost of each variable and (2) results in a set of posterior model probabilities that corresponds to a generalized cost-adjusted version of the Bayesian information criterion (BIC), and (b) we compare this method with a decision-theoretic cost-benefit approach based on maximizing expected utility. We use reversible-jump Markov chain Monte Carlo (RJMCMC) methods to search the model space, and we check the stability of our findings with two variants of the MCMC model composition ($\mathit{MC}^3$) algorithm.
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