Savitsky Terrance D, Paddock Susan M
RAND Corporation, 1776 Main Street, Box 2138, Santa Monica, CA 90401-2138 USA.
Ann Appl Stat. 2013 Jun 1;7(2). doi: 10.1214/12-AOAS620.
We develop a dependent Dirichlet process (DDP) model for repeated measures multiple membership (MM) data. This data structure arises in studies under which an intervention is delivered to each client through a sequence of elements which overlap with those of other clients on different occasions. Our interest concentrates on study designs for which the overlaps of sequences occur for clients who receive an intervention in a shared or grouped fashion whose memberships may change over multiple treatment events. Our motivating application focuses on evaluation of the effectiveness of a group therapy intervention with treatment delivered through a sequence of cognitive behavioral therapy session blocks, called modules. An open-enrollment protocol permits entry of clients at the beginning of any new module in a manner that may produce unique MM sequences across clients. We begin with a model that composes an addition of client and multiple membership module random effect terms, which are assumed independent. Our MM DDP model relaxes the assumption of conditionally independent client and module random effects by specifying a collection of random distributions for the client effect parameters that are indexed by the unique set of module attendances. We demonstrate how this construction facilitates examining heterogeneity in the relative effectiveness of group therapy modules over repeated measurement occasions.
我们为重复测量的多重成员（MM）数据开发了一种相依狄利克雷过程（DDP）模型。这种数据结构出现在这样的研究中：通过一系列元素向每个客户提供干预，这些元素在不同场合与其他客户的元素重叠。我们的兴趣集中在这样的研究设计上：对于以共享或分组方式接受干预的客户，其序列重叠会在多个治疗事件中发生，且其成员身份可能会发生变化。我们的激励性应用聚焦于评估一种团体治疗干预的效果，该治疗通过一系列称为模块的认知行为治疗会话块来实施。开放注册协议允许客户在任何新模块开始时加入，这可能会在客户之间产生独特的MM序列。我们从一个由客户和多重成员模块随机效应项相加组成的模型开始，假设它们是独立的。我们的MM DDP模型通过为客户效应参数指定一组由唯一的模块参与集索引的随机分布，放宽了条件独立的客户和模块随机效应的假设。我们展示了这种构建如何便于在重复测量场合下检查团体治疗模块相对有效性的异质性。
