Sellke and Siegmund (1983) developed the Brownian approximation to the Cox partial likelihood score as a process of calendar time, laying the foundation for group sequential analysis of survival studies. We extend their results to cover situations in which treatment allocations may depend on observed outcomes. The new development makes use of the entry time and calendar time along with the corresponding σ-filtrations to handle the natural information accumulation. Large sample properties are established under suitable regularity conditions.

中文翻译：

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响应自适应分配下Cox模型的序列分析

Sellke 和 Siegmund (1983) 开发了 Cox 部分似然分数的布朗近似作为日历时间的过程，为生存研究的组序贯分析奠定了基础。我们将他们的结果扩展到涵盖治疗分配可能取决于观察到的结果的情况。新的开发利用进入时间和日历时间以及相应的 σ-过滤来处理自然信息积累。大样本属性是在合适的规律性条件下建立的。