主 题：Principled analysis of crossover designs: causal effects, efficient estimation, and robust inference交叉设计的原理性分析：因果效应、高效估计与稳健推断
主讲人：加州大学伯克利分校丁鹏副教授
主持人：统计与数据科学学院林华珍教授
时间：2026年1月6日（周二）下午16：00-17：00
地点：柳林校区弘远楼408会议室
主办单位：统计与数据科学学院和统计研究中心 科研处
主讲人简介：
Peng Ding is an Associate Professor in the Department of Statistics at UC Berkeley. He researches causal inference, missing data, and applied statistics. He obtained my Ph.D. from the Department of Statistics, Harvard University in May 2015 and worked as a postdoctoral researcher in the Department of Epidemiology, Harvard T. H. Chan School of Public Health until December 2015. Previously, he received my B.S. in Mathematics, B.A. in Economics, and M.S. in Statistics from Peking University.
丁鹏（Peng Ding）是加州大学伯克利分校统计系的副教授。他的研究方向包括因果推断、缺失数据与应用统计学。他于2015年5月获得哈佛大学统计系博士学位，并在同年12月之前担任哈佛大学陈曾熙公共卫生学院流行病学系的博士后研究员。在此之前，他在北京大学获得了数学学士、经济学学士以及统计学硕士学位。
内容提要：
Crossover designs randomly assign each unit to receive a sequence of treatments. By comparing outcomes within the same unit, these designs can effectively eliminate between-unit variation and facilitate the identification of both instantaneous effects of current treatments and carryover effects from past treatments. They are widely used in traditional biomedical studies and are increasingly adopted in modern digital platforms. However, standard analyses of crossover designs often rely on strong parametric models, making inference vulnerable to model misspecification. This paper adopts a design-based framework to analyze general crossover designs. We make two main contributions. First, we use potential outcomes to formally define the causal estimands and assumptions on the data-generating process. For any given type of crossover design and assumptions on potential outcomes, we outline a procedure for identification and estimation, emphasizing the central role of the treatment assignment mechanism in design-based inference. Second, we unify the analysis of crossover designs using least squares, with restrictions on the coefficients and weights on the units. Based on the theory, we recommend the specification of the regression function, weighting scheme, and coefficient restrictions to assess identifiability, construct efficient estimators, and estimate variances in a unified fashion. Crucially, the least squares procedure is simple to implement, and yields not only consistent and efficient point estimates but also valid variance estimates even when the working regression model is misspecified.
交叉设计（crossover designs）通过随机分配每个个体接受一系列干预措施，通过比较同一个体在不同时期的结果，能有效消除个体间异质性，从而有助于识别当前干预的即时效应与既往干预的遗留效应。该方法在传统生物医学研究中应用广泛，并日益受到现代数字化平台的青睐。然而，针对交叉设计的标准分析通常依赖于强参数模型，使得统计推断易受模型设定偏差的影响。本文采用基于设计的分析框架，对一般化的交叉设计进行研究，主要贡献包括两方面：首先，利用潜在结果明确定义因果估计量及数据生成过程的假设；针对任意给定的交叉设计类型与潜在结果假设，系统阐述了因果识别与估计的流程，并强调了干预分配机制在基于设计的推断中的核心作用。其次，通过最小二乘法统一分析交叉设计，同时对系数与个体权重施加约束。基于理论分析，本文提出了回归函数设定、加权方案选择及系数约束的策略，以统一的方式评估可识别性、构建高效估计量并进行方差估计。关键之处在于，这一最小二乘方法实施简便，不仅能够提供一致且高效的估计值，即使在回归模型设定错误的情况下，仍能给出有效的方差估计。
