Large sample behavior of dynamic information borrowing (DIB) estimators is investigated. Asymptotic properties of several DIB approaches (adaptive risk minimization, adaptive LASSO, Bayesian procedures with empirical power prior, fully Bayesian procedures, and a Bayes-frequentist compromise) are explored against shrinking to zero alternatives. As shown theoretically and with simulations, local asymptotic distributions of DIB estimators are often non-normal. A simple Gaussian setting with external information borrowing illustrates that none of the considered DIB methods outperforms others in terms of mean squared error (MSE): at different conflict values, the MSEs of DIBs are changing between the MSEs of the maximum likelihood estimators based on the current and pooled data. To uniquely determine an optimality criterion for DIB, a prior distribution on the conflict needs be either implicitly or explicitly determined using data independent considerations. Data independent assumptions on the conflict are also needed for DIB-based hypothesis testing. New families of DIB estimators parameterized by a sensitivity-to-conflict parameter S are suggested and their use is illustrated in an infant mortality example. The choice of S is determined in a data-independent manner by a cost-benefit compromise associated with the use of external data.

翻译：本文研究了动态信息借用（DIB）估计量的大样本性质。探讨了多种DIB方法（自适应风险最小化、自适应LASSO、基于经验幂先验的贝叶斯方法、完全贝叶斯方法以及一种贝叶斯-频率折中方法）在备择假设趋于零时的渐近性质。理论与模拟结果表明，DIB估计量的局部渐近分布通常是非正态的。通过一个借用外部信息的简单高斯模型示例说明，在均方误差（MSE）准则下，所有考虑的DIB方法均未表现出绝对优势：在不同冲突值下，DIB的MSE值介于仅使用当前数据的最大似然估计与使用合并数据的最大似然估计的MSE之间。为唯一确定DIB的最优性准则，需要基于独立于数据的考量，隐式或显式地确定冲突参数的先验分布。基于DIB的假设检验同样需要关于冲突的独立于数据的假设。本文提出了由冲突敏感度参数S参数化的新DIB估计量族，并通过婴儿死亡率案例说明其应用。参数S的选择通过权衡使用外部数据的成本与收益，以独立于数据的方式确定。