Background. The Expected Value of Sample Information (EVSI) measures the expected benefits that could be obtained by collecting additional data. Estimating EVSI using the traditional nested Monte Carlo method is computationally expensive but the recently developed Gaussian approximation (GA) approach can efficiently estimate EVSI across different sample sizes. However, the conventional GA may result in biased EVSI estimates if the decision models are highly nonlinear. This bias may lead to suboptimal study designs when GA is used to optimize the value of different studies. Therefore, we extend the conventional GA approach to improve its performance for nonlinear decision models. Methods. Our method provides accurate EVSI estimates by approximating the conditional benefit based on two steps. First, a Taylor series approximation is applied to estimate the conditional benefit as a function of the conditional moments of the parameters of interest using a spline, which is fitted to the samples of the parameters and the corresponding benefits. Next, the conditional moments of parameters are approximated by the conventional GA and Fisher information. The proposed approach is applied to several data collection exercises involving non-Gaussian parameters and nonlinear decision models. Its performance is compared with the nested Monte Carlo method, the conventional GA approach, and the nonparametric regression-based method for EVSI calculation. Results. The proposed approach provides accurate EVSI estimates across different sample sizes when the parameters of interest are non-Gaussian and the decision models are nonlinear. The computational cost of the proposed method is similar to other novel methods. Conclusions. The proposed approach can estimate EVSI across sample sizes accurately and efficiently, which may support researchers in determining an economically optimal study design using EVSI.

翻译：背景：预期样本信息价值（EVSI）衡量通过收集额外数据可能获得的期望收益。使用传统嵌套蒙特卡洛方法估算EVSI计算成本高昂，但近期发展的高斯近似（GA）方法能够高效估算不同样本量下的EVSI。然而当决策模型高度非线性时，传统GA可能导致有偏的EVSI估计。这种偏差在使用GA优化不同研究价值时可能产生次优的研究设计。因此，我们扩展了传统GA方法以提高其对非线性决策模型的性能。方法：我们的方法通过两步近似条件收益来提供精确的EVSI估计。首先，应用泰勒级数近似，利用样条将条件收益估计为由关注参数的条件矩构成的函数，该样条通过拟合参数样本及其对应收益获得。其次，通过传统GA和Fisher信息近似参数的条件矩。该方法被应用于涉及非高斯参数和非线性决策模型的若干数据收集案例。其性能与嵌套蒙特卡洛法、传统GA法以及基于非参数回归的EVSI计算方法进行了比较。结果：当关注参数为非高斯分布且决策模型为非线性时，所提方法在不同样本量下均能提供精确的EVSI估计。其计算开销与其他新颖方法相当。结论：所提方法能够准确高效地估算不同样本量下的EVSI，这可为研究者利用EVSI确定经济最优的研究设计提供支持。