Accurate EVSI Estimation for Nonlinear Models Using the Gaussian Approximation Method

Abstract

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 expectation of the benefit based on 2 steps. First, a Taylor series approximation is applied to estimate the conditional expectation of the 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 that of 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. Highlights The Gaussian approximation method efficiently estimates the expected value of sample information (EVSI) for clinical trials with varying sample sizes, but it may introduce bias when health economic models have a nonlinear structure. We introduce the spline-based Taylor series approximation method and combine it with the original Gaussian approximation to correct the nonlinearity-induced bias in EVSI estimation. Our approach can provide more precise EVSI estimates for complex decision models without sacrificing computational efficiency, which can enhance the resource allocation strategies from the cost-effective perspective.