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Summary Randomized experiments have been the gold standard for drawing causal inference. The conventional model-based approach has been one of the most popular methods of analysing treatment effects from randomized experiments, which is often carried out through inference for certain model parameters. In this paper, we provide a systematic investigation of model-based analyses for treatment effects under the randomization-based inference framework. This framework does not impose any distributional assumptions on the outcomes, covariates and their dependence, and utilizes only randomization as the reasoned basis. We first derive the asymptotic theory for $ Z $-estimation in completely randomized experiments, and propose sandwich-type conservative covariance estimation. We then apply the developed theory to analyse both average and individual treatment effects in randomized experiments. For the average treatment effect, we consider model-based, model-imputed and model-assisted estimation strategies, where the first two strategies can be sensitive to model misspecification or require specific methods for parameter estimation. The model-assisted approach is robust to arbitrary model misspecification and always provides consistent average treatment effect estimation. We propose optimal ways to conduct model-assisted estimation using generally nonlinear least squares for parameter estimation. For the individual treatment effects, we propose directly modelling the relationship between individual effects and covariates, and discuss the model’s identifiability, inference and interpretation allowing for model misspecification. 

The electric power grid is a critical societal resource connecting multiple infrastructural domains such as agriculture, transportation, and manufacturing. The electrical grid as an infrastructure is shaped by human activity and public policy in terms of demand and supply requirements. Further, the grid is subject to changes and stresses due to diverse factors including solar weather, climate, hydrology, and ecology. The emerging interconnected and complex network dependencies make such interactions increasingly dynamic, posing novel risks, and presenting new challenges to manage the coupled human–natural system. This paper provides a survey of models and methods that seek to explore the significant interconnected impact of the electric power grid and interdependent domains. We also provide relevant critical risk indicators (CRIs) across diverse domains that may be used to assess risks to electric grid reliability, including climate, ecology, hydrology, finance, space weather, and agriculture. We discuss the convergence of indicators from individual domains to explore possible systemic risk, i.e., holistic risk arising from cross-domain interconnections. Further, we propose a compositional approach to risk assessment that incorporates diverse domain expertise and information, data science, and computer science to identify domain-specific CRIs and their union in systemic risk indicators. Our study provides an important first step towards data-driven analysis and predictive modeling of risks in interconnected human–natural systems.