Causal reasoning from imperfect experiments and fuzzy information

Imperfect experiments are experiments that deviate from the ideal protocol of randomized control. For example, when subjects in a randomized trial do not fully comply with their assigned treatments, which compromises their identification of causal effects. Pearl developed a linear programming model to derive bounds for the causal effects of interests. However, it is hard to improve the estimation by the linear programming model without further information. In this study, we show how referable knowledge and reusable information from related experiments can help improve the estimation of the causal effects. The referable knowledge from related studies or experiments can be introduced into the linear programming model as extra constraints. Since the referable knowledge involves fuzzy information and relationships, Pearl's linear programming model is extended to a nonlinear programming model and provides stricter bounds than the linear programming model does.