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The estimation of causal effects is a fundamental goal in the field of causalinference. However, it is challenging for various reasons. One reason is thatthe exposure (or treatment) is naturally continuous in many real-worldscenarios. When dealing with continuous exposure, dichotomizing the exposurevariable based on a pre-defined threshold may result in a biased understandingof causal relationships. In this paper, we propose a novel causal inferenceframework that can measure the causal effect of continuous exposure. We definethe expectation of a derivative of potential outcomes at a specific exposurelevel as the average causal derivative effect. Additionally, we propose amatching method for this estimator and propose a permutation approach to testthe hypothesis of no local causal effect. We also investigate the asymptoticproperties of the proposed estimator and examine its performance throughsimulation studies. Finally, we apply this causal framework in a real dataexample of Chronic Obstructive Pulmonary Disease (COPD) patients.

Local causal effects with continuous exposures: A matching estimator for the average causal derivative effect