Hypothesis Testing of Blip Effects in Sequential Causal Inference

In this article, we study the hypothesis testing of the blip / net effects of treatments in a treatment sequence. We illustrate that the likelihood ratio test and the score test may suffer from the curse of dimensionality, the null paradox and the high-dimensional constraint on standard parameters under the null hypothesis. On the other hand, we construct the Wald test via a small number of point effects of treatments in single-point causal inference. We show that the Wald test can avoid these problems under the same assumptions as the Wald test for testing the point effect of treatment. The simulation study illustrates that the Wald test achieves the nominal level of type I error and a low level of type II error. A real medical example illustrates how to conduct the Wald test in practice.

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