New \(G\)-formula for the sequential causal effect and blip effect of treatment in sequential causal inference.

*(English)*Zbl 1439.62183In the framework of single-point causal inference, every treatment in the treatment sequence has the point causal effect of treatment. The point causal effect of treatment is equal to the point observable effect of treatment. The point observable effect can be estimated by ML without knowing the influences of the subsequent treatments and observable covariates. In an attempt to extent the methodology from single-point causal inference to sequential causal inference, the new G-formula is derived which expresses the sequential causal effect and the blip effect in terms of the point observable effects instead of the standardized parameterers. The new G-formula is applied to estimate the sequential causal effect and the blip effect via the point observable effects by ML and compare the proposed method with other methods in the literature. Some interesting discussion is given finally.

Reviewer: Rózsa Horváth-Bokor (Budakalász)

##### MSC:

62L12 | Sequential estimation |

62H12 | Estimation in multivariate analysis |

62H15 | Hypothesis testing in multivariate analysis |

62F03 | Parametric hypothesis testing |

62F30 | Parametric inference under constraints |

##### Keywords:

blip effect; curse of dimensionality; new \(G\)-formula; null paradox; point observable effect; sequential causal effect
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\textit{X. Wang} and \textit{L. Yin}, Ann. Stat. 48, No. 1, 138--160 (2020; Zbl 1439.62183)

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