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New $$G$$-formula for the sequential causal effect and blip effect of treatment in sequential causal inference. (English) Zbl 1439.62183
In 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.
##### MSC:
 62L12 Sequential estimation 62H12 Estimation in multivariate analysis 62H15 Hypothesis testing in multivariate analysis 62F03 Parametric hypothesis testing 62F30 Parametric inference under constraints
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##### References:
 [1] Little, R. J. A. and Rubin, D. B. (2002). Statistical Analysis with Missing Data, 2nd ed. Wiley Series in Probability and Statistics. Wiley Interscience, Hoboken, NJ. · Zbl 1011.62004 [2] McCullagh, P. and Nelder, J. A. (1999). Generalized Linear Models. Chapman & Hall/CRC, Boca Raton, FL. · Zbl 0588.62104 [3] Petersen, M. L., Porter, K. E., Gruber, S., Wang, Y. and van der Laan, M. J. (2012). Diagnosing and responding to violations in the positivity assumption. Stat. Methods Med. Res. 21 31-54. [4] Robins, J. (1986). A new approach to causal inference in mortality studies with a sustained exposure period—application to control of the healthy worker survivor effect. Math. Model. 7 1393-1512. · Zbl 0614.62136 [5] Robins, J. M. (1997). Causal inference from complex longitudinal data. In Latent Variable Modeling and Applications to Causality (Los Angeles, CA, 1994) (M. Berkane, ed.). Lect. Notes Stat. 120 69-117. Springer, New York. · Zbl 0969.62072 [6] Robins, J. M. (1999). Association, causation, and marginal structural models. Synthese 121 151-179. · Zbl 1078.62523 [7] Robins, J. M. (2009). Longitudinal data analysis. In Handbooks of Modern Statistical Methods (G. Fitzmaurice, ed.) 553-599. Chapman & Hall/CRC, Boca Raton, FL. [8] Rosenbaum, P. R. and Rubin, D. B. (1983). The central role of the propensity score in observational studies for causal effects. Biometrika 70 41-55. · Zbl 0522.62091 [9] Rubin, D. B. (2005). Causal inference using potential outcomes: Design, modeling, decisions. J. Amer. Statist. Assoc. 100 322-331. · Zbl 1117.62418 [10] Splawa-Neyman, J. (1990). On the application of probability theory to agricultural experiments. Essay on principles. Section 9. Statist. Sci. 5 465-472. Translated from the Polish and edited by D. M. Da̧browska and T. P. Speed. · Zbl 0955.01560 [11] Taubman, S. L., Robins, J. M., Mittleman, M. A. and Hernán, M. A. (2009). Intervening on risk factors for coronary heart disease: An application of the parametric g-formula. Int. J. Epidemiol. 38 1599-1611. [12] Wang, X. and Yin, L. (2015). Identifying and estimating net effects of treatments in sequential causal inference. Electron. J. Stat. 9 1608-1643. · Zbl 1327.62350 [13] Wang, X. and Yin, L. (2020). Supplement to “New $$G$$-formula for the sequential causal effect and blip effect of treatment in sequential causal inference.” https://doi.org/10.1214/18-AOS1795SUPP. [14] Zeger, S. L. and Diggle, P. J. (1994). Semiparametric models for longitudinal data with application to CD4 cell numbers in HIV seroconverters. Biometrics 50 689-699. · Zbl 0821.62093
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