Marginal structural models versus structural nested models as tools for causal inference.

*(English)* Zbl 0986.62094
Halloran, M. Elizabeth (ed.) et al., Statistical models in epidemiology, the environment, and clinical trials. IMA summer program on Statistics in the health sciences, Univ. of Minnesota, Minneapolis, MN, USA, 1997. New York, NY: Springer. IMA Vol. Math. Appl. 116, 95-133 (2000).

Summary: The author [see, e.g., Lect. Notes Stat 120, 69-117 (1997;

Zbl 0969.62072); Commun. Stat., Theory Methods 23, No. 8, 2379-2412 (1994;

Zbl 0825.62203)] has developed a set of causal or counterfactual models, the structural nested models (SNMs). This paper describes an alternative new class of causal models – the (non-nested) marginal structural models (MSMs). We will then describe a class of semiparametric estimators for the parameters of these new models under a sequential randomization (i.e., ignorability) assumption. We then compare the strengths and weaknesses of MSMs versus SNMs for causal inference from complex longitudinal data with time-dependent treatments and confounders. Our results provide an extension to continuous treatments of propensity score estimators of an average treatment effect.

##### MSC:

62P10 | Applications of statistics to biology and medical sciences |

62G05 | Nonparametric estimation |

62N99 | Survival analysis and censored data |