Linganisha mbinu

	Mfumo Imara wa Kiunzi cha Uamuzi wa Athari (Robust Marginal Structural Model)	Uzito wa Alama ya Mwelekeo (PSW / IPW)
Nyanja	Uhitimisho wa Kisababishi	Uhitimisho wa Kisababishi
Familia	Regression model	Regression model
Mwaka wa asili	2000–2004	1983 (propensity score); 2003 (efficient IPW estimator)
Mwanzilishi	Robins, Hernán & Brumback; robustness extensions by Scharfstein, Rotnitzky, Lunceford & Davidian	Rosenbaum & Rubin (propensity score); Hirano, Imbens & Ridder (efficient weighting)
Aina	Causal inference / weighted regression	Causal inference / reweighting
Chanzo asilia	Robins, J. M., Hernán, M. A., & Brumback, B. (2000). Marginal structural models and causal inference in epidemiology. Epidemiology, 11(5), 550-560.	Rosenbaum, P. R., & Rubin, D. B. (1983). The central role of the propensity score in observational studies for causal effects. Biometrika, 70(1), 41-55.
Majina mbadala	robust MSM, doubly-robust MSM, sandwich-SE MSM, robust IPTW marginal structural model	PSW, inverse probability weighting, IPW, propensity-based weighting
Zinazohusiana	6	6
Muhtasari	Robust Marginal Structural Models (robust MSMs) extend the standard MSM framework — which uses inverse probability of treatment weighting to handle time-varying confounding — by pairing IPTW estimation with sandwich (robust) standard errors or doubly-robust estimators. This combination yields valid causal estimates and reliable inference even when the outcome regression model is mildly misspecified or weights are moderately variable.	Propensity score weighting is a causal-inference method that reweights observations so that the covariate distributions of treated and untreated units look exchangeable, enabling unbiased estimation of average treatment effects from observational data. Each unit receives a weight that is the inverse of its probability of receiving the treatment it actually received — a strategy formalised by Rosenbaum and Rubin (1983) and given its efficient semiparametric form by Hirano, Imbens and Ridder (2003).