Causal Inference for Statistics, Social, and Biomedical Sciences¶
Imbens, G. W., & Rubin, D. B. (2015). Causal Inference for Statistics, Social, and Biomedical Sciences: An Introduction. Cambridge University Press.
Cited by¶
2 citations across 2 artifacts.
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Primes¶
- Control Sample
- … $Y_T = \mu + \beta_{\text{placebo}} + \tau + \varepsilon_T$ and $Y_C = \mu + \beta_{\text{placebo}} + \varepsilon_C$, where $\mu$ is the baseline, $\beta_{\text{placebo}}$ is the expectation/regression-to-mean/natural-history effect present in both arms, $\tau$ is the active drug effect, and $\varepsilon$ is noise.
This sourcePotential-outcomes decomposition of treatment vs. control arms and randomization making background terms equal in expectation, so that the difference E[Y_T - Y_C] isolates the treatment effect with shared terms cancelling.
- … $Y_T = \mu + \beta_{\text{placebo}} + \tau + \varepsilon_T$ and $Y_C = \mu + \beta_{\text{placebo}} + \varepsilon_C$, where $\mu$ is the baseline, $\beta_{\text{placebo}}$ is the expectation/regression-to-mean/natural-history effect present in both arms, $\tau$ is the active drug effect, and $\varepsilon$ is noise.
- Minimal Modification Principle
- The resulting difference in outcomes is then attributed to treatment, because minimal modification is satisfied: treatment changed, background did not, as Imbens and Rubin (2015) develop systematically across randomized trials, instrumental variables, and observational designs.
This sourceComprehensive development of the potential-outcomes framework across randomized experiments, instrumental variables, regression discontinuity, and matching methods; each design enforces minimal modification by holding background conditions fixed (in expectation or by construction) while varying treatment.
- The resulting difference in outcomes is then attributed to treatment, because minimal modification is satisfied: treatment changed, background did not, as Imbens and Rubin (2015) develop systematically across randomized trials, instrumental variables, and observational designs.
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