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.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Control Sample
- Each arm's outcome decomposes into the same background terms plus an arm-specific effect: \(Y_T = \mu + \beta_{\text{placebo}} + \tau + \varepsilon_T\) 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.
Supported in partVerified against the publisher's abstract
Imbens & Rubin's abstract supplies the potential-outcomes framing and randomization-based cancellation of shared terms, but not this arm-specific equation or its beta_placebo term.
“In this approach, causal effects are comparisons of such potential outcomes. The fundamental problem of causal inference is that we can only observe one of the potential outcomes for a particular subject. The authors discuss how randomized experiments allow us to assess causal effects”
- Each arm's outcome decomposes into the same background terms plus an arm-specific effect: \(Y_T = \mu + \beta_{\text{placebo}} + \tau + \varepsilon_T\) 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.
Supported in partVerified against the publisher's abstract
Confirms the book develops the potential-outcomes framework across randomized experiments, observational studies, and instrumental variables, but its abstract never states the 'minimal modification' attribution.
“The authors discuss how randomized experiments allow us to assess causal effects and then turn to observational studies. They lay out the assumptions needed for causal inference and describe the leading analysis methods, including matching, propensity-score methods, and instrumental variables.”
- 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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