Ch7-10 因果推断的偏差¶
因果推断中可能会出现多种偏差，包括 - confounding bias, - selection bias, - measurement error and - random variability.
Single-world intervention graphs¶
Exchangeability is translated into graph language as the lack of open paths between the treatment \(A\) and outcome \(Y\) nodes–other than those originating from \(A\)–that would result in an association between \(A\) and \(Y\).
A new type of graph–Single-world intervention graphs (SWIGs)– unify the counterfactual and graphical approaches by explicitly including the counterfactual variables on the graph.
A SWIG is a graph that represents a counterfactual world created by a single intervention. In contrast, the vari- ables on a standard causal diagram represent the actual world.
Selection bias and censoring¶
Since censoring \(C\) is now viewed as a treatment, it follows that we will need to
ensure that the identifiability conditions of exchangeability, positivity, and consistency hold for \(C\) as well as for \(A\), and
use analytical methods that are identical to those we would have to use if we wanted to estimate the effect of censoring \(C\).
Under these identifiability conditions and using these methods, selection bias can be eliminated via analytic adjustment and, in the absence of measurement error and confounding, the causal effect of treatment \(A\) on outcome \(Y\) can be identified.
信息因果模型中，系统一的每个信息传递都是信息干预。
Intention-to-treat effect: the effect of a misclassified treatment¶
Alternatively, one could view the bias due to mismeasured confounders as a form of unmeasured confounding rather than as a form of measurement bias. The particular choice of terminology–unmeasured confounding versus bias due to mismeasurement of the confounders–is irrelevant for practical purposes.
In real randomized experiments we need to distinguish between two treat- ment variables: the assigned treatment \(Z\) (1 if the person is assigned to trans- plant, 0 otherwise) and the received treatment \(A\) (1 if the person receives a transplant, 0 otherwise).
per-protocol effect： In randomized experiments, the per-protocol effect is the causal effect of treatment that would have been observed if all individuals had adhered to their assigned treatment as specified in the protocol of the experiment.
intention-to-treat effect： The causal effect of randomized assignment is referred to as the intention-to-treat effect.
The conditionality “principle”¶
The likelihood for the observed data has three factors: the density of \(Y\) given \(A\) and \(L\), the density of \(A\) given \(L\), and the marginal density of \(L\). The conditionality principle states that one should always perform inference on the parameter of interest conditional on any ancillary statistics.