Topics in Bayesian Inference for Causal Effects

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Topics in Bayesian Inference for Causal Effects

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Title: Topics in Bayesian Inference for Causal Effects
Author: Garcia Horton, Viviana
Citation: Garcia Horton, Viviana. 2015. Topics in Bayesian Inference for Causal Effects. Doctoral dissertation, Harvard University, Graduate School of Arts & Sciences.
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Abstract: This manuscript addresses two topics in Bayesian inference for causal effects.

1) Treatment noncompliance is frequent in clinical trials, and because the treatment actually received may be different from that assigned, comparisons between groups as randomized will no longer assess the effect of the treatment received.
To address this complication, we create latent subgroups based on the potential outcomes of treatment received and focus on the subgroup of compliers, where under certain assumptions the estimands of causal effects of assignment can be interpreted as causal effects of receipt of treatment.
We propose estimands of causal effects for right-censored time-to event endpoints, and discuss a framework to estimate those causal effects that relies on modeling survival times as parametric functions of pre-treatment variables.
We demonstrate a Bayesian estimation strategy that multiply imputes the missing data using posterior predictive distributions using a randomized clinical trial involving breast cancer patients.
Finally, we establish a connection with the commonly used parametric proportional hazards and accelerated failure time models, and briefly discuss the consequences of relaxing the assumption of independent censoring.

2) Bayesian inference for causal effects based on data obtained from ignorable assignment mechanisms can be sensitive to the model specified for the data.
Ignorability is defined with respect to specific models for an assignment mechanism and data, which we call the ``true'' generating data models, generally unknown to the statistician; these, in turn, determine a true posterior distribution for a causal estimand of interest.
On the other hand, the statistician poses a set of models to conduct the analysis, which we call the ``statistician's'' models; a posterior distribution for the causal estimand can be obtained assuming these models.
Let $\Delta_M$ denote the difference between the true models and the statistician's models, and let $\Delta_D$ denote the difference between the true posterior distribution and the statistician's posterior distribution (for a specific estimand).
For fixed $\Delta_M$ and fixed sample size, $\Delta_D$ varies more with data-dependent assignment mechanisms than with data-free assignment mechanisms.

We illustrate this through a sequence of examples of $\Delta_M$, and
under various ignorable assignment mechanisms, namely, complete randomization design, rerandomization design, and the finite selection model design.
In each case, we create the 95\% posterior interval for an estimand under a statistician's model, and then compute its coverage probability for the correct posterior distribution; this Bayesian coverage probability is our choice of measure $\Delta_D$.
The objective of these examples is to provide insights into the ranges of data models for which Bayesian inference for causal effects from datasets obtained through ignorable assignment mechanisms is approximately valid from the Bayesian perspective, and how these validities are influenced by data-dependent assignment mechanisms.
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