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1.  Causal assessment of surrogacy in a meta-analysis of colorectal cancer trials 
Biostatistics (Oxford, England)  2011;12(3):478-492.
When the true end points (T) are difficult or costly to measure, surrogate markers (S) are often collected in clinical trials to help predict the effect of the treatment (Z). There is great interest in understanding the relationship among S, T, and Z. A principal stratification (PS) framework has been proposed by Frangakis and Rubin (2002) to study their causal associations. In this paper, we extend the framework to a multiple trial setting and propose a Bayesian hierarchical PS model to assess surrogacy. We apply the method to data from a large collection of colon cancer trials in which S and T are binary. We obtain the trial-specific causal measures among S, T, and Z, as well as their overall population-level counterparts that are invariant across trials. The method allows for information sharing across trials and reduces the nonidentifiability problem. We examine the frequentist properties of our model estimates and the impact of the monotonicity assumption using simulations. We also illustrate the challenges in evaluating surrogacy in the counterfactual framework that result from nonidentifiability.
doi:10.1093/biostatistics/kxq082
PMCID: PMC3114655  PMID: 21252079
Bayesian estimation; Counterfactual model; Identifiability; Multiple trials; Principal stratification; Surrogate marker
2.  Bayesian inference for causal mediation effects using principal stratification with dichotomous mediators and outcomes 
Biostatistics (Oxford, England)  2010;11(2):353-372.
Most investigations in the social and health sciences aim to understand the directional or causal relationship between a treatment or risk factor and outcome. Given the multitude of pathways through which the treatment or risk factor may affect the outcome, there is also an interest in decomposing the effect of a treatment of risk factor into “direct” and “mediated” effects. For example, child's socioeconomic status (risk factor) may have a direct effect on the risk of death (outcome) and an effect that may be mediated through the adulthood socioeconomic status (mediator). Building on the potential outcome framework for causal inference, we develop a Bayesian approach for estimating direct and mediated effects in the context of a dichotomous mediator and dichotomous outcome, which is challenging as many parameters cannot be fully identified. We first define principal strata corresponding to the joint distribution of the observed and counterfactual values of the mediator, and define associate, dissociative, and mediated effects as functions of the differences in the mean outcome under differing treatment assignments within the principal strata. We then develop the likelihood properties and calculate nonparametric bounds of these causal effects assuming randomized treatment assignment. Because likelihood theory is not well developed for nonidentifiable parameters, we consider a Bayesian approach that allows the direct and mediated effects to be expressed in terms of the posterior distribution of the population parameters of interest. This range can be reduced by making further assumptions about the parameters that can be encoded in prior distribution assumptions. We perform sensitivity analyses by using several prior distributions that make weaker assumptions than monotonicity or the exclusion restriction. We consider an application that explores the mediating effects of adult poverty on the relationship between childhood poverty and risk of death.
doi:10.1093/biostatistics/kxp060
PMCID: PMC2830580  PMID: 20101045
Direct effect; Mediated effect; Monotonicity; Mortality; Poverty

Results 1-2 (2)