Recent Advances in Bayesian Methods for Causal Inference
Presenter: Jason Roy
When: Tuesday, July 12, 2016 Time: 4:00 PM - 5:30 PM
Room: Salon A Carson Hall (Level 2)
Session Synopsis:
A New Approach to Causal Inference Using Bayesian Nonparametric Methods
Bayesian methods have not been widely used for causal inference in observational studies. A possible reason for this is that causal inference in a likeihood-based framework often requires modeling the joint distirbution of all of the observed data, including covariates. However, recent developments in Bayesian nonparametric (BNP) modeling, along with increasing computing capacity, have opened the door to a new, potentially powerful approach to causal inference in a variety of settings. We develop a general joint Dirchlet process mixture model and show how it can be used to obtain posterior inference for any causal effect of interest. The extra effort needed to model a full observed data distribution has many potential benefits, including efficiency gains, full posterior inference rather than just point estimates and confidence intervals, automatic imputation of missing data, and a general way to account for uncertainty about a variety of assumptions. We compare our method with inverse probability of treatment-weighted estimators in simulation studies. We apply our method to data from a study of different antitetroviral treatment regimens in an HIV/HCV co-infected cohort.
Recent Advances in Bayesian Methods for Causal Inference
Presenter: Michael Elliott
When: Tuesday, July 12, 2016 Time: 4:00 PM - 5:30 PM
Room: Salon A Carson Hall (Level 2)
Session Synopsis:
Surrogacy Assessment Using Principal Stratification and a Gaussian Copula Model
In clinical trials, a surrogate outcome variable (S) can be measured before the outcome of interest (T) and may provide early information regarding the treatment (Z) effect on T. Many methods of surrogacy validation rely on models for the conditional distribution of T given Z and S. However, S is a post-randomization variable, and unobserved, simultaneous predictors of S and T may exists, resulting in a non-causal interpretation. Frangakis and Rubin (2002) developed the concept of principal surrogacy, stratifying on the joint distribution of the surrogate marker under treatment and control to assess the association between the causal effects of treatment on the marker and the causal effects of treatment on the outcome. Effective surrogate markers will have a causal treatment effect if and only if there is an effect on the outcome. Working within the principal surrogacy framework, we address the scenario of an ordinal categorical variable as a surrogate for a censored failure time true endpoint. A Gaussian copula model is used to model the joint distribution. A Gaussian copula model is used to model the joint distribution of the potential outcomes of T, given the potential outcomes of S. Because the proposed model cannot be fully identified from the data, we use a Bayesian estimation approach to aid in the estimation of non-identified parameters and use prior distributions that are consistent with reasonable assumptions in the surrogacy assessment setting. The method is applied to data from an advanced colorectal cancer clinical trial.
Recent Advances in Bayesian Methods for Causal Inference
Presenter: Andrea Mercatanti
When: Tuesday, July 12, 2016 Time: 4:00 PM - 5:30 PM
Room: Salon A Carson Hall (Level 2)
Session Synopsis:
Bayesian Inference for causal effects on bivariate outcomes with application to the evaluation of a job training program in Luxembourg
We focus on the evaluational of the effect of a training program on a bivariate outcome: hours worked and wage, using data from the global social security database on labour force in Luxembourg (IGSS) and the administrative data collected by the Employment Agency (ADEM). Causal inference in this context presents unique challenges because (1) data come from an observational study; (2) focus is on a bivariate outcome, and (3) one of the outcome of interest, wage, is censored due to death: wages are defined for employed individuals only. We first deal with the observational nature of the study focusing on the design phase of the study: under strong ignorability we use matching methods to create sub-samples of the original treated and control groups with similar covariate distributions. We then move to the analysis phase, focusing on describing and addressing the complications arising from the multivariate nature of the outcome and the presence of an outcome truncated by death using a Bayesian approach with the framework of principal stratification.
Recent Advances in Bayesian Methods for Causal Inference
Presenter: Lawrence McCandless
When: Tuesday, July 12, 2016 Time: 4:00 PM - 5:30 PM
Room: Salon A Carson Hall (Level 2)
Session Synopsis:
Unmeasured confounding, large datasets, and the role of Bayesian inference
Bayesian sensitivity analysis for unmeasured confounding is a statistical method to model uncertainty from bias in observational studies. In this presentation, we examine the method in settings where the exposure effect and the effects of measured and unmeasured confounders follow a logistic regression model. We illustrate the surprising result there are scenarios where the data can influence Bayesian assessments of uncertainty about unmeasured confounding. We show that there are certain combinations of data and prior distributions that can result in prior-to-posterior changes in uncertainty about bias parameters. This occurs because the application of Bayes theorem in a non-identifiable model will sometimes rule out certain patterns of unmeasured confounding that are not compatible with the data. An immediate consequence is that Bayesian interval estimates may differ from the corresponding Monte Carlo sensitivity analysis intervals that are obtained by sampling bias parameters directly from the prior. To understand this result, we describe a reparametrization of the model for unmeasured confounding that isolates the flow of information into the posterior distribution of bias parameters. We develop a numerical procedure to calculate the large sample limiting posterior distribution for bias parameters under different assumptions about the priors and data generating mechanism.
