Advances in methodology for causal inference
Presenter: David Benkeser
When: Tuesday, July 12, 2016 Time: 11:00 AM - 12:30 PM
Room: Oak Bay 1-2 (Level 1)
Session Synopsis:
Nonparametric doubly-robust inference
Doubly-robust estimators have recently gained immense popularity, particularly in the field of causal inference. By definition, doubly-robust estimators are consistent for the target parameter of interest if one of two nuisance parameters is consistently estimated. This gives a natural appeal of DR estimators: bias induced by misspecification of one nuisance parameter may be mitigated by the consistent estimation of the other. While the conceptual appeal of DR estimators is apparent, questions remain about how these estimators should be constructed in practice. Parametric nuisance models and maximum likelihood estimation have been the most popular approach taken in recent years and the theory necessary for performing inference is well understood in these settings. However, in many settings parametric models may be overly restrictive and Kang and Schafer (2007) demonstrated that misspecified parametric models can lead to arbitrarily poor behavior of doubly-robust estimators.This has lead to the consideration of nonparametric models and data-adaptive estimation techniques for constructing doubly-robust estimators. Such estimators may demonstrate superior performance by reducing the bias of nuisance parameters; however, the theory for performing inference using these estimators is not well understood. In this talk, we discuss recent theoretical advances that allow the construction of doubly-robust confidence intervals and p-values when nonparametric models and data-adaptive estimation techniques are employed.
Advances in methodology for causal inference
Presenter: Alexander Luedtke
When: Tuesday, July 12, 2016 Time: 11:00 AM - 12:30 PM
Room: Oak Bay 1-2 (Level 1)
Session Synopsis:
Adaptive Sampling for Subgroup Analyses
Consider a population of patients partitioned into strata based on baseline covariates, each stratum covering a small proportion p, say 5%, with respect to the population�s fixed covariate distribution. We investigate the effect of a binary treatment in an adaptive trial setting where the sampling distribution for covariates is determined by investigators. We wish to estimate the largest conditional average treatment effect within unions of m strata covering a proportion mp of the population, say 10%, while sampling from the corresponding optimal union of m strata as often as possible. The multi-armed bandit literature studies this problem in terms of regret. We study it in terms of inference for the conditional average treatment effect in the optimal union of m strata. From our perspective, an optimal design should satisfy two conditions when the optimal union is unique. First, the resulting estimator should have the same asymptotic variance as the semiparametric efficient estimator in a trial where one only samples from the optimal union of strata. Second, the proportion of samples belonging to the suboptimal covariate strata should decay at the optimal rate given in the multi-armed bandit literature. Defining optimality is less straightforward when the optimal union is non-unique, but we will show why we expect massive variance gains over i.i.d. sampling regardless of the optimal union's uniqueness. This is joint work with Antoine Chambaz.
Advances in methodology for causal inference
Presenter: Forrest Crawford
When: Tuesday, July 12, 2016 Time: 11:00 AM - 12:30 PM
Room: Oak Bay 1-2 (Level 1)
Session Synopsis:
Confidence intervals for means under constrained dependence
We develop a general framework for conducting inference on the mean of dependent random variables given constraints on their dependency graph. We establish the consistency of an oracle variance estimator of the mean when the dependency graph is known, along with an associated central limit theorem. We derive an integer linear program for finding an upper bound for the estimated variance when the graph is unknown, but topological and degree-based constraints are available. We develop alternative bounds, including a closed-form bound, under an additional homoskedasticity assumption. We establish a basis for Wald-type confidence intervals for the mean that are guaranteed to have asymptotically conservative coverage. We apply the approach to inference from a social network link-tracing study and provide statistical software implementing the approach.
Advances in methodology for causal inference
Presenter: James Robins
When: Tuesday, July 12, 2016 Time: 11:00 AM - 12:30 PM
Room: Oak Bay 1-2 (Level 1)
Session Synopsis:
Some Open Issues in Inference based on higher order influence function
I discuss what I consider important open issues to the development of inference with higher order influence functions
