Speaker: Dr Rhian Daniel, University of Cardiff
Abstract: When making inferences about the causal effect of a point binary exposure on an outcome, inverse weighting by the propensity score (IPW) is perceived to be relatively robust to parametric model misspecification, since it does not rely on a model for the outcome given exposure and confounders. Robins and Rotnitzky (2001) showed that simple IPW can be improved upon. In particular, they showed that by specifying both a model for the exposure given confounders and a model for the outcome given exposure and confounders, an estimator can be constructed (henceforth the standard doubly robust estimator, SDR) that is consistent if at least one of the two models is correct and is locally asymptotically efficient in the sense that when both models are correctly specified, there is no estimator relying on the correct specification of the first model that has a smaller asymptotic variance than the SDR estimator. The SDR estimator also has appealing properties in high-dimensional settings when data-adaptive estimation is desirable: the fact that the estimator is orthogonal to the scores corresponding to the nuisance functionals means that convergence rates are better than for other estimators, and standard inference possible. Following a critical paper by Kang and Schafer (2007) “Demystifying double robustness”, which showed that – at least in some situations – the non-local finite sample performance of SDR can be poor, a number of alternative DR estimators have been proposed (including Cao et al, 2009; Rotnitzky et al, 2011; Gruber and van der Laan, 2011; Vermeulen and Vansteelandt, 2014). These alternative DR estimators share the desirable asymptotic, local, convergence and inferential properties of the SDR but promise better performance in finite samples and/or under misspecification of one or both of the nuisance models. In this talk, I shall review these alternative DR estimators and compare their performance in a range of high-dimensional settings.