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1.  Improved double-robust estimation in missing data and causal inference models 
Biometrika  2012;99(2):439-456.
Recently proposed double-robust estimators for a population mean from incomplete data and for a finite number of counterfactual means can have much higher efficiency than the usual double-robust estimators under misspecification of the outcome model. In this paper, we derive a new class of double-robust estimators for the parameters of regression models with incomplete cross-sectional or longitudinal data, and of marginal structural mean models for cross-sectional data with similar efficiency properties. Unlike the recent proposals, our estimators solve outcome regression estimating equations. In a simulation study, the new estimator shows improvements in variance relative to the standard double-robust estimator that are in agreement with those suggested by asymptotic theory.
doi:10.1093/biomet/ass013
PMCID: PMC3635709  PMID: 23843666
Drop-out; Marginal structural model; Missing at random
2.  A note on overadjustment in inverse probability weighted estimation 
Biometrika  2010;97(4):997-1001.
Summary
Standardized means, commonly used in observational studies in epidemiology to adjust for potential confounders, are equal to inverse probability weighted means with inverse weights equal to the empirical propensity scores. More refined standardization corresponds with empirical propensity scores computed under more flexible models. Unnecessary standardization induces efficiency loss. However, according to the theory of inverse probability weighted estimation, propensity scores estimated under more flexible models induce improvement in the precision of inverse probability weighted means. This apparent contradiction is clarified by explicitly stating the assumptions under which the improvement in precision is attained.
doi:10.1093/biomet/asq049
PMCID: PMC3371719  PMID: 22822256
Causal inference; Propensity score; Standardized mean
3.  On doubly robust estimation in a semiparametric odds ratio model 
Biometrika  2009;97(1):171-180.
We consider the doubly robust estimation of the parameters in a semiparametric conditional odds ratio model. Our estimators are consistent and asymptotically normal in a union model that assumes either of two variation independent baseline functions is correctly modelled but not necessarily both. Furthermore, when either outcome has finite support, our estimators are semiparametric efficient in the union model at the intersection submodel where both nuisance functions models are correct. For general outcomes, we obtain doubly robust estimators that are nearly efficient at the intersection submodel. Our methods are easy to implement as they do not require the use of the alternating conditional expectations algorithm of Chen (2007).
doi:10.1093/biomet/asp062
PMCID: PMC3412601  PMID: 23049119
Doubly robust; Generalized odds ratio; Locally efficient; Semiparametric logistic regression

Results 1-3 (3)