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1.  Double-Robust Estimation of an Exposure-Outcome Odds Ratio Adjusting for Confounding in Cohort and Case-control Studies 
Statistics in medicine  2010;30(4):335-347.
Modern epidemiologic studies often aim to evaluate the causal effect of a point exposure on the risk of a disease from cohort or case-control observational data. Because confounding bias is of serious concern in such non-experimental studies, investigators routinely adjust for a large number of potential confounders in a logistic regression analysis of the effect of exposure on disease outcome. Unfortunately, when confounders are not correctly modeled, standard logistic regression is likely biased in its estimate of the effect of exposure, potentially leading to erroneous conclusions. We partially resolve this serious limitation of standard logistic regression analysis with a new iterative approach that we call ProRetroSpective estimation, which carefully combines standard logistic regression with a logistic regression analysis in which exposure is the dependent variable and the outcome and confounders are the independent variables. As a result, we obtain a correct estimate of the exposure-outcome odds ratio, if either the standard logistic regression of the outcome given exposure and confounding factors is correct, or the regression model of exposure given the outcome and confounding factors is correct but not necessarily both, that is, it is double-robust. In fact, it also has certain advantadgeous efficiency properties. The approach is general in that it applies to both cohort and case-control studies whether the design of the study is matched or unmatched on a subset of covariates. Finally, an application illustrates the methods using data from the National Cancer Institute's Black/White Cancer Survival Study.
PMCID: PMC3059519  PMID: 21225896
2.  A note on overadjustment in inverse probability weighted estimation 
Biometrika  2010;97(4):997-1001.
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.
PMCID: PMC3371719  PMID: 22822256
Causal inference; Propensity score; Standardized mean
3.  Dynamic Regime Marginal Structural Mean Models for Estimation of Optimal Dynamic Treatment Regimes, Part II: Proofs of Results* 
In this companion article to “Dynamic Regime Marginal Structural Mean Models for Estimation of Optimal Dynamic Treatment Regimes, Part I: Main Content” [Orellana, Rotnitzky and Robins (2010), IJB, Vol. 6, Iss. 2, Art. 7] we present (i) proofs of the claims in that paper, (ii) a proposal for the computation of a confidence set for the optimal index when this lies in a finite set, and (iii) an example to aid the interpretation of the positivity assumption.
PMCID: PMC2854089  PMID: 20405047
dynamic treatment regime; double-robust; inverse probability weighted; marginal structural model; optimal treatment regime; causality

Results 1-3 (3)