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1.  Causal Effect Models for Realistic Individualized Treatment and Intention to Treat Rules* 
Marginal structural models (MSM) are an important class of models in causal inference. Given a longitudinal data structure observed on a sample of n independent and identically distributed experimental units, MSM model the counterfactual outcome distribution corresponding with a static treatment intervention, conditional on user-supplied baseline covariates. Identification of a static treatment regimen-specific outcome distribution based on observational data requires, beyond the standard sequential randomization assumption, the assumption that each experimental unit has positive probability of following the static treatment regimen. The latter assumption is called the experimental treatment assignment (ETA) assumption, and is parameter-specific. In many studies the ETA is violated because some of the static treatment interventions to be compared cannot be followed by all experimental units, due either to baseline characteristics or to the occurrence of certain events over time. For example, the development of adverse effects or contraindications can force a subject to stop an assigned treatment regimen.
In this article we propose causal effect models for a user-supplied set of realistic individualized treatment rules. Realistic individualized treatment rules are defined as treatment rules which always map into the set of possible treatment options. Thus, causal effect models for realistic treatment rules do not rely on the ETA assumption and are fully identifiable from the data. Further, these models can be chosen to generalize marginal structural models for static treatment interventions. The estimating function methodology of Robins and Rotnitzky (1992) (analogue to its application in Murphy, et. al. (2001) for a single treatment rule) provides us with the corresponding locally efficient double robust inverse probability of treatment weighted estimator.
In addition, we define causal effect models for “intention-to-treat” regimens. The proposed intention-to-treat interventions enforce a static intervention until the time point at which the next treatment does not belong to the set of possible treatment options, at which point the intervention is stopped. We provide locally efficient estimators of such intention-to-treat causal effects.
PMCID: PMC2613338  PMID: 19122793
counterfactual; causal effect; causal inference; double robust estimating function; dynamic treatment regimen; estimating function; individualized stopped treatment regimen; individualized treatment rule; inverse probability of treatment weighted estimating functions; locally efficient estimation; static treatment intervention
2.  Statistical Learning of Origin-Specific Statically Optimal Individualized Treatment Rules 
Consider a longitudinal observational or controlled study in which one collects chronological data over time on a random sample of subjects. The time-dependent process one observes on each subject contains time-dependent covariates, time-dependent treatment actions, and an outcome process or single final outcome of interest. A statically optimal individualized treatment rule (as introduced in van der Laan et. al. (2005), Petersen et. al. (2007)) is a treatment rule which at any point in time conditions on a user-supplied subset of the past, computes the future static treatment regimen that maximizes a (conditional) mean future outcome of interest, and applies the first treatment action of the latter regimen. In particular, Petersen et. al. (2007) clarified that, in order to be statically optimal, an individualized treatment rule should not depend on the observed treatment mechanism. Petersen et. al. (2007) further developed estimators of statically optimal individualized treatment rules based on a past capturing all confounding of past treatment history on outcome. In practice, however, one typically wishes to find individualized treatment rules responding to a user-supplied subset of the complete observed history, which may not be sufficient to capture all confounding. The current article provides an important advance on Petersen et. al. (2007) by developing locally efficient double robust estimators of statically optimal individualized treatment rules responding to such a user-supplied subset of the past. However, failure to capture all confounding comes at a price; the static optimality of the resulting rules becomes origin-specific. We explain origin-specific static optimality, and discuss the practical importance of the proposed methodology. We further present the results of a data analysis in which we estimate a statically optimal rule for switching antiretroviral therapy among patients infected with resistant HIV virus.
PMCID: PMC2613337  PMID: 19122792
counterfactual; causal inference; double robust estimating function; dynamic treatment regime; history-adjusted marginal structural model; inverse probability weighting

Results 1-2 (2)