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Augmented Weighted Estimators Dealing with Practical Positivity Violation to Causal inferences in a Random Coefficient Model.
The inverse probability of treatment weighted (IPTW) estimator can be used to make causal inferences under two assumptions: (1) no unobserved confounders (ignorability) and (2) positive probability of treatment and of control at every level of the confounders (positivity), but is vulnerable to bias if by chance, the proportion of the sample assigned to treatment, or proportion of control, is zero at certain levels of the confounders. We propose to deal with this sampling zero problem, also known as practical violation of the positivity assumption, in a setting where the observed confounder is cluster identity, i.e., treatment assignment is ignorable within clusters. Specifically, based on a random coefficient model assumed for the potential outcome, we augment the IPTW estimating function with the estimated potential outcomes of treatment (or of control) for clusters that have no observation of treatment (or control). If the cluster-specific potential outcomes are estimated correctly, the augmented estimating function can be shown to converge in expectation to zero and therefore yield consistent causal estimates. The proposed method can be implemented in the existing software, and it performs well in simulated data as well as with real-world data from a teacher preparation evaluation study
An evaluation of exact matching and propensity score methods as applied in a comparative effectiveness study of inhaled corticosteroids in asthma
Peer reviewedPublisher PD
A practical illustration of the importance of realistic individualized treatment rules in causal inference
The effect of vigorous physical activity on mortality in the elderly is
difficult to estimate using conventional approaches to causal inference that
define this effect by comparing the mortality risks corresponding to
hypothetical scenarios in which all subjects in the target population engage in
a given level of vigorous physical activity. A causal effect defined on the
basis of such a static treatment intervention can only be identified from
observed data if all subjects in the target population have a positive
probability of selecting each of the candidate treatment options, an assumption
that is highly unrealistic in this case since subjects with serious health
problems will not be able to engage in higher levels of vigorous physical
activity. This problem can be addressed by focusing instead on causal effects
that are defined on the basis of realistic individualized treatment rules and
intention-to-treat rules that explicitly take into account the set of treatment
options that are available to each subject. We present a data analysis to
illustrate that estimators of static causal effects in fact tend to
overestimate the beneficial impact of high levels of vigorous physical activity
while corresponding estimators based on realistic individualized treatment
rules and intention-to-treat rules can yield unbiased estimates. We emphasize
that the problems encountered in estimating static causal effects are not
restricted to the IPTW estimator, but are also observed with the
-computation estimator, the DR-IPTW estimator, and the targeted MLE. Our
analyses based on realistic individualized treatment rules and
intention-to-treat rules suggest that high levels of vigorous physical activity
may confer reductions in mortality risk on the order of 15-30%, although in
most cases the evidence for such an effect does not quite reach the 0.05 level
of significance.Comment: Published in at http://dx.doi.org/10.1214/07-EJS105 the Electronic
Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Robust and Flexible Estimation of Stochastic Mediation Effects: A Proposed Method and Example in a Randomized Trial Setting
Causal mediation analysis can improve understanding of the mechanisms
underlying epidemiologic associations. However, the utility of natural direct
and indirect effect estimation has been limited by the assumption of no
confounder of the mediator-outcome relationship that is affected by prior
exposure---an assumption frequently violated in practice. We build on recent
work that identified alternative estimands that do not require this assumption
and propose a flexible and double robust semiparametric targeted minimum
loss-based estimator for data-dependent stochastic direct and indirect effects.
The proposed method treats the intermediate confounder affected by prior
exposure as a time-varying confounder and intervenes stochastically on the
mediator using a distribution which conditions on baseline covariates and
marginalizes over the intermediate confounder. In addition, we assume the
stochastic intervention is given, conditional on observed data, which results
in a simpler estimator and weaker identification assumptions. We demonstrate
the estimator's finite sample and robustness properties in a simple simulation
study. We apply the method to an example from the Moving to Opportunity
experiment. In this application, randomization to receive a housing voucher is
the treatment/instrument that influenced moving to a low-poverty neighborhood,
which is the intermediate confounder. We estimate the data-dependent stochastic
direct effect of randomization to the voucher group on adolescent marijuana use
not mediated by change in school district and the stochastic indirect effect
mediated by change in school district. We find no evidence of mediation. Our
estimator is easy to implement in standard statistical software, and we provide
annotated R code to further lower implementation barriers.Comment: 24 pages, 2 tables, 2 figure
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