298 research outputs found
Entropy balancing is doubly robust
Covariate balance is a conventional key diagnostic for methods used
estimating causal effects from observational studies. Recently, there is an
emerging interest in directly incorporating covariate balance in the
estimation. We study a recently proposed entropy maximization method called
Entropy Balancing (EB), which exactly matches the covariate moments for the
different experimental groups in its optimization problem. We show EB is doubly
robust with respect to linear outcome regression and logistic propensity score
regression, and it reaches the asymptotic semiparametric variance bound when
both regressions are correctly specified. This is surprising to us because
there is no attempt to model the outcome or the treatment assignment in the
original proposal of EB. Our theoretical results and simulations suggest that
EB is a very appealing alternative to the conventional weighting estimators
that estimate the propensity score by maximum likelihood.Comment: 23 pages, 6 figures, Journal of Causal Inference 201
Cross-screening in observational studies that test many hypotheses
We discuss observational studies that test many causal hypotheses, either
hypotheses about many outcomes or many treatments. To be credible an
observational study that tests many causal hypotheses must demonstrate that its
conclusions are neither artifacts of multiple testing nor of small biases from
nonrandom treatment assignment. In a sense that needs to be defined carefully,
hidden within a sensitivity analysis for nonrandom assignment is an enormous
correction for multiple testing: in the absence of bias, it is extremely
improbable that multiple testing alone would create an association insensitive
to moderate biases. We propose a new strategy called "cross-screening",
different from but motivated by recent work of Bogomolov and Heller on
replicability. Cross-screening splits the data in half at random, uses the
first half to plan a study carried out on the second half, then uses the second
half to plan a study carried out on the first half, and reports the more
favorable conclusions of the two studies correcting using the Bonferroni
inequality for having done two studies. If the two studies happen to concur,
then they achieve Bogomolov-Heller replicability; however, importantly,
replicability is not required for strong control of the family-wise error rate,
and either study alone suffices for firm conclusions. In randomized studies
with a few hypotheses, cross-split screening is not an attractive method when
compared with conventional methods of multiplicity control, but it can become
attractive when hundreds or thousands of hypotheses are subjected to
sensitivity analyses in an observational study. We illustrate the technique by
comparing 46 biomarkers in individuals who consume large quantities of fish
versus little or no fish.Comment: 33 pages, 2 figures, 5 table
Multiple conditional randomization tests
We establish a general sufficient condition on constructing multiple "nearly
independent" conditional randomization tests, in the sense that the joint
distribution of their p-values is almost uniform under the global null. This
property implies that the tests are jointly valid and can be combined using
standard methods. Our theory generalizes existing techniques in the literature
that use independent treatments, sequential treatments, or post-randomization,
to construct multiple randomization tests. In particular, it places no
condition on the experimental design, allowing for arbitrary treatment
variables, assignment mechanisms and unit interference. The flexibility of this
framework is illustrated through developing conditional randomization tests for
lagged treatment effects in stepped-wedge randomized controlled trials. A
weighted Z-score test is further proposed to maximize the power when the tests
are combined. We compare the efficiency and robustness of the commonly used
mixed-effect models and the proposed conditional randomization tests using
simulated experiments and real trial data.Comment: 34 pages; Part of the original version of this paper can be found at
arXiv:2203.1098
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