786 research outputs found
A Bayesian view of doubly robust causal inference
In causal inference confounding may be controlled either through regression
adjustment in an outcome model, or through propensity score adjustment or
inverse probability of treatment weighting, or both. The latter approaches,
which are based on modelling of the treatment assignment mechanism and their
doubly robust extensions have been difficult to motivate using formal Bayesian
arguments, in principle, for likelihood-based inferences, the treatment
assignment model can play no part in inferences concerning the expected
outcomes if the models are assumed to be correctly specified. On the other
hand, forcing dependency between the outcome and treatment assignment models by
allowing the former to be misspecified results in loss of the balancing
property of the propensity scores and the loss of any double robustness. In
this paper, we explain in the framework of misspecified models why doubly
robust inferences cannot arise from purely likelihood-based arguments, and
demonstrate this through simulations. As an alternative to Bayesian propensity
score analysis, we propose a Bayesian posterior predictive approach for
constructing doubly robust estimation procedures. Our approach appropriately
decouples the outcome and treatment assignment models by incorporating the
inverse treatment assignment probabilities in Bayesian causal inferences as
importance sampling weights in Monte Carlo integration.Comment: Author's original version. 21 pages, including supplementary materia
Testing for an ignorable sampling bias under random double truncation
In clinical and epidemiological research doubly truncated data often appear. This is the case, for instance, when the data registry is formed by interval sampling. Double truncation generally induces a sampling bias on the target variable, so proper corrections of ordinary estimation and inference procedures must be used. Unfortunately, the nonparametric maximum likelihood estimator
of a doubly truncated distribution has several drawbacks, like potential nonexistence and nonuniqueness issues, or large estimation variance. Interestingly, no correction for double truncation is needed when the sampling bias is ignorable, which may occur with interval sampling and other sampling designs. In such a case the ordinary empirical distribution function is a consistent and fully
efficient estimator that generally brings remarkable variance improvements compared to the nonparametric maximum likelihood estimator. Thus, identification of such situations is critical for the simple and efficient estimation of the target distribution. In this article, we introduce for the first time formal testing procedures for the null hypothesis of ignorable sampling bias with doubly truncated data. The asymptotic properties of the proposed test statistic are investigated. A bootstrap algorithm to approximate the null distribution of the test in practice is introduced. The finite sample performance of the method is studied in simulated scenarios. Finally, applications to data on onset for childhood cancer and Parkinson’s disease are given. Variance improvements in estimation are
discussed and illustrated.Agencia Estatal de InvestigaciĂłn | Ref. PID2020-118101GB-I0
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