5,734 research outputs found
Bayesian nonparametric models for spatially indexed data of mixed type
We develop Bayesian nonparametric models for spatially indexed data of mixed
type. Our work is motivated by challenges that occur in environmental
epidemiology, where the usual presence of several confounding variables that
exhibit complex interactions and high correlations makes it difficult to
estimate and understand the effects of risk factors on health outcomes of
interest. The modeling approach we adopt assumes that responses and confounding
variables are manifestations of continuous latent variables, and uses
multivariate Gaussians to jointly model these. Responses and confounding
variables are not treated equally as relevant parameters of the distributions
of the responses only are modeled in terms of explanatory variables or risk
factors. Spatial dependence is introduced by allowing the weights of the
nonparametric process priors to be location specific, obtained as probit
transformations of Gaussian Markov random fields. Confounding variables and
spatial configuration have a similar role in the model, in that they only
influence, along with the responses, the allocation probabilities of the areas
into the mixture components, thereby allowing for flexible adjustment of the
effects of observed confounders, while allowing for the possibility of residual
spatial structure, possibly occurring due to unmeasured or undiscovered
spatially varying factors. Aspects of the model are illustrated in simulation
studies and an application to a real data set
On Partial Identification of the Pure Direct Effect
In causal mediation analysis, nonparametric identification of the pure
(natural) direct effect typically relies on, in addition to no unobserved
pre-exposure confounding, fundamental assumptions of (i) so-called
"cross-world-counterfactuals" independence and (ii) no exposure- induced
confounding. When the mediator is binary, bounds for partial identification
have been given when neither assumption is made, or alternatively when assuming
only (ii). We extend existing bounds to the case of a polytomous mediator, and
provide bounds for the case assuming only (i). We apply these bounds to data
from the Harvard PEPFAR program in Nigeria, where we evaluate the extent to
which the effects of antiretroviral therapy on virological failure are mediated
by a patient's adherence, and show that inference on this effect is somewhat
sensitive to model assumptions.Comment: 24 pages, 4 figure
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