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Bayesian Model Selection Approach to Multiple Change-Points Detection with Non-Local Prior Distributions
We propose a Bayesian model selection (BMS) boundary detection procedure using non-local prior distributions for a sequence of data with multiple systematic mean changes. By using the non-local priors in the BMS framework, the BMS method can effectively suppress the non-boundary spike points with large instantaneous changes. Further, we speedup the algorithm by reducing the multiple change points to a series of single change point detection problems. We establish the consistency of the estimated number and locations of the change points under various prior distributions. From both theoretical and numerical perspectives, we show that the non-local inverse moment prior leads to the fastest convergence rate in identifying the true change points on the boundaries. Extensive simulation studies are conducted to compare the BMS with existing methods, and our method is illustrated with application to the magnetic resonance imaging guided radiation therapy data
Generalized Quantile Treatment Effect: A Flexible Bayesian Approach Using Quantile Ratio Smoothing
We propose a new general approach for estimating the effect of a binary
treatment on a continuous and potentially highly skewed response variable, the
generalized quantile treatment effect (GQTE). The GQTE is defined as the
difference between a function of the quantiles under the two treatment
conditions. As such, it represents a generalization over the standard
approaches typically used for estimating a treatment effect (i.e., the average
treatment effect and the quantile treatment effect) because it allows the
comparison of any arbitrary characteristic of the outcome's distribution under
the two treatments. Following Dominici et al. (2005), we assume that a
pre-specified transformation of the two quantiles is modeled as a smooth
function of the percentiles. This assumption allows us to link the two quantile
functions and thus to borrow information from one distribution to the other.
The main theoretical contribution we provide is the analytical derivation of a
closed form expression for the likelihood of the model. Exploiting this result
we propose a novel Bayesian inferential methodology for the GQTE. We show some
finite sample properties of our approach through a simulation study which
confirms that in some cases it performs better than other nonparametric
methods. As an illustration we finally apply our methodology to the 1987
National Medicare Expenditure Survey data to estimate the difference in the
single hospitalization medical cost distributions between cases (i.e., subjects
affected by smoking attributable diseases) and controls.Comment: Published at http://dx.doi.org/10.1214/14-BA922 in the Bayesian
Analysis (http://projecteuclid.org/euclid.ba) by the International Society of
Bayesian Analysis (http://bayesian.org/
Hierarchical models for semi-competing risks data with application to quality of end-of-life care for pancreatic cancer
Readmission following discharge from an initial hospitalization is a key
marker of quality of health care in the United States. For the most part,
readmission has been used to study quality of care for patients with acute
health conditions, such as pneumonia and heart failure, with analyses typically
based on a logistic-Normal generalized linear mixed model. Applying this model
to the study readmission among patients with increasingly prevalent advanced
health conditions such as pancreatic cancer is problematic, however, because it
ignores death as a competing risk. A more appropriate analysis is to imbed such
studies within the semi-competing risks framework. To our knowledge, however,
no comprehensive statistical methods have been developed for cluster-correlated
semi-competing risks data. In this paper we propose a novel hierarchical
modeling framework for the analysis of cluster-correlated semi-competing risks
data. The framework permits parametric or non-parametric specifications for a
range of model components, including baseline hazard functions and
distributions for key random effects, giving analysts substantial flexibility
as they consider their own analyses. Estimation and inference is performed
within the Bayesian paradigm since it facilitates the straightforward
characterization of (posterior) uncertainty for all model parameters including
hospital-specific random effects. The proposed framework is used to study the
risk of readmission among 5,298 Medicare beneficiaries diagnosed with
pancreatic cancer at 112 hospitals in the six New England states between
2000-2009, specifically to investigate the role of patient-level risk factors
and to characterize variation in risk across hospitals that is not explained by
differences in patient case-mix
Generalized Quantile Treatment Effect
We propose a new general approach for estimating the effect of a binary treat-ment on a continuous and potentially highly skewed response variable, the generalized quantile treatment effect (GQTE). The GQTE is defined as the difference between a function of the quantiles under the two treatment conditions. As such, it represents a generalization over the standard approaches typically used for estimating a treatment effect (i.e., the average treatment effect and the quantile treatment effect) because it allows the comparison of any arbitrary characteristic of the outcome’s distribution under the two treatments. Following (Dominici et al., 2005), we assume that a pre-specified transformation of the two quantiles is modeled as a smooth function of the percentiles. This assumption allows us to link the two quantile functions and thus to borrow information from one distribution to the other. The main theoretical con-tribution we provide is the analytical derivation of a closed form expression for the likelihood of the model. Exploiting this result we propose a novel Bayesian inferential methodology for the GQTE. We show some finite sample properties of our approach through a simulation study which confirms that in some cases it performs better than other nonparametric methods. As an illustration we finally apply our methodology to the 1987 National Medicare Expenditure Survey data to estimate the difference in the single hospitalization medical cost distributions between cases (i.e., subjects affected by smoking attributable diseases) and controls
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