325 research outputs found
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/
Uncertainty and the Value of Diagnostic Information With Application to Axillary Lymph Node Dissection in Breast Cancer
In clinical decision making, it is common to ask whether, and how much, a diagnostic procedure is contributing to subsequent treatment decisions. Statistically, quantification of the value of the information provided by a diagnostic procedure can be carried out using decision trees with multiple decision points, representing both the diagnostic test and the subsequent treatments that may depend on the test\u27s results. This article investigates probabilistic sensitivity analysis approaches for exploring and communicating parameter uncertainty in such decision trees. Complexities arise because uncertainty about a model\u27s inputs determines uncertainty about optimal decisions at all decision nodes of a tree. We present the expected utility solution strategy for multistage decision problems in the presence of uncertainty on input parameters, propose a set of graphical displays and summarization tools for probabilistic sensitivity analysis in multistage decision trees, and provide an application to axillary lymph node dissection in breast cancer
Defining Replicability of Prediction Rules
In this article I propose an approach for defining replicability for
prediction rules. Motivated by a recent NAS report, I start from the
perspective that replicability is obtaining consistent results across studies
suitable to address the same prediction question, each of which has obtained
its own data. I then discuss concept and issues in defining key elements of
this statement. I focus specifically on the meaning of "consistent results" in
typical utilization contexts, and propose a multi-agent framework for defining
replicability, in which agents are neither partners nor adversaries. I recover
some of the prevalent practical approaches as special cases. I hope to provide
guidance for a more systematic assessment of replicability in machine learning
COMBINATIONAL MIXTURES OF MULTIPARAMETER DISTRIBUTIONS
We introduce combinatorial mixtures - a flexible class of models for inference on mixture distributions whose component have multidimensional parameters. The key idea is to allow each element of the component-specific parameter vectors to be shared by a subset of other components. This approach allows for mixtures that range from very flexible to very parsimonious, and unifies inference on component-specific parameters with inference on the number of components. We develop Bayesian inference and computation approaches for this class of distributions, and illustrate them in an application. This work was originally motivated by the analysis of cancer subtypes: in terms of biological measures of interest, subtypes may be characterized by differences in location, scale, correlations or any of the combinations. We illustrate our approach using data on molecular subtypes of lung cancer
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