62 research outputs found
Getting Unstuck - Stretching out of our comfort zones. A research report
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A hierarchical Bayesian model of the rate of non-acceptable in-patient hospital utilization.
Full text linkA Non-Acceptable Claim (NAC) is an insurance claim for an unnecessary hospital stay. This study establishes a statistical model which predicts the NAC rate. The model supplements current insurer programs that rely on detailed audits of patient medical records. Hospital discharge claim records are used as inputs in the statistical model to predict retrospectively the probability that a hospital admission is non-acceptable. The data obtained from each claim record include: primary diagnosis code, age, sex, length of stay, admission type, and type of service. A full Bayesian hierarchical logistic regression model is used with regression coefficients that are random across the primary diagnosis codes. The NAC prediction model assumes that the logits are linear functions of the data with normally distributed errors. The model is first estimated on one data set and then validated with data collected at a later time. Using the model data, the posterior distributions of the parameters are estimated by the Gibbs sampler. A novel use of the Hastings-Metropolis algorithm is used to obtain the posterior distribution of the logits. A set of estimated regression coefficients is derived for each primary diagnosis code for the model data. The signs and magnitudes of the estimated parameters are consistent with initial notions of non-acceptable utilization. For example, the probability that a claim is NAC decreases with an increase in the length of the hospital stay, while the probability increases if the type of service is medical. NACs are predicted by the posterior probabilities of a claim being a NAC. The hierarchical Bayesian model provides better fits and predictions than standard methods which pool across primary diagnosis codes. These predictions allow results to be summarized by hospital, insured group, or other aggregate forms. The integration of the model into an insurer's cost containment program is simple and inexpensive to maintain.Ph.D.Health and Environmental SciencesHealth care managementPure SciencesStatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/129305/2/9423302.pd
Heavy-tailed longitudinal data modeling using copulas
No full textIn this paper, we consider "heavy-tailed" data, that is, data where extreme values are likely to occur. Heavy-tailed data have been analyzed using flexible distributions such as the generalized beta of the second kind, the generalized gamma and the Burr. These distributions allow us to handle data with either positive or negative skewness, as well as heavy tails. Moreover, it has been shown that they can also accommodate cross-sectional regression models by allowing functions of explanatory variables to serve as distribution parameters. The objective of this paper is to extend this literature to accommodate longitudinal data, where one observes repeated observations of cross-sectional data. Specifically, we use copulas to model the dependencies over time, and heavy-tailed regression models to represent the marginal distributions. We also introduce model exploration techniques to help us with the initial choice of the copula and a goodness-of-fit test of elliptical copulas for model validation. In a longitudinal data context, we argue that elliptical copulas will be typically preferred to the Archimedean copulas. To illustrate our methods, Wisconsin nursing homes utilization data from 1995 to 2001 are analyzed. These data exhibit long tails and negative skewness and so help us to motivate the need for our new techniques. We find that time and the nursing home facility size as measured through the number of beds and square footage are important predictors of future utilization. Moreover, using our parametric model, we provide not only point predictions but also an entire predictive distribution.
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