6,058 research outputs found
A Review on Joint Models in Biometrical Research
In some fields of biometrical research joint modelling of longitudinal measures and event time data has become very popular. This article reviews the work in that area of recent fruitful research by classifying approaches on joint models in three categories: approaches with focus on serial trends, approaches with focus on event time data and approaches with equal focus on both outcomes. Typically longitudinal measures and event time data are modelled jointly by introducing shared random effects or by considering conditional distributions together with marginal distributions. We present the approaches in an uniform nomenclature, comment on sub-models applied to longitudinal measures and event time data outcomes individually and exemplify applications in biometrical research
Quantile regression for mixed models with an application to examine blood pressure trends in China
Cardiometabolic diseases have substantially increased in China in the past 20
years and blood pressure is a primary modifiable risk factor. Using data from
the China Health and Nutrition Survey, we examine blood pressure trends in
China from 1991 to 2009, with a concentration on age cohorts and urbanicity.
Very large values of blood pressure are of interest, so we model the
conditional quantile functions of systolic and diastolic blood pressure. This
allows the covariate effects in the middle of the distribution to vary from
those in the upper tail, the focal point of our analysis. We join the
distributions of systolic and diastolic blood pressure using a copula, which
permits the relationships between the covariates and the two responses to share
information and enables probabilistic statements about systolic and diastolic
blood pressure jointly. Our copula maintains the marginal distributions of the
group quantile effects while accounting for within-subject dependence, enabling
inference at the population and subject levels. Our population-level regression
effects change across quantile level, year and blood pressure type, providing a
rich environment for inference. To our knowledge, this is the first quantile
function model to explicitly model within-subject autocorrelation and is the
first quantile function approach that simultaneously models multivariate
conditional response. We find that the association between high blood pressure
and living in an urban area has evolved from positive to negative, with the
strongest changes occurring in the upper tail. The increase in urbanization
over the last twenty years coupled with the transition from the positive
association between urbanization and blood pressure in earlier years to a more
uniform association with urbanization suggests increasing blood pressure over
time throughout China, even in less urbanized areas. Our methods are available
in the R package BSquare.Comment: Published at http://dx.doi.org/10.1214/15-AOAS841 in the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
A Fully Nonparametric Modelling Approach to Binary Regression
We propose a general nonparametric Bayesian framework for binary regression,
which is built from modeling for the joint response-covariate distribution. The
observed binary responses are assumed to arise from underlying continuous
random variables through discretization, and we model the joint distribution of
these latent responses and the covariates using a Dirichlet process mixture of
multivariate normals. We show that the kernel of the induced mixture model for
the observed data is identifiable upon a restriction on the latent variables.
To allow for appropriate dependence structure while facilitating
identifiability, we use a square-root-free Cholesky decomposition of the
covariance matrix in the normal mixture kernel. In addition to allowing for the
necessary restriction, this modeling strategy provides substantial
simplifications in implementation of Markov chain Monte Carlo posterior
simulation. We present two data examples taken from areas for which the
methodology is especially well suited. In particular, the first example
involves estimation of relationships between environmental variables, and the
second develops inference for natural selection surfaces in evolutionary
biology. Finally, we discuss extensions to regression settings with
multivariate ordinal responses
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