Use Of Semi-parametric Models Research Articles

Multivariate lifetime data in presence of censoring and covariates: Use of semiparametric models under a Bayesian approach

A generalization of the popular proportional hazards model introduced by Cox (1972) is given by the class of semiparametric or transformation models to be used in the analysis of lifetime data in presence of censored data and covariates. In this study, we consider the use of semiparametric (transformation models) for the situation where there are two or more responses associated to the same individual or unit. We assume a hierarchical Bayesian analysis for semiparametric models considering the complete likelihood function obtained from the transformation models considering the unknown hazard functions as unknown latent variables and Markov Chain Monte Carlo (MCMC) methods to get the posterior summaries of interest. The dependence between multivariate responses for the same individual is captured by the introduction of another latent variable or frailty. Illustrations of the proposed methodology are presented considering two medical multivariate lifetime data sets.

Linking watershed nutrient loading to estuary water quality with generalized additive models.

Evaluating estuary water quality responses to reductions (or increases) in nutrient loading attributed to on the ground management actions can be challenging due to the strong influence of environmental drivers on nutrient loads and non-linear relationships. This study applied generalized additive models to calculate watershed nutrient loads and assess responses in estuary water quality to seasonally-adjusted freshwater inflow and flow-adjusted nutrient loads in Lavaca Bay, Texas. Lavaca Bay is a secondary embayment on the Texas coast displaying early potential for eutrophication and water quality degradation. Use of flow-adjusted nutrient loads allowed the study to evaluate the response in water quality to changes in nutrient loads driven by anthropogenic sources. Cross-validation indicated that, despite data constraints, semiparametric models performed well at nutrient load prediction. Based on these models, delivered annual nutrient loads varied substantially from year to year. In contrast, minimal changes in flow-normalized loads indicate that nutrient loadings were driven by natural variation in precipitation and runoff as opposed to changes in management of nonpoint sources. Models indicated no evidence of long-term changes in dissolved oxygen or chlorophyll-a within Lavaca Bay. However, site specific long-term increases in both organic and inorganic nitrogen are concerning for their potential to fuel eutrophication. Further analysis found freshwater inflow had strong influences on nutrient and chlorophyll-a concentrations but there was no evidence that changes in watershed nutrient loading explained additional variation in dissolved oxygen and limited evidence that watershed nutrient loadings explained chlorophyll-a concentrations. In addition to providing a baseline assessment of watershed nutrient loading and water quality responses in the Lavaca Bay watershed, this study provides methodological support for the use of semiparametric models in load regression models and estuary assessments.

Evaluation of Multiple Failure Time Analyses of Observational Data in Patients Treated for HIV

The development of protease inhibitors and nonnucleoside reverse transcriptase inhibitors has substantially increased the number of combinations available for multi-drug therapies in human immunodeficiency virus (HIV) infection. Unfortunately, all antiretroviral therapies lose efficacy over time or induce side effects, thus making secondary and tertiary alternatives necessary. With the multiplicity of multi-drug combination therapies, the challenge is to determine which multi-drug combination to use as initial therapy and which to use as subsequent therapy to maximize survival. No standard methodologic approach has been developed to answer this question within the context of observational clinical HIV data. We demonstrate the use of semi-parametric models employing repeated, multiple failure time analysis to compare the relative efficacy of treatments containing zidovudine, stavudine, or other multi-drug combinations for patients in the CHORUS (Collaborations in HIV Outcomes Research - US) database.

The practical use of semiparametric models in field trials

This article examines the practical use of semiparametric models in the analysis of field trials—that is, models with parameterized treatment effects and additive terms derived by a data-driven approach using a locally weighted running line smoother (loess). We discuss graphical methods to identify spatial structure in the data and model selection procedures to choose the degree of smoothing. Once the spatial part of the model has been chosen, hypotheses about the treatment effects may be tested. Semiparametric models are used to analyze two barley field trials exhibiting spatial trends. The first has a single experimental treatment and a row-column design. The second has a split-plot design, and we use a semiparametric model which accounts for the randomization at the different strata of this design. We compare the semiparametric analyses with classical analyses of variance and with alternative spatial models. We find that semiparametric models give a good insight into spatial variation in the field and can improve the precision of parameter estimates.

Semi-parametric modelling in finance: theoretical foundations

The benchmark theory of mathematical finance is the Black-Scholes-Merton theory, based on Brownian motion as the driving noise process for asset prices. Here the distributions of returns of the assets in a portfolio are multivariate normal. The two most obvious limitations here concern symmetry and thin tails, neither being consistent with real data. The most common replacements for the multinormal are parametric—stable, generalized hyperbolic, variance gamma. In this paper we advocate the use of semi-parametric models for distributions, where the mean vector μ and covariance Σ are parametric components and the so-called density generator (function) g is the non-parametric component. We work mainly within the family of elliptically contoured distributions, focusing particularly on normal variance mixtures with self-decomposable mixing distributions. We show how the parametric cases can be treated in a unified, systematic way within the non-parametric framework and obtain the density generators for the most important cases.