3,650 research outputs found
Cusp Catastrophe Regression and Its Application in Public Health and Behavioral Research
The cusp catastrophe model is an innovative approach for investigating a phenomenon that consists of both continuous and discrete changes in one modeling framework. However, its application to empirical health and behavior data has been hindered by the complexity in data-model fit. In this study, we reported our work in the development of a new modeling methodâcusp catastrophe regression (RegCusp in short) by casting the cusp catastrophe into a statistical regression. With the RegCusp approach, unbiased model parameters can be estimated with the maximum likelihood estimation method. To validate the RegCusp method, a series of simulations were conducted to demonstrate the unbiasedness of parameter estimation. Since the estimated residual variance with the Fisher information matrix method was over-dispersed, a bootstrap re-sampling procedure was developed and used as a remedy. We also demonstrate the practical applicability of the RegCusp with empirical data from an NIH-funded project to evaluate an HIV prevention intervention program to educate adolescents in the Bahamas for condom use. Study findings indicated that the model parameters estimated with RegCusp were practically more meaningful than those estimated with comparable methods, especially the estimated cusp point
Robustness of the shrinkage estimator for the relative potency in the combination of multivariate bioassays
ABSTRACTThis article investigates the robustness of the shrinkage Bayesian estimator for the relative potency parameter in the combinations of multivariate bioassays proposed in Chen et al. (1999), which incorporated prior information on the model parameters based on Jeffreysâ rules. This investigation is carried out for the families of t-distribution and Cauchy-distribution based on the characteristics of bioassay theory since the t-distribution approaches the normal distribution which is the most commonly used distribution in the applications of bioassay as the degrees of freedom increases and the t-distribution approaches the Cauchy-distribution as the degrees of freedom approaches 1 which is also an important distribution in bioassay. A real data is used to illustrate the application of this investigation. This analysis further supports the application of the shrinkage Bayesian estimator to the theory of bioassay along with the empirical Bayesian estimator
Mixture of linear experts model for censored data: A novel approach with scale-mixture of normal distributions
The classical mixture of linear experts (MoE) model is one of the widespread
statistical frameworks for modeling, classification, and clustering of data.
Built on the normality assumption of the error terms for mathematical and
computational convenience, the classical MoE model has two challenges: 1) it is
sensitive to atypical observations and outliers, and 2) it might produce
misleading inferential results for censored data. The paper is then aimed to
resolve these two challenges, simultaneously, by proposing a novel robust MoE
model for model-based clustering and discriminant censored data with the
scale-mixture of normal class of distributions for the unobserved error terms.
Based on this novel model, we develop an analytical expectation-maximization
(EM) type algorithm to obtain the maximum likelihood parameter estimates.
Simulation studies are carried out to examine the performance, effectiveness,
and robustness of the proposed methodology. Finally, real data is used to
illustrate the superiority of the new model.Comment: 21 pages
Comparing geographic area-based and classical population-based incidence and prevalence rates, and their confidence intervals
To quantify the HIV epidemic, the classical population-based prevalence and incidence rates (P rates) are the two
most commonly used measures used for policy interventions. However, these P rates ignore the heterogeneity of
the size of geographic regionwhere the population resides. It is intuitive that with the sameP rates, the likelihood
for HIV can be much greater to spread in a population residing in a crowed small urban area than the same
number of population residing in a large rural area. With this limitation, Chen and Wang (2017) proposed the
geographic area-based rates (G rates) to complement the classical P rates. They analyzed the 2000â2012 US
data on new HIV infections and persons living with HIV and found, as compared with other methods, using G
rates enables researchers to more quickly detect increases in HIV rates. This capacity to reveal increasing rates
in a more efficient and timely manner is a crucial methodological contribution to HIV research. To enhance
this newly proposed concept of G rates, this article presents a discussion of 3 areas for further development of
this important concept: (1) analysis of global HIV epidemic data using the newly proposed G rates to capture
the changes globally; (2) development of the associated population density-based rates (D rates) to incorporate
the heterogeneities from both geographical area and total population-at-risk; and (3) development of methods
to calculate variances and confidence intervals for the P rates, G rates, and D rates to capture the variability of
these indices.http: //ees.elsevier.com/pmedam2017Statistic
Robustness of the shrinkage estimator for the relative potency in the combination of multivariate bioassays
This paper investigates the robustness of the shrinkage Bayesian estimator for the
relative potency parameter in the combinations of multivariate bioassays proposed
in Chen et al.(1999), which incorporated prior information on the model parame-
ters based on Je reys' rules. This investigation is carried out for the families of
t-distribution and Cauchy-distribution based on the characteristics of bioassay the-
ory since the t-distribution approaches the normal distribution which is the most
commonly used distribution in the applications of bioassay as the degrees of freedom
increases and the t-distribution approaches the Cauchy-distribution as the degrees
of freedom approaches 1 which is also an important distribution in bioassay. A real
data is used to illustrate the application of this investigation. This analysis further
supports the application of the shrinkage Bayesian estimator to the theory of bioassay
along with the empirical Bayesian estimator.http://www.tandfonline.com/loi/lsta202017-09-30hb2016Statistic
Longitudinal effects of metabolic syndrome on Alzheimer and vascular related brain pathology.
Background/aimsThis study examines the longitudinal effect of metabolic syndrome (MetS) on brain-aging indices among cognitively normal (CN) and amnestic mild cognitive impairment (aMCI) groups [single-domain aMCI (saMCI) and multiple-domain aMCI (maMCI)].MethodsThe study population included 739 participants (CN = 226, saMCI = 275, and maMCI = 238) from the Alzheimer's Disease Neuroimaging Initiative, a clinic-based, multi-center prospective cohort. Confirmatory factor analysis was employed to determine a MetS latent composite score using baseline data of vascular risk factors. We examined the changes of two Alzheimer's disease (AD) biomarkers, namely [(18)F]fluorodeoxyglucose (FDG)-positron emission tomography (PET) regions of interest and medial temporal lobe volume over 5 years. A cerebrovascular aging index, cerebral white matter (cWM) volume, was examined as a comparison.ResultsThe vascular risk was similar in all groups. Applying generalized estimating equation modeling, all brain-aging indices declined significantly over time. Higher MetS scores were associated with a faster decline of cWM in the CN and maMCI groups but with a slower decrement of regional glucose metabolism in FDG-PET in the saMCI and maMCI groups.ConclusionAt the very early stage of cognitive decline, the vascular burden such as MetS may be in parallel with or independent of AD pathology in contributing to cognitive impairment in terms of accelerating the disclosure of AD pathology
A Randomized Clinical Trial of an Identity Intervention Programme for Women with Eating Disorders
Objective Findings of a randomized trial of an identity intervention programme (IIP) designed to build new positive selfâschemas that are separate from other conceptions of the self in memory as the means to promote improved health in women diagnosed with eating disorders are reported. Method After baseline data collection, women with anorexia nervosa or bulimia nervosa were randomly assigned to IIP ( n â=â34) or supportive psychotherapy (SPI) ( n â=â35) and followed at 1, 6, and 12âmonths postâintervention. Results The IIP and supportive psychotherapy were equally effective in reducing eating disorder symptoms at 1âmonth postâintervention, and changes were stable through the 12âmonth followâup period. The IIP tended to be more effective in fostering development of positive selfâschemas, and the increase was stable over time. Regardless of baseline level, an increase in the number of positive selfâschemas between preâintervention and 1âmonth postâintervention predicted a decrease in desire for thinness and an increase in psychological wellâbeing and functional health over the same period. Discussion A cognitive behavioural intervention that focuses on increasing the number of positive selfâschemas may be central to improving emotional health in women with anorexia nervosa and bulimia nervosa. Copyright © 2012 John Wiley & Sons, Ltd and Eating Disorders Association.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/96416/1/erv2195.pd
Efficient and direct estimation of the varianceâcovariance matrix in EM algorithm with interpolation method
The expectationâmaximization (EM) algorithm is a seminal method to calculate the maximum likelihood estimators (MLEs) for incomplete data. However, one drawback of this algorithm is that the asymptotic varianceâcovariance matrix of the MLE is not automatically produced. Although there are several methods proposed to resolve this drawback, limitations exist for these methods. In this paper, we propose an innovative interpolation procedure to directly estimate the asymptotic varianceâcovariance matrix of the MLE obtained by the EM algorithm. Specifically we make use of the cubic spline interpolation to approximate the first-order and the second-order derivative functions in the Jacobian and Hessian matrices from the EM algorithm. It does not require iterative procedures as in other previously proposed numerical methods, so it is computationally efficient and direct. We derive the truncation error bounds of the functions theoretically and show that the truncation error diminishes to zero as the mesh size approaches zero. The optimal mesh size is derived as well by minimizing the global error. The accuracy and the complexity of the novel method is compared with those of the well-known SEM method. Two numerical examples and a real data are used to illustrate the accuracy and stability of this novel method.The National Research Foundation of South Africa and the South African Medical Research Council (SAMRC).http://www.elsevier.com/locate/jspihj2022Statistic
Bayesian inference for stochastic cusp catastrophe model with partially observed data
The purpose of this paper is to develop a data augmentation technique for statistical
inference concerning stochastic cusp catastrophe model subject to missing data and partially observed
observations. We propose a Bayesian inference solution that naturally treats missing observations as
parameters and we validate this novel approach by conducting a series of Monte Carlo simulation
studies assuming the cusp catastrophe model as the underlying model. We demonstrate that this
Bayesian data augmentation technique can recover and estimate the underlying parameters from the
stochastic cusp catastrophe model.South Africa DST-NRF-SAMRC SARChI Research Chair in Biostatistics.https://www.mdpi.com/journal/mathematicsam2022Statistic
Robust Bayesian nonlinear mixedâeffects modeling of time to positivity in tuberculosis trials
Early phase 2 tuberculosis (TB) trials are conducted to characterize the early bactericidal activity (EBA) of antiâTB drugs. The EBA of antiâTB drugs has conventionally been calculated as the rate of decline in colony forming unit (CFU) count during the first 14 days of treatment. The measurement of CFU count, however, is expensive and prone to contamination. Alternatively to CFU count, time to positivity (TTP), which is a potential biomarker for longâterm efficacy of antiâTB drugs, can be used to characterize EBA. The current Bayesian nonlinear mixedâeffects (NLME) regression model for TTP data, however, lacks robustness to gross outliers that often are present in the data. The conventional way of handling such outliers involves their identification by visual inspection and subsequent exclusion from the analysis. However, this process can be questioned because of its subjective nature. For this reason, we fitted robust versions of the Bayesian nonlinear mixedâeffects regression model to a wide range of TTP datasets. The performance of the explored models was assessed through model comparison statistics and a simulation study. We conclude that fitting a robust model to TTP data obviates the need for explicit identification and subsequent âdeletionâ of outliers but ensures that gross outliers exert no undue influence on model fits. We recommend that the current practice of fitting conventional normal theory models be abandoned in favor of fitting robust models to TTP data.http://wileyonlinelibrary.com/journal/pst2019-09-01hj2018Statistic
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