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 method—cusp 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 Jeffreys’ 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 2000–2012 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 self‐schemas 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  = 34) or supportive psychotherapy (SPI) ( n  = 35) and followed at 1, 6, and 12 months post‐intervention. Results The IIP and supportive psychotherapy were equally effective in reducing eating disorder symptoms at 1 month post‐intervention, and changes were stable through the 12‐month follow‐up period. The IIP tended to be more effective in fostering development of positive self‐schemas, and the increase was stable over time. Regardless of baseline level, an increase in the number of positive self‐schemas between pre‐intervention and 1‐month post‐intervention predicted a decrease in desire for thinness and an increase in psychological well‐being and functional health over the same period. Discussion A cognitive behavioural intervention that focuses on increasing the number of positive self‐schemas 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 variance–covariance matrix in EM algorithm with interpolation method

The expectation–maximization (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 variance–covariance 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 variance–covariance 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

Meta-analysis of two studies with random effects?

A meta-analysis (MA) combines similar studies resulting in a larger number of subjects to improve the degree of belief in the significance declared. Its major purpose is to increase the number of observations and the associated statistical power, thereby increasing the precision for the estimates of the effect size as it relates to an association or an intervention. As commonly known, there are discrepancies between MAs and the large randomized clinical trials. The conclusions drawn are subject to bias because they are affected by the small size of clinical studies. However, large randomized clinical trials are the most reliable way of obtaining reproducible results; in other words, we expect the same results if we repeated the experiment. On the other hand, large trials do not guarantee that the protocol or the conclusions were appropriate. Although it is intuitive to believe an MA of similar trials is more likely to result in valid conclusions, studies show this is not always the case. By the same argument, adding studies with diverse protocols makes an MA less reliable. Because an MA is a summation, its reliability depends on the combined trials. Inclusion/exclusion criteria, conclusions, reliability of the results, and applicability for the conclusions affect the bias. Hence, we cannot declare that MA represents the final and accurate viewpoint on an area of research. Several statistical methods similar to what have been used to perform analyses on individual subject data have been modified to improve the reliability of MA.https://www.journals.elsevier.com/journal-of-minimally-invasive-gynecology2018-07-30hj2018Statistic