A vine copula mixed effect model for trivariate meta-analysis of diagnostic test accuracy studies accounting for disease prevalence

A bivariate copula mixed model has been recently proposed to synthesize diagnostic test accuracy studies and it has been shown that it is superior to the standard generalized linear mixed model in this context. Here, we call trivariate vine copulas to extend the bivariate meta-analysis of diagnostic test accuracy studies by accounting for disease prevalence. Our vine copula mixed model includes the trivariate generalized linear mixed model as a special case and can also operate on the original scale of sensitivity, specificity, and disease prevalence. Our general methodology is illustrated by re-analyzing the data of two published meta-analyses. Our study suggests that there can be an improvement on trivariate generalized linear mixed model in fit to data and makes the argument for moving to vine copula random effects models especially because of their richness, including reflection asymmetric tail dependence, and computational feasibility despite their three dimensionality

Eliciting Dirichlet and Gaussian copula prior distributions for multinomial models

In this paper, we propose novel methods of quantifying expert opinion about prior distributions for multinomial models. Two different multivariate priors are elicited using median and quartile assessments of the multinomial probabilities. First, we start by eliciting a univariate beta distribution for the probability of each category. Then we elicit the hyperparameters of the Dirichlet distribution, as a tractable conjugate prior, from those of the univariate betas through various forms of reconciliation using least-squares techniques. However, a multivariate copula function will give a more flexible correlation structure between multinomial parameters if it is used as their multivariate prior distribution. So, second, we use beta marginal distributions to construct a Gaussian copula as a multivariate normal distribution function that binds these marginals and expresses the dependence structure between them. The proposed method elicits a positive-definite correlation matrix of this Gaussian copula. The two proposed methods are designed to be used through interactive graphical software written in Java

A copula model for marked point processes

The final publication (Diao, Liqun, Richard J. Cook, and Ker-Ai Lee. (2013) A copula model for marked point processes. Lifetime Data Analysis, 19(4): 463-489) is available at Springer via http://dx.doi.org/10.1007/s10985-013-9259-3Many chronic diseases feature recurring clinically important events. In addition, however, there often exists a random variable which is realized upon the occurrence of each event reflecting the severity of the event, a cost associated with it, or possibly a short term response indicating the effect of a therapeutic intervention. We describe a novel model for a marked point process which incorporates a dependence between continuous marks and the event process through the use of a copula function. The copula formulation ensures that event times can be modeled by any intensity function for point processes, and any multivariate model can be specified for the continuous marks. The relative efficiency of joint versus separate analyses of the event times and the marks is examined through simulation under random censoring. An application to data from a recent trial in transfusion medicine is given for illustration.Natural Sciences and Engineering Research Council of Canada (RGPIN 155849); Canadian Institutes for Health Research (FRN 13887); Canada Research Chair (Tier 1) – CIHR funded (950-226626

Caribbean-Wide, Long-Term Study of Seagrass Beds Reveals Local Variations, Shifts in Community Structure and Occasional Collapse

The CARICOMP monitoring network gathered standardized data from 52 seagrass sampling stations at 22 sites (mostly Thalassia testudinum-dominated beds in reef systems) across the Wider Caribbean twice a year over the period 1993 to 2007 (and in some cases up to 2012). Wide variations in community total biomass (285 to >2000 g dry m−2) and annual foliar productivity of the dominant seagrass T. testudinum (2000 g dry m−2) were found among sites. Solar-cycle related intra-annual variations in T. testudinum leaf productivity were detected at latitudes > 16°N. Hurricanes had little to no long-term effects on these well-developed seagrass communities, except for 1 station, where the vegetation was lost by burial below ∼1 m sand. At two sites (5 stations), the seagrass beds collapsed due to excessive grazing by turtles or sea-urchins (the latter in combination with human impact and storms). The low-cost methods of this regional-scale monitoring program were sufficient to detect long-term shifts in the communities, and fifteen (43%) out of 35 long-term monitoring stations (at 17 sites) showed trends in seagrass communities consistent with expected changes under environmental deterioration.UCR::Vicerrectoría de Investigación::Unidades de Investigación::Ciencias Básicas::Centro de Investigación en Ciencias del Mar y Limnología (CIMAR

Dependence modeling for multi‐type recurrent events via copulas

This is the peer reviewed version of the following article: Jooyoung Lee and Richard J. Cook, Dependence modeling for multi-type recurrent events via copulas, Statistics in Medicine (2019), 38(21): 4066–4082 which has been published in final form at https://doi.org/10.1002/sim.8283.This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.When several types of recurrent events may arise, interest often lies in marginal modeling and studying the nature of the dependence structure. In this paper, we propose a multivariate mixed-Poisson model with the dependence between events accommodated by type-specific random effects which are associated through use of a Gaussian copula. Such models retain marginal features with a simple interpretation, reflect the heterogeneity in risk for each type of event, and provide insight into the dependence between the different types of events. Semiparametric inference is proposed based on composite likelihood to avoid high dimensional integration. An application to a study of nutritional supplements in malnourished children is given in which the goal is to evaluate the reduction in the rate of several different kinds of infection.This research was supported by grants from the Natural Sciences and Engineering Research Council of Canada (RGPIN 155849) and the Canadian Institutes for Health Research (FRN 13887). Richard Cook is a Canada Research Chair in Statistical Methods for Health Research