Design of experiments for bivariate binary responses modelled by Copula functions

Optimal design for generalized linear models has primarily focused on univariate data. Often experiments are performed that have multiple dependent responses described by regression type models, and it is of interest and of value to design the experiment for all these responses. This requires a multivariate distribution underlying a pre-chosen model for the data. Here, we consider the design of experiments for bivariate binary data which are dependent. We explore Copula functions which provide a rich and flexible class of structures to derive joint distributions for bivariate binary data. We present methods for deriving optimal experimental designs for dependent bivariate binary data using Copulas, and demonstrate that, by including the dependence between responses in the design process, more efficient parameter estimates are obtained than by the usual practice of simply designing for a single variable only. Further, we investigate the robustness of designs with respect to initial parameter estimates and Copula function, and also show the performance of compound criteria within this bivariate binary setting.

Genome-wide association analysis identifies 11 risk variants associated with the asthma with hay fever phenotype

Background To date, no genome-wide association study (GWAS) has considered the combined phenotype of asthma with hay fever. Previous analyses of family data from the Tasmanian Longitudinal Health Study provide evidence that this phenotype has a stronger genetic cause than asthma without hay fever. Objective We sought to perform a GWAS of asthma with hay fever to identify variants associated with having both diseases. Methods We performed a meta-analysis of GWASs comparing persons with both physician-diagnosed asthma and hay fever (n = 6,685) with persons with neither disease (n = 14,091). Results At genome-wide significance, we identified 11 independent variants associated with the risk of having asthma with hay fever, including 2 associations reaching this level of significance with allergic disease for the first time: ZBTB10 (rs7009110; odds ratio [OR], 1.14; P = 4 × 10−9) and CLEC16A (rs62026376; OR, 1.17; P = 1 × 10−8). The rs62026376:C allele associated with increased asthma with hay fever risk has been found to be associated also with decreased expression of the nearby DEXI gene in monocytes. The 11 variants were associated with the risk of asthma and hay fever separately, but the estimated associations with the individual phenotypes were weaker than with the combined asthma with hay fever phenotype. A variant near LRRC32 was a stronger risk factor for hay fever than for asthma, whereas the reverse was observed for variants in/near GSDMA and TSLP. Single nucleotide polymorphisms with suggestive evidence for association with asthma with hay fever risk included rs41295115 near IL2RA (OR, 1.28; P = 5 × 10−7) and rs76043829 in TNS1 (OR, 1.23; P = 2 × 10−6). Conclusion By focusing on the combined phenotype of asthma with hay fever, variants associated with the risk of allergic disease can be identified with greater efficiency.

Univariate, bivariate, and multivariate methods in corpus-based lexicography : A study of synonymy

In this dissertation, I present an overall methodological framework for studying linguistic alternations, focusing specifically on lexical variation in denoting a single meaning, that is, synonymy. As the practical example, I employ the synonymous set of the four most common Finnish verbs denoting THINK, namely ajatella, miettiä, pohtia and harkita ‘think, reflect, ponder, consider’. As a continuation to previous work, I describe in considerable detail the extension of statistical methods from dichotomous linguistic settings (e.g., Gries 2003; Bresnan et al. 2007) to polytomous ones, that is, concerning more than two possible alternative outcomes. The applied statistical methods are arranged into a succession of stages with increasing complexity, proceeding from univariate via bivariate to multivariate techniques in the end. As the central multivariate method, I argue for the use of polytomous logistic regression and demonstrate its practical implementation to the studied phenomenon, thus extending the work by Bresnan et al. (2007), who applied simple (binary) logistic regression to a dichotomous structural alternation in English. The results of the various statistical analyses confirm that a wide range of contextual features across different categories are indeed associated with the use and selection of the selected think lexemes; however, a substantial part of these features are not exemplified in current Finnish lexicographical descriptions. The multivariate analysis results indicate that the semantic classifications of syntactic argument types are on the average the most distinctive feature category, followed by overall semantic characterizations of the verb chains, and then syntactic argument types alone, with morphological features pertaining to the verb chain and extra-linguistic features relegated to the last position. In terms of overall performance of the multivariate analysis and modeling, the prediction accuracy seems to reach a ceiling at a Recall rate of roughly two-thirds of the sentences in the research corpus. The analysis of these results suggests a limit to what can be explained and determined within the immediate sentential context and applying the conventional descriptive and analytical apparatus based on currently available linguistic theories and models. The results also support Bresnan’s (2007) and others’ (e.g., Bod et al. 2003) probabilistic view of the relationship between linguistic usage and the underlying linguistic system, in which only a minority of linguistic choices are categorical, given the known context – represented as a feature cluster – that can be analytically grasped and identified. Instead, most contexts exhibit degrees of variation as to their outcomes, resulting in proportionate choices over longer stretches of usage in texts or speech.

Short-window spectral analysis using AMVAR and multitaper methods: a comparison

We compare two popular methods for estimating the power spectrum from short data windows, namely the adaptive multivariate autoregressive (AMVAR) method and the multitaper method. By analyzing a simulated signal (embedded in a background Ornstein-Uhlenbeck noise process) we demonstrate that the AMVAR method performs better at detecting short bursts of oscillations compared to the multitaper method. However, both methods are immune to jitter in the temporal location of the signal. We also show that coherence can still be detected in noisy bivariate time series data by the AMVAR method even if the individual power spectra fail to show any peaks. Finally, using data from two monkeys performing a visuomotor pattern discrimination task, we demonstrate that the AMVAR method is better able to determine the termination of the beta oscillations when compared to the multitaper method.

Analysis of volatility transmissions in integrated and interconnected markets: The case of the Iberian and French markets

This paper models the mean and volatility spillovers of prices within the integrated Iberian and the interconnected Spanish and French electricity markets. Using the constant (CCC) and dynamic conditional correlation (DCC) bivariate models with three different specifications of the univariate variance processes, we study the extent to which increasing interconnection and harmonization in regulation have favoured price convergence. The data consist of daily prices calculated as the arithmetic mean of the hourly prices over a span from July 1st 2007 until February 29th 2012. The DCC model in which the variances of the univariate processes are specified with a VARMA(1,1) fits the data best for the integrated MIBEL whereas a CCC model with a GARCH(1,1) specification for the univariate variance processes is selected to model the price series in Spain and France. Results show that there are significant mean and volatility spillovers in the MIBEL, indicating strong interdependence between the two markets, while there is a weaker evidence of integration between the Spanish and French markets. We provide new evidence that the EU target of achieving a single electricity market largely depends on increasing trade between countries and homogeneous rules of market functioning.

Metrical dental analysis on golden monkey (Rhinopithecus roxellana)

Dental variation in the Chinese golden monkey (Rhinopithecus roxellana) is here evaluated by univariate, bivariate, and multivariate analyses. Allometric analyses indicate that canines and P3s are positively, but other dimensions negatively scaled to mandible and maxilla, and to body size. With the exception of the mesiodistal dimensions of I-1 and M-3, and the buccolingual dimension of Pq, mandibular dental variables show similar scaling relative to body size. Analysis of residuals shows that males have significantly larger canine, P-3 and buccolingual dimensions of the postcanine teeth (M-2 and M-3) than females. A significant difference in shape between the sexes is found in the buccolingual dimension of the upper teeth, but not in the mandible. Unlike the situation in some other species, Female golden monkeys do nor exhibit relatively larger postcanine teeth than males, in fact, the reverse is true, especially for M(2)s and M(3)s. The fact that most of the dental variables show low negative allometry to body size might be related a cold environment that has led to the development of larger body size with I-educed energy loss. When the raw data are examined by Discriminant Function Analysis the sexes are clearly distinguishable.

An Examination of Transformation Techniques to Investigate and Interpret Multivariate Geochemical Data Analysis: Tellus Case Study

This research aims to use the multivariate geochemical dataset, generated by the Tellus project, to investigate the appropriate use of transformation methods to maintain the integrity of geochemical data and inherent constrained behaviour in multivariate relationships. The widely used normal score transform is compared with the use of a stepwise conditional transform technique. The Tellus Project, managed by GSNI and funded by the Department of Enterprise Trade and Development and the EU’s Building Sustainable Prosperity Fund, involves the most comprehensive geological mapping project ever undertaken in Northern Ireland. Previous study has demonstrated spatial variability in the Tellus data but geostatistical analysis and interpretation of the datasets requires use of an appropriate methodology that reproduces the inherently complex multivariate relations. Previous investigation of the Tellus geochemical data has included use of Gaussian-based techniques. However, earth science variables are rarely Gaussian, hence transformation of data is integral to the approach. The multivariate geochemical dataset generated by the Tellus project provides an opportunity to investigate the appropriate use of transformation methods, as required for Gaussian-based geostatistical analysis. In particular, the stepwise conditional transform is investigated and developed for the geochemical datasets obtained as part of the Tellus project. The transform is applied to four variables in a bivariate nested fashion due to the limited availability of data. Simulation of these transformed variables is then carried out, along with a corresponding back transformation to original units. Results show that the stepwise transform is successful in reproducing both univariate statistics and the complex bivariate relations exhibited by the data. Greater fidelity to multivariate relationships will improve uncertainty models, which are required for consequent geological, environmental and economic inferences.

Accuracy of LightCycler SeptiFast for the detection and identification of pathogens in the blood of patients with suspected sepsis: a systematic review and meta-analysis

Purpose: There is an urgent need to develop diagnostic tests to improve the detection of pathogens causing life-threatening infection (sepsis). SeptiFast is a CE-marked multi-pathogen real-time PCR system capable of detecting DNA sequences of bacteria and fungi present in blood samples within a few hours. We report here a systematic review and meta-analysis of diagnostic accuracy studies of SeptiFast in the setting of suspected sepsis.

Methods: A comprehensive search strategy was developed to identify studies that compared SeptiFast with blood culture in suspected sepsis. Methodological quality was assessed using QUADAS. Heterogeneity of studies was investigated using a coupled forest plot of sensitivity and specificity and a scatter plot in receiver operator characteristic space. Bivariate model method was used to estimate summary sensitivity and specificity.

Results: From 41 phase III diagnostic accuracy studies, summary sensitivity and specificity for SeptiFast compared with blood culture were 0.68 (95 % CI 0.63–0.73) and 0.86 (95 % CI 0.84–0.89) respectively. Study quality was judged to be variable with important deficiencies overall in design and reporting that could impact on derived diagnostic accuracy metrics.

Conclusions: SeptiFast appears to have higher specificity than sensitivity, but deficiencies in study quality are likely to render this body of work unreliable. Based on the evidence presented here, it remains difficult to make firm recommendations about the likely clinical utility of SeptiFast in the setting of suspected sepsis.

Relationships between Religion and Two Forms of Homonegativity in Europe—A Multilevel Analysis of Effects of Believing, Belonging and Religious Practice

This paper examines relationships between religion and two forms of homonegativity
across 43 European countries using a bivariate response binary logistic multilevel model. The model analyzes effects of religious believing, belonging and practice on two response variables: a) a moral rejection of homosexuality as a practice and b) intolerance toward homosexuals as a group. The findings indicate that both forms of homonegativity are prevalent in Europe. Traditional doctrinal religious believing (belief in a personal God) is positively related to a moral rejection of homosexuality but to a much lesser extent associated with intolerance toward homosexuals as a group. Members of religious denominations are more likely than non-members to reject homosexuality as morally wrong and to reject homosexuals as neighbors. The analysis found significant differences between denominations that are likely context-dependent. Attendance at religious services is positively related to homonegativity in a majority of countries. The findings vary considerably across countries: Religion is more strongly related to homonegativity in Western than in Eastern Europe. In the post-soviet countries homonegativity appears to be largely a secular phenomenon. National contexts of high religiosity, high perceived government corruption, high income inequality and shortcomings in the implementation of gay rights in the countries’ legislations are statistically related to higher levels of both moralistic homonegativity and intolerance toward homosexuals as a group.

Problems of allometric scaling analysis: examples from mammalian reproductive biology.

Biological scaling analyses employing the widely used bivariate allometric model are beset by at least four interacting problems: (1) choice of an appropriate best-fit line with due attention to the influence of outliers; (2) objective recognition of divergent subsets in the data (allometric grades); (3) potential restrictions on statistical independence resulting from phylogenetic inertia; and (4) the need for extreme caution in inferring causation from correlation. A new non-parametric line-fitting technique has been developed that eliminates requirements for normality of distribution, greatly reduces the influence of outliers and permits objective recognition of grade shifts in substantial datasets. This technique is applied in scaling analyses of mammalian gestation periods and of neonatal body mass in primates. These analyses feed into a re-examination, conducted with partial correlation analysis, of the maternal energy hypothesis relating to mammalian brain evolution, which suggests links between body size and brain size in neonates and adults, gestation period and basal metabolic rate. Much has been made of the potential problem of phylogenetic inertia as a confounding factor in scaling analyses. However, this problem may be less severe than suspected earlier because nested analyses of variance conducted on residual variation (rather than on raw values) reveals that there is considerable variance at low taxonomic levels. In fact, limited divergence in body size between closely related species is one of the prime examples of phylogenetic inertia. One common approach to eliminating perceived problems of phylogenetic inertia in allometric analyses has been calculation of 'independent contrast values'. It is demonstrated that the reasoning behind this approach is flawed in several ways. Calculation of contrast values for closely related species of similar body size is, in fact, highly questionable, particularly when there are major deviations from the best-fit line for the scaling relationship under scrutiny.

A zooarchaeological analysis of a late Dorset faunal assemblage from the KcFs-2 site (Nunavik, Quebec).

Ce mémoire consiste en une analyse zooarchéologique d’un assemblage faunique provenant d’un site Dorsétien des Îles Nuvuk dans l’Arctique canadien. Les données fauniques ont été analysées statistiquement en appliquant des indices d’utilité économique et des indices de densité des os. Une étude concernant le niveau de conservation de l’assemblage a révélé peu d’évidence de modification taphonomique des spécimens. Les analyses fauniques ont permis d’identifier une stratégie de subsistance de type généraliste et basée sur l’exploitation de mammifères marins, surtout des phoques annelés, pratiquée par les occupants du site de KcFs-2. Une prédominance d’individus immatures (phoques annelés) dans l’assemblage indique une abondance de ressources marines dans les régions du nord de la Baie d’Hudson et du détroit d’Hudson au moment de l’occupation, ce qui est aussi manifeste dans des études antérieures concernant les économies des peuples du Paléoesquimau tardif pour la période donnée. L’occupation du site de KcFs-2 s’est produite durant la période du Dorsétien récent au Nunavik (1500-800 B.P.), et la séquence est définie comme ayant été multi-saisonnière (de l’hiver à l’été). L’analyse des produits de l’industrie osseuse (têtes de harpons et sculptures en ivoire) a permis de confirmer l’affiliation culturelle des occupants.

Regression models for bivariate survival data

Multivariate lifetime data arise in various forms including recurrent event data when individuals are followed to observe the sequence of occurrences of a certain type of event; correlated lifetime when an individual is followed for the occurrence of two or more types of events, or when distinct individuals have dependent event times. In most studies there are covariates such as treatments, group indicators, individual characteristics, or environmental conditions, whose relationship to lifetime is of interest. This leads to a consideration of regression models.The well known Cox proportional hazards model and its variations, using the marginal hazard functions employed for the analysis of multivariate survival data in literature are not sufficient to explain the complete dependence structure of pair of lifetimes on the covariate vector. Motivated by this, in Chapter 2, we introduced a bivariate proportional hazards model using vector hazard function of Johnson and Kotz (1975), in which the covariates under study have different effect on two components of the vector hazard function. The proposed model is useful in real life situations to study the dependence structure of pair of lifetimes on the covariate vector . The well known partial likelihood approach is used for the estimation of parameter vectors. We then introduced a bivariate proportional hazards model for gap times of recurrent events in Chapter 3. The model incorporates both marginal and joint dependence of the distribution of gap times on the covariate vector . In many fields of application, mean residual life function is considered superior concept than the hazard function. Motivated by this, in Chapter 4, we considered a new semi-parametric model, bivariate proportional mean residual life time model, to assess the relationship between mean residual life and covariates for gap time of recurrent events. The counting process approach is used for the inference procedures of the gap time of recurrent events. In many survival studies, the distribution of lifetime may depend on the distribution of censoring time. In Chapter 5, we introduced a proportional hazards model for duration times and developed inference procedures under dependent (informative) censoring. In Chapter 6, we introduced a bivariate proportional hazards model for competing risks data under right censoring. The asymptotic properties of the estimators of the parameters of different models developed in previous chapters, were studied. The proposed models were applied to various real life situations.

Modelling and Analysis of Recurrent Event Data with Multiple Causes

This thesis Entitled “modelling and analysis of recurrent event data with multiple causes.Survival data is a term used for describing data that measures the time to occurrence of an event.In survival studies, the time to occurrence of an event is generally referred to as lifetime.Recurrent event data are commonly encountered in longitudinal studies when individuals are followed to observe the repeated occurrences of certain events. In many practical situations, individuals under study are exposed to the failure due to more than one causes and the eventual failure can be attributed to exactly one of these causes.The proposed model was useful in real life situations to study the effect of covariates on recurrences of certain events due to different causes.In Chapter 3, an additive hazards model for gap time distributions of recurrent event data with multiple causes was introduced. The parameter estimation and asymptotic properties were discussed .In Chapter 4, a shared frailty model for the analysis of bivariate competing risks data was presented and the estimation procedures for shared gamma frailty model, without covariates and with covariates, using EM algorithm were discussed. In Chapter 6, two nonparametric estimators for bivariate survivor function of paired recurrent event data were developed. The asymptotic properties of the estimators were studied. The proposed estimators were applied to a real life data set. Simulation studies were carried out to find the efficiency of the proposed estimators.

Nonparametric Estimation of Survivor Function in Bivariate Competing Risk Models’

So far, in the bivariate set up, the analysis of lifetime (failure time) data with multiple causes of failure is done by treating each cause of failure separately. with failures from other causes considered as independent censoring. This approach is unrealistic in many situations. For example, in the analysis of mortality data on married couples one would be interested to compare the hazards for the same cause of death as well as to check whether death due to one cause is more important for the partners’ risk of death from other causes. In reliability analysis. one often has systems with more than one component and many systems. subsystems and components have more than one cause of failure. Design of high-reliability systems generally requires that the individual system components have extremely high reliability even after long periods of time. Knowledge of the failure behaviour of a component can lead to savings in its cost of production and maintenance and. in some cases, to the preservation of human life. For the purpose of improving reliability. it is necessary to identify the cause of failure down to the component level. By treating each cause of failure separately with failures from other causes considered as independent censoring, the analysis of lifetime data would be incomplete. Motivated by this. we introduce a new approach for the analysis of bivariate competing risk data using the bivariate vector hazard rate of Johnson and Kotz (1975).

Bayesian analysis of an inverse Gaussian correlated frailty model

In survival analysis frailty is often used to model heterogeneity between individuals or correlation within clusters. Typically frailty is taken to be a continuous random effect, yielding a continuous mixture distribution for survival times. A Bayesian analysis of a correlated frailty model is discussed in the context of inverse Gaussian frailty. An MCMC approach is adopted and the deviance information criterion is used to compare models. As an illustration of the approach a bivariate data set of corneal graft survival times is analysed. (C) 2006 Elsevier B.V. All rights reserved.