Bivariate Response Research Articles

Bivariate odd-log-logistic-Weibull regression model for oral health-related quality of life

We study a bivariate response regression model with arbitrary marginal distributions and joint distributions using Frank and Clayton’s families of copulas. The proposed model is used for fitting dependent bivariate data with explanatory variables using the log-odd log-logistic Weibull distribution. We consider likelihood inferential procedures based on constrained parameters. For different parameter settings and sample sizes, various simulation studies are performed and compared to the performance of the bivariate odd-log-logistic-Weibull regression model. Sensitivity analysis methods (such as local and total influence) are investigated under three perturbation schemes. The methodology is illustrated in a study to assess changes on schoolchildren’s oral health-related quality of life (OHRQoL) in a follow-up exam after three years and to evaluate the impact of caries incidence on the OHRQoL of adolescents.

A new R-based statistical software package for fitting multivariate generalized linear mixed models to large and complex datasets

ABSTRACT
 ObjectiveTo demonstrate the efficiency and efficacy of the new freeware MGLMM in the statistical modelling of large and complex datasets.
 ApproachThe new R-based software MGLMM (shortly to become available on the CRAN website https://cran.r-project.org/) can be used to fit a range of different multivariate generalized linear mixed models, thereby permitting a better representation of the multivariate nature of many complex socio-economic processes which may involve a range of different response types. The software MGLMM will also set records for the time taken to fit these complex models to large sets of data. The efficiency and efficacy of this new software will be demonstrated by way of a number of applications.
 One such example will come from the STAR Project in which pupils were followed from kindergarten in 1985 (aged 5) to 1989 (third grade, aged 8). The pupils were assessed on their ability in both mathematics and English on an annual basis between 1985 and 1989. At the end of the kindergarten year, some of the students were reallocated to different class sizes in order ‘to achieve sexual and racial balance and to separate incompatible children’. In the fourth grade, the pupils returned to regular classes and the experiment ended.
 We can regard the two score variables ‘Maths’ and ‘English’ as constituting repeated, correlated, bivariate continuous data. We will use the new package MGLMM to apply a series of bivariate normal mixed models with correlated random effects. These models will allow us to distinguish the role of prior attainment in mathematics and English on current attainment in mathematics and English in an experimental setting, for pupils in small and regular class sizes. The models will permit an examination of the effect of class size on this bivariate response, whilst controlling for a set of individual-level confounding factors such as gender and age.
 ResultsWe will present the results of these analyses, thereby demonstrating the efficacy of MGLMM. We will also compare the performance of the new software with existing packages such as Stata.
 ConclusionsWe will have demonstrated the gain in efficiency through the use of MGLMM, compared to other standard software packages, in the statistical modelling of large and complex datasets.

Including non-informative parents in transmission-based association tests.

The classical transmission disequilibrium test (TDT) based on a trio design uses information only on the allele transmitted by a heterozygous parent at a marker locus as homozygous parents are non-informative about linkage. However, the phenotype of an offspring depends on the alleles transmitted by both parents, irrespective of whether the parents are homozygous or heterozygous, and hence carry useful information on association. In this article, we propose modifications to the TDT procedures by incorporating transmission data on both parents in an informative trio to explore possible gain in power in detecting association. For a binary trait, we use a goodness-of-fit χ2 test, whereas for a quantitative trait, we devise two tests: one based on a bivariate response logistic model and the other using a quasi-likelihood approach. We evaluate the type 1 errors and the powers of the proposed tests with those of the classical TDT procedures for both binary and quantitative traits based on extensive simulations. We find that the inclusion of transmission data on non-informative parents yields marginally higher power in the logistic regression approach but results in substantial gain in power in the quasi-likelihood approach. We apply our proposed methods to analyze a count phenotype related to alcoholism.

Different responses of influenza epidemic to weather factors among Shanghai, Hong Kong, and British Columbia.

Weather factors have long been considered as key sources for regional heterogeneity of influenza seasonal patterns. As influenza peaks coincide with both high and low temperature in subtropical cities, weather factors may nonlinearly or interactively affect influenza activity. This study aims to assess the nonlinear and interactive effects of weather factors with influenza activity and compare the responses of influenza epidemic to weather factors in two subtropical regions of southern China (Shanghai and Hong Kong) and one temperate province of Canada (British Columbia). Weekly data on influenza activity and weather factors (i.e., mean temperature and relative humidity (RH)) were obtained from pertinent government departments for the three regions. Absolute humidity (AH) was measured by vapor pressure (VP), which could be converted from temperature and RH. Generalized additive models were used to assess the exposure-response relationship between weather factors and influenza virus activity. Interactions of weather factors were further assessed by bivariate response models and stratification analyses. The exposure-response curves of temperature and VP, but not RH, were consistent among three regions/cities. Bivariate response model revealed a significant interactive effect between temperature (or VP) and RH (P<0.05). Influenza peaked at low temperature or high temperature with high RH. Temperature and VP are important weather factors in developing a universal model to explain seasonal outbreaks of influenza. However, further research is needed to assess the association between weather factors and influenza activity in a wider context of social and environmental conditions.

Copula regression models for discrete and mixed bivariate responses

ABSTRACTEstimation of the dependencies between bivariate discrete or mixed responses can be difficult. In this article, we propose a copula-based model with latent variables associated with discrete margins to account for correlations between bivariate discrete responses. Furthermore, we generalize this strategy for jointly modeling the dependencies between mixed responses in regression mixed models. The proposed method allows the adoption of flexible discrete margins and copula functions for various types of data. Maximum likelihood is used for model estimation; particularly, the estimation for bivariate responses in copula-based regression mixed models can be implemented using the SAS PROC NLMIXED procedure via adaptive Gaussian quadrature. In addition, a mixed model with non-Gaussian random effects can also be easily fitted using the same SAS procedure after reformulating the likelihood function by multiplying and dividing by a Gaussian density. Simulation results show good performance for bivariate di...

The effects of Sulphur dioxide on acute mortality and years of life lost are modified by temperature in Chengdu, China

The effect modification of meteorological factors on the association between ambient Sulphur dioxide (SO2) and mortality is critical for designing intervention policy. Existing studies did not result in consistent conclusions on the effect modification, and Years of life lost (YLLs) was rarely used as a health impact indicator to examine the modifying effect. This study aims to estimate the mean air temperature and relative humidity modification effects on the impact of SO2 on daily mortality and YLLs in Chengdu, China. Mortality, YLLs, air pollution and meteorological data were collected for 2011–2014. Three analytical approaches based on generalized additive models (GAMs) were used, including bivariate response surface model, product term model, and stratification model. We found that the effects of SO2 on mortality and YLLs depended on temperature at various lags, but did not depend on relative humidity. SO2 exhibited larger adverse effects on mortality in high temperature level (22.8–29.4°C) days than in low temperature level (−0.3–9.3°C) days, with a 10μg/m3 increment in SO2, non-accidental death increased by 0.8% (0.001, 0.015)at low temperature level, but increased by 1.4% (0.005, 0.024) at high temperature level. On the contrary, SO2 showed greater adverse effects on YLLs in low temperature days than in high temperature days, with a 10μg/m3 increment in SO2, non-accidental YLL increased by 40.580 (31.478, 49.682) at high temperature level, but increased by −2.703 (−14.668, 9.261) at low temperature level. We concluded that the effect of SO2 on mortality and YLLs may depend on temperature in Chengdu, China. Our results highlight the importance of considering the interaction between SO2 and temperature on health outcomes in future research. Also, policy makers should enhance the emission control of SO2 in extreme temperature days in Chengdu.

Theoretical evaluation of prediction error in linear regression with a bivariate response variable containing missing data

ABSTRACTMethods for linear regression with multivariate response variables are well described in statistical literature. In this study we conduct a theoretical evaluation of the expected squared prediction error in bivariate linear regression where one of the response variables contains missing data. We make the assumption of known covariance structure for the error terms. On this basis, we evaluate three well-known estimators: standard ordinary least squares, generalized least squares, and a James–Stein inspired estimator. Theoretical risk functions are worked out for all three estimators to evaluate under which circumstances it is advantageous to take the error covariance structure into account.

Recursive bivariate response models of the ex-ante intentions to link perceived acceptability among charge and refund options for alternative road pricing schemes

Road pricing (RP) is currently under development as a way to mitigate the acute traffic congestion in Jakarta. The RP has been recognized as a powerful tool in delivering efficient road use. Despite of a well-established rationale that tackled congestion, RP policy faces lack of public support and is seen rather controversial due to charge required to enter charging zone. To encounter shortcomings of RP, we introduce a parking deposit system (PDS) as an alternative. The PDS is based on refunds to car users. Refunds are offered only on parking fees or as discounts on purchases within the charging zone. Thus, this paper explores the key influences and the extent to which RP and PDS schemes are acceptable to the public. Taking into account citizen’s consciousness based on a fictitious voting conducted in Jakarta, we estimated recursive simultaneous bivariate voting models to link perceived acceptability among RP and PDS bundles. We found that there is a complementary relationship between acceptance and consciousness, with PDS offers better approval and there is a substantially strong link between voting intentions and perceived acceptability.

International sign predictability of stock returns: The role of the United States

We study the directional predictability of monthly excess stock market returns in the U.S. and ten other markets using univariate and bivariate binary response models. We introduce a new bivariate (two-equation) probit model that allows us to examine the benefits of predicting the signs of returns jointly, focusing on the predictive power originating from the U.S. to foreign markets. Our in-sample and out-of-sample forecasting results indicate superior predictive performance of the new model over competing univariate binary response models, and conventional predictive regressions, by statistical measures and market timing performance. This highlights the importance of predictive information from the U.S. to the other markets providing also practical improvement in investors' market timing decisions.

BRAID: A Unifying Paradigm for the Analysis of Combined Drug Action.

With combination therapies becoming increasingly vital to understanding and combatting disease, a reliable method for analyzing combined dose response is essential. The importance of combination studies both in basic and translational research necessitates a method that can be applied to a wide range of experimental and analytical conditions. However, despite increasing demand, no such unified method has materialized. Here we introduce the Bivariate Response to Additive Interacting Doses (BRAID) model, a response surface model that combines the simplicity and intuitiveness needed for basic interaction classifications with the versatility and depth needed to analyze a combined response in the context of pharmacological and toxicological constraints. We evaluate the model in a series of simulated combination experiments, a public combination dataset, and several experiments on Ewing’s Sarcoma. The resulting interaction classifications are more consistent than those produced by traditional index methods, and show a strong relationship between compound mechanisms and nature of interaction. Furthermore, analysis of fitted response surfaces in the context of pharmacological constraints yields a more concrete prediction of combination efficacy that better agrees with in vivo evaluations.

Model Fit after Pairwise Maximum Likelihood.

Maximum likelihood factor analysis of discrete data within the structural equation modeling framework rests on the assumption that the observed discrete responses are manifestations of underlying continuous scores that are normally distributed. As maximizing the likelihood of multivariate response patterns is computationally very intensive, the sum of the log–likelihoods of the bivariate response patterns is maximized instead. Little is yet known about how to assess model fit when the analysis is based on such a pairwise maximum likelihood (PML) of two–way contingency tables. We propose new fit criteria for the PML method and conduct a simulation study to evaluate their performance in model selection. With large sample sizes (500 or more), PML performs as well the robust weighted least squares analysis of polychoric correlations.

Modelling a non-stationary BINAR(1) Poisson process

ABSTRACTNon-stationarity in bivariate time series of counts may be induced by a number of time-varying covariates affecting the bivariate responses due to which the innovation terms of the individual series as well as the bivariate dependence structure becomes non-stationary. So far, in the existing models, the innovation terms of individual INAR(1) series and the dependence structure are assumed to be constant even though the individual time series are non-stationary. Under this assumption, the reliability of the regression and correlation estimates is questionable. Besides, the existing estimation methodologies such as the conditional maximum likelihood (CMLE) and the composite likelihood estimation are computationally intensive. To address these issues, this paper proposes a BINAR(1) model where the innovation series follow a bivariate Poisson distribution under some non-stationary distributional assumptions. The method of generalized quasi-likelihood (GQL) is used to estimate the regression effects while the serial and bivariate correlations are estimated using a robust moment estimation technique. The application of model and estimation method is made in the simulated data. The GQL method is also compared with the CMLE, generalized method of moments (GMM) and generalized estimating equation (GEE) approaches where through simulation studies, it is shown that GQL yields more efficient estimates than GMM and equally or slightly more efficient estimates than CMLE and GEE.

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.

Multivariate longitudinal data analysis with mixed effects hidden Markov models.

Multiple longitudinal responses are often collected as a means to capture relevant features of the true outcome of interest, which is often hidden and not directly measurable. We outline an approach which models these multivariate longitudinal responses as generated from a hidden disease process. We propose a class of models which uses a hidden Markov model with separate but correlated random effects between multiple longitudinal responses. This approach was motivated by a smoking cessation clinical trial, where a bivariate longitudinal response involving both a continuous and a binomial response was collected for each participant to monitor smoking behavior. A Bayesian method using Markov chain Monte Carlo is used. Comparison of separate univariate response models to the bivariate response models was undertaken. Our methods are demonstrated on the smoking cessation clinical trial dataset, and properties of our approach are examined through extensive simulation studies.

Bayesian bivariate quantile regression

Quantile regression (QR) has become a widely used tool to study the impact of covariates on quantiles of a response distribution. QR provides a detailed description of the conditional response when considering a dense set of quantiles, without assuming a closed form for its distribution. The Bayesian version of QR, which can be implemented by considering the asymmetric Laplace distribution (ALD) as an auxiliary error distribution, is an attractive alternative to other methods because it returns knowledge on the whole parameter distribution instead of solely point estimations. While for the univariate case there has been a lot of development in the last few years, multivariate responses have only been treated to a little extent in the literature, especially in the Bayesian case. By using a multivariate version of the location scale mixture representation for the ALD, we are able to apply inference techniques developed for multivariate Gaussian models on multivariate quantile regression and make thus the impact of covariates on the quantiles of more than one dependent variable feasible. The model structure also facilitates the determination of conditional correlations between bivariate responses on different quantile levels after adjusting for covariate effects.

Estimating continuous body size-based shifts in δ15N–δ13C space using multivariate hierarchical models

Stable isotopes (δ15N and δ13C) offer one representation of an individual’s trophic niche and are important tools for elucidating ecological patterns and testing a diversity of hypotheses. Because δ15N and δ13C values are often obtained from the same sample, they compose a bivariate response that researchers commonly analyze using multivariate statistical methods. However, stable isotope data sets often exhibit hierarchical structure whereby samples may be clustered or grouped at multiple levels either as an artifact of sampling design or due to structure inherent in the sampled population (e.g., samples from individuals grouped according to life history stages, social groups, ages, or sizes classes). Ignoring such structure can result in overly optimistic confidence intervals and heighten the risk of observing significant differences where none exist. To address these issues, we suggest researchers utilize multivariate hierarchical models, which are a simple extension of univariate hierarchical methods. The models account for potential dependencies between δ15N and δ13C values, permit valid predictions of shifts in δ15N–δ13C space related to predictor variables, provide more accurate estimates of parameter uncertainty, and improved inferences on coefficients that correspond to groups with small to moderate quantities of data. We demonstrate advantages of multivariate hierarchical models by examining size-dependent shifts in δ15N–δ13C space in outmigrating post-smolt Chinook salmon sampled from an estuarine habitat. Given the prevalence of complex structure in ecological stable isotope data sets, multivariate hierarchical models should hold considerable value to food web and stable isotope ecologists.

A Comparison of Bayesian Mixed Data Models for Austrian SILC data

In many applications multidimensional outcome variables measured on different scales are of interest. In this paper we consider regression modelling of a bivariate response with a normal and a binary component. We use three different approaches to model dependence: a joint logit-normal model for the two responses, a factorization model with linear dependence and a a factorization model with flexible non-linear dependence. We apply these approaches to Austrian SILC data to analyse material deprivation and household income.

Assessing High-Risk Scenarios by Full-Range Tail Dependence Copulas

Copulas with a full-range tail dependence property can cover the widest range of positive dependence in the tail, so that a regression model can be built accounting for dynamic tail dependence patterns between variables. We propose a model that incorporates both regression on each marginal of bivariate response variables and regression on the dependence parameter for the response variables. An ACIG copula that possesses the full-range tail dependence property is implemented in the regression analysis. Comparisons between regression analysis based on ACIG and Gumbel copulas are conducted, showing that the ACIG copula is generally better than the Gumbel copula when there is intermediate upper tail dependence. A simulation study is conducted to illustrate that dynamic tail dependence structures between loss and ALAE can be captured by using the one-parameter ACIG copula. Finally, we apply the ACIG and Gumbel regression models for a dataset from the U.S. Medical Expenditure Panel Survey. The empirical analysis suggests that the regression model with the ACIG copula improves the assessment of high-risk scenarios, especially for aggregated dependent risks.

The Relationship Between Cytokine Levels and Symptoms in Patients (Pts) With Myelofibrosis (MF) From COMFORT-II, a Phase 3 Study of Ruxolitinib (RUX) Vs Best Available Therapy (BAT)

BackgroundRUX is a JAK1/ JAK 2 inhibitor that has demonstrated improvements in splenomegaly, MF-related symptoms, and quality of life measures in the 2 phase 3 COMFORT studies. We recently demonstrated possible prognostic/predictive relationships between baseline (BL) cytokine levels and changes in spleen volume. Here, we evaluated the associations between cytokine levels and symptoms in COMFORT-II. MethodsTen symptoms, (fever, weight loss, easily tired, loss of appetite, pain, itching, sleeping well, lack of energy, night sweats, and trouble sleeping) were assessed at BL and weeks 8, 24, and 48 using the Functional Assessment of Cancer Therapy-Lymphoma (FACT-Lym) instrument (0 to 4 scale). In this exploratory analysis, reverse coding of symptoms (except sleeping well) was performed. A high score reflects low symptom burden, and a positive change indicates improvement. Plasma samples were analyzed using Rules-Based Medicine's HumanMAP v1.6, measuring 89 cytokines at weeks 4, 24 and 48. Cytokines with ≥ 30% of values below lower limit of quantification were excluded. Two binary (0/1) variables were defined; Symptom Present = 1 when symptom score ² 2 and Improvement = 1 when change from BL symptom score > 0.Associations between Symptom Present and BL cytokine level were evaluated using univariate logistic regression (adjusted for IPSS risk and JAK2 mutation status), and for those associated at BL, the relationship between the fold-change in cytokine level (log2) and the Improvement over time was evaluated. Improvement and fold-change in a cytokine were considered as a bivariate response vector, and if the components of the response vector correlated it implied that the change in symptom score and change in cytokine were correlated over time. ResultsOf the 10 symptoms analyzed, 9 had BL associations with cytokines (Figure). Table shows cytokines and symptoms for which changes from BL were associated over time.At BL, lower ferritin levels were associated with itching and night sweats, lower leptin levels with weight loss, higher IL 1 receptor-α (IL1RA) levels with loss of appetite and higher CD40L, Pal1, and RANTES levels with not sleeping well. RUX-treated pts were more likely to have improvements in itching and night sweats than BAT-treated pts and had larger increases in ferritin levels over time. Larger changes in leptin levels with RUX treatment positively correlated with improvements in weight loss. IL1RA decreased significantly with time in the RUX arm and negatively correlated with loss of appetite, which improved over time. ConclusionsBoth BL levels and changes over time of various cytokines significantly correlated with MF-related symptoms. Ferritin levels appeared to be an important component of itching and night sweats. Additional analyses are required to explore the relationships between changes in cytokine levels and quality of life measures. These observations suggest a link between individual cytokines and symptoms in MF enhancing our understanding of the disease and providing a potential basis for future patient management tools. [Display omitted] [Display omitted] Disclosures:Squires:Novartis Phama AG: Employment. Harrison:Novartis: Honoraria, Membership on an entity's Board of Directors or advisory committees, Research Funding, Speakers Bureau; Sanofi: Honoraria, Membership on an entity's Board of Directors or advisory committees, Speakers Bureau; YM Bioscience: Honoraria, Membership on an entity's Board of Directors or advisory committees; Celgene: Honoraria; Shire: Speakers Bureau; S Bio: Honoraria, Membership on an entity's Board of Directors or advisory committees; Gilead: Honoraria, Membership on an entity's Board of Directors or advisory committees. Vannucchi:Novartis: Honoraria, Membership on an entity's Board of Directors or advisory committees. Gisslinger:AOP Orphan Pharmaceuticals: Advisory Board Other, Honoraria; Novartis: Advisory Board, Advisory Board Other, Research Funding; Sanofi-Aventis: Advisory Board, Advisory Board Other, Honoraria; Shire: Advisory Board, Advisory Board Other, Honoraria; Celgene: Advisory Board Other, Honoraria; Janseen: Advisory Board, Advisory Board Other, Honoraria. Passamonti:Sanofi: Honoraria; Novartis: Honoraria. Al-Ali:Novartis: Consultancy, Honoraria; Celgene: Honoraria, Research Funding. Kiladjian:Novartis: Honoraria, Membership on an entity's Board of Directors or advisory committees, Research Funding; Celgene: Research Funding; Sanofi: Honoraria, Membership on an entity's Board of Directors or advisory committees; AOP Orphan: Honoraria, Membership on an entity's Board of Directors or advisory committees, Research Funding. Marker:Novartis: Employment. Mendelson:Novartis: Employment. Stalbovskaya:Novartis: Employment, Equity Ownership. Cervantes:Novartis: Membership on an entity's Board of Directors or advisory committees, Speakers Bureau; Sanofi Aventis: Membership on an entity's Board of Directors or advisory committees, Speakers Bureau. Knoops:Novartis: Consultancy; BMS: Consultancy.

Interactive short-term effects of equivalent temperature and air pollution on human mortality in Berlin and Lisbon

There is substantial evidence that both temperature and air pollution are predictors of mortality. Thus far, few studies have focused on the potential interactive effects between the thermal environment and different measures of air pollution. Such interactions, however, are biologically plausible, as (extreme) temperature or increased air pollution might make individuals more susceptible to the effects of each respective predictor. This study investigated the interactive effects between equivalent temperature and air pollution (ozone and particulate matter) in Berlin (Germany) and Lisbon (Portugal) using different types of Poisson regression models. The findings suggest that interactive effects exist between air pollutants and equivalent temperature. Bivariate response surface models and generalised additive models (GAMs) including interaction terms showed an increased risk of mortality during periods of elevated equivalent temperatures and air pollution. Cold effects were mostly unaffected by air pollution. The study underscores the importance of air pollution control in mitigating heat effects.