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This paper presents a novel approach for analyzing bivariate positive data, taking into account a covariate vector and left-censored observations, by introducing a hierarchical Bayesian analysis. The proposed method assumes marginal Weibull distributions and employs either a usual Weibull likelihood or Weibull–Tobit likelihood approaches. A latent variable or frailty is included in the model to capture the possible correlation between the bivariate responses for the same sampling unit. The posterior summaries of interest are obtained through Markov Chain Monte Carlo methods. To demonstrate the effectiveness of the proposed methodology, we apply it to a bivariate data set from stellar astronomy that includes left-censored observations and covariates. Our results indicate that the new bivariate model approach, which incorporates the latent factor to capture the potential dependence between the two responses of interest, produces accurate inference results. We also compare the two models using the different likelihood approaches (Weibull or Weibull–Tobit likelihoods) in the application. Overall, our findings suggest that the proposed hierarchical Bayesian analysis is a promising approach for analyzing bivariate positive data with left-censored observations and covariate information. [ABSTRACT FROM AUTHOR]

We introduce the bivariate unit-log-symmetric model based on the bivariate log-symmetric distribution (BLS) defined in Vila et al. [25] as a flexible family of bivariate distributions over the unit square. We then study its mathematical properties such as stochastic representations, quantiles, conditional distributions, independence of the marginal distributions and marginal moments. Maximum likelihood estimation method is discussed and examined through Monte Carlo simulation. Finally, the proposed model is used to analyze some soccer data sets. [ABSTRACT FROM AUTHOR]

In medical diagnostic research, it is customary to collect multiple continuous biomarker measures to improve the accuracy of diagnostic tests. A prevalent practice is to combine the measurements of these biomarkers into one single composite score. However, incorporating those biomarker measurements into a single score depends on the combination of methods and may lose vital information needed to make an effective and accurate decision. Furthermore, a diagnostic cut-off is required for such a combined score, and it is difficult to interpret in actual clinical practice. The paper extends the classical biomarkers' accuracy and predictive values from univariate to bivariate markers. Also, we will develop a novel pseudo-measures system to maximize the vital information from multiple biomarkers. We specified these pseudo-and-or classifiers for the true positive rate, true negative rate, false-positive rate, and false-negative rate. We used them to redefine classical measures such as the Youden index, diagnostics odds ratio, likelihood ratios, and predictive values. We provide optimal cut-off point selection based on the modified Youden index with numerical illustrations and real data analysis for this paper's newly developed pseudo measures. [ABSTRACT FROM AUTHOR]

Although there have been a number of available tests of bivariate exchangeability, i.e. bivariate symmetry for bivariate distributions, the literature is void of tests whether a multivariate distribution with more than two dimensions is exchangeable or not. In this paper, multivariate permutation tests of exchangeability of multivariate distributions are proposed, which are based on the non-parametric combination methodology, i.e. on combining non-parametric bivariate exchangeability tests. Numerical experiments on real as well as simulated multivariate data with more than two dimensions are presented here. The multivariate permutation test turns out to be typically more powerful than a bivariate exchangeability test performed only over a single pair of variables, and also more suitable compared to tests exploiting the approaches of Benjamini–Yekutieli or Bonferroni. [ABSTRACT FROM AUTHOR]

Marshall–Olkin bivariate exponential distribution is used to statistically infer the adaptive type II progressive hybrid censored data under dependent competition risk model. For complex censored data with only partial failure reasons observed, maximum likelihood estimation and approximate confidence interval based on Fisher information are established. At the same time, Bayesian estimation is performed under the highly flexible Gamma–Dirichlet prior distribution and the highest posterior density interval using Gibbs sampling and Metropolis–Hastings algorithm is obtained. Then the performance of two methods is compared through several indexes. In addition, the Monte Carlo method is used for data simulation of multiple sets of variables to give experimental suggestions. Finally, a practical example is given to illustrate the operability and applicability of the proposed algorithm to efficiently carry out reliability test. [ABSTRACT FROM AUTHOR]

Geyser eruption is one of the most popular signature attractions at the Yellowstone National Park. The interdependence of geyser eruptions and impacts of covariates are of interest to researchers in geyser studies. In this paper, we propose a parametric covariate-adjusted recurrent event model for estimating the eruption gap time. We describe a general bivariate recurrent event process, where a bivariate lognormal distribution and a Gumbel copula with different marginal distributions are used to model an interdependent dual-type event system. The maximum likelihood approach is used to estimate model parameters. The proposed method is applied to analyzing the Yellowstone geyser eruption data for a bivariate geyser system and offers a deeper understanding of the event occurrence mechanism of individual events as well as the system as a whole. A comprehensive simulation study is conducted to evaluate the performance of the proposed method. [ABSTRACT FROM AUTHOR]

Bivariate correlation coefficients (BCCs) are often calculated to gauge the relationship between two variables in medical research. In a family-type clustered design where multiple participants from same units/families are enrolled, BCCs can be defined and estimated at various hierarchical levels (subject level, family level and marginal BCC). Heterogeneity usually exists between subject groups and, as a result, subject level BCCs may differ between subject groups. In the framework of bivariate linear mixed effects modeling, we define and estimate BCCs at various hierarchical levels in a family-type clustered design, accommodating subject group heterogeneity. Simplified and modified asymptotic confidence intervals are constructed to the BCC differences and Wald type tests are conducted. A real-world family-type clustered study of Alzheimer disease (AD) is analyzed to estimate and compare BCCs among well-established AD biomarkers between mutation carriers and non-carriers in autosomal dominant AD asymptomatic individuals. Extensive simulation studies are conducted across a wide range of scenarios to evaluate the performance of the proposed estimators and the type-I error rate and power of the proposed statistical tests. Abbreviations: BCC: bivariate correlation coefficient; BLM: bivariate linear mixed effects model; CI: confidence interval; AD: Alzheimer's disease; DIAN: The Dominantly Inherited Alzheimer Network; SA: simple asymptotic; MA: modified asymptotic [ABSTRACT FROM AUTHOR]

In this paper, a new bivariate discrete generalized exponential distribution, whose marginals are discrete generalized exponential distributions, is studied. It is observed that the proposed bivariate distribution is a flexible distribution whose cumulative distribution function has an analytical structure. In addition, a new bivariate geometric distribution can be obtained as a special case. We study different properties of this distribution and propose estimation of its parameters. We will see that the maximum of the variables involved in the proposed bivariate distribution defines some new classes of univariate discrete distributions, which are interesting in their own sake, and can be used to analyze some Reliability systems whose components are positive dependent. Some important futures of this new univariate family of discrete distributions are also studied in details. In addition, a general class of bivariate discrete distributions, whose marginals are exponentiated discrete distributions, is introduced. Moreover, the analysis of two real bivariate data sets is performed to indicate the effectiveness of the proposed models. Finally, we conclude the paper. [ABSTRACT FROM AUTHOR]

The aim of this paper is to explore multivariate survival techniques for the analysis of bivariate right-censoring failure time data. In particular, a new family of parametric bivariate frailty models is investigated. To take into account the correlation between two survival times, the Marshall–Olkin Bivariate Exponential Distribution (MOBVE) is exploited to model the joint distribution of two frailties. The reason is twofold: on the one hand, it allows one to model shocks that affect individual-specific frailties; on the other hand, the parameter underlying the Poisson process characterizing the common shock is used to capture the dependence between two lifetimes. The proposed methodology is applied to the investigation of association in death on different-sex couples followed within the Cache County Study on Memory Health and Aging (CCSMHA). A cure rate extension of the model is also described. [ABSTRACT FROM AUTHOR]

This paper presents a simple and robust method for obtaining a comprehensive understanding of the joint period and radius distribution in Kepler exoplanets. The proposed method is based on particle swarm optimization and bivariate Normal Inverse Gaussian distribution. Furthermore, in the construction of the probability density function, this study selects planet-host stars with the GK-type. The injecting approach is also employed to solve the survey completeness of sample. The resulting occurrence rate of Earth analogs is 0.025 with a 95% bootstrap confidence interval between 0.023 and 0.032. [ABSTRACT FROM AUTHOR]

Many research fields increasingly involve analyzing data of a complex structure. Models investigating the dependence of a response on a predictor have moved beyond the ordinary scalar-on-vector regression. We propose a regression model for a scalar response and a surface (or a bivariate function) predictor. The predictor has a random component and the regression model falls in the framework of linear random effects models. We estimate the model parameters via maximizing the log-likelihood with the ECME (Expectation/Conditional Maximization Either) algorithm. We use the approach to analyze a data set where the response is the neuroticism score and the predictor is the resting-state brain function image. In the simulations we tried, the approach has better performance than two other approaches, a functional principal component regression approach and a smooth scalar-on-image regression approach. [ABSTRACT FROM AUTHOR]

The modeling and analysis of lifetime data in which the main endpoints are the times when an event of interest occurs is of great interest in medical studies. In these studies, it is common that two or more lifetimes associated with the same unit such as the times to deterioration levels or the times to reaction to a treatment in pairs of organs like lungs, kidneys, eyes or ears. In medical applications, it is also possible that a cure rate is present and needed to be modeled with lifetime data with long-term survivors. This paper presented a comparative study under a Bayesian approach among some existing continuous and discrete bivariate distributions such as the bivariate exponential distributions and the bivariate geometric distributions in presence of cure rate, censored data and covariates. In presence of lifetimes related to cured patients, it is assumed standard mixture cure rate models in the data analysis. The posterior summaries of interest are obtained using Markov Chain Monte Carlo methods. To illustrate the proposed methodology two real medical data sets are considered. [ABSTRACT FROM AUTHOR]

In this paper, we develop a conditional model for analyzing mixed bivariate continuous and ordinal longitudinal responses. We propose a quantile regression model with random effects for analyzing continuous responses. For this purpose, an Asymmetric Laplace Distribution (ALD) is allocated for continuous response given random effects. For modeling ordinal responses, a cumulative logit model is used, via specifying a latent variable model, with considering other random effects. Therefore, the intra-association between continuous and ordinal responses is taken into account using their own exclusive random effects. But, the inter-association between two mixed responses is taken into account by adding a continuous response term in the ordinal model. We use a Bayesian approach via Markov chain Monte Carlo method for analyzing the proposed conditional model and to estimate unknown parameters, a Gibbs sampler algorithm is used. Moreover, we illustrate an application of the proposed model using a part of the British Household Panel Survey data set. The results of data analysis show that gender, age, marital status, educational level and the amount of money spent on leisure have significant effects on annual income. Also, the associated parameter is significant in using the best fitting proposed conditional model, thus it should be employed rather than analyzing separate models. [ABSTRACT FROM AUTHOR]

Two types of bivariate models for categorical response variables are introduced to deal with special categories such as ‘unsure’ or ‘unknown’ in combination with other ordinal categories, while taking additional hierarchical data structures into account. The latter is achieved by the use of different covariance structures for a trivariate random effect. The models are applied to data from the INSIDA survey, where interest goes to the effect of covariates on the association between HIV risk perception (quadrinomial with an ‘unknown risk’ category) and HIV infection status (binary). The final model combines continuation-ratio with cumulative link logits for the risk perception, together with partly correlated and partly shared trivariate random effects for the household level. The results indicate that only age has a significant effect on the association between HIV risk perception and infection status. The proposed models may be useful in various fields of application such as social and biomedical sciences, epidemiology and public health. [ABSTRACT FROM AUTHOR]

In this paper, the destructive negative binomial (DNB) cure rate model with a latent activation scheme [V. Cancho, D. Bandyopadhyay, F. Louzada, and B. Yiqi, The DNB cure rate model with a latent activation scheme, Statistical Methodology 13 (2013b), pp. 48–68] is extended to the case where the observations are grouped into clusters. Parameter estimation is performed based on the restricted maximum likelihood approach and on a Bayesian approach based on Dirichlet process priors. An application to a real data set related to a sealant study in a dentistry experiment is considered to illustrate the performance of the proposed model. [ABSTRACT FROM AUTHOR]

For analyzing incidence data on diabetes and health problems, the bivariate geometric probability distribution is a natural choice but remained unexplored largely due to lack of models linking covariates with the probabilities of bivariate incidence of correlated outcomes. In this paper, bivariate geometric models are proposed for two correlated incidence outcomes. The extended generalized linear models are developed to take into account covariate dependence of the bivariate probabilities of correlated incidence outcomes for diabetes and heart diseases for the elderly population. The estimation and test procedures are illustrated using the Health and Retirement Study data. Two models are shown in this paper, one based on conditional-marginal approach and the other one based on the joint probability distribution with an association parameter. The joint model with association parameter appears to be a very good choice for analyzing the covariate dependence of the joint incidence of diabetes and heart diseases. Bootstrapping is performed to measure the accuracy of estimates and the results indicate very small bias. [ABSTRACT FROM PUBLISHER]

The monitoring of web servers through statistical frameworks is of utmost important in order to verify possible suspicious anomalies in network traffic or misuse actions that compromise integrity, confidentiality, and availability of information. In this paper, by considering the Plackett copula function, we propose a bivariate beta-autoregressive moving average time-series model for proportion data over time, which is the case for variables present in web server monitoring such as error rates. To illustrate the proposed methodology, we monitor a Brazilian web server's rate of connection synchronization and rejection errors in a web system, with error logging rate in the past 10 min. In essence, the entire methodology may be generalized to any number of time-series of error rates. [ABSTRACT FROM PUBLISHER]

Discrete lifetime data are very common in engineering and medical researches. In many cases the lifetime is censored at a random or predetermined time and we do not know the complete survival time. There are many situations that the lifetime variable could be dependent on the time of censoring. In this paper we propose the dependent right censoring scheme in discrete setup when the lifetime and censoring variables have a bivariate geometric distribution. We obtain the maximum likelihood estimators of the unknown parameters with their risks in closed forms. The Bayes estimators as well as the constrained Bayes estimates of the unknown parameters under the squared error loss function are also obtained. We considered an extension to the case where covariates are present along with the data. Finally we provided a simulation study and an illustrative example with a real data. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to identify a relationship between pupils' mathematics and reading test scores and the characteristics of students themselves, stratifying for classes, schools and geographical areas. The data set of interest contains detailed information about more than 500,000 students at the first year of junior secondary school in the year 2012/2013, provided by the Italian Institute for the Evaluation of Educational System. The innovation of this work is in the use of multivariate multilevel models, in which the outcome is bivariate: reading and mathematics achievement. Using the bivariate outcome enables researchers to analyze the correlations between achievement levels in the two fields and to predict statistically significant school and class effects after adjusting for pupil's characteristics. The statistical model employed here explicates account for the potential covariance between the two topics, and at the same time it allows the school effect to vary among them. The results show that while for most cases the direction of school's effect is coherent for reading and mathematics (i.e. positive/negative), there are cases where internal school factors lead to different performances in the two fields. [ABSTRACT FROM AUTHOR]

The purpose of the current work is to introduce stratified bivariate ranked set sampling (SBVRSS) and investigate its performance for estimating the population mean using both naïve and ratio methods. The properties of the proposed estimator are derived along with the optimal allocation with respect to stratification. We conduct a simulation study to demonstrate the relative efficiency of SBVRSS as compared to stratified bivariate simple random sampling (SBVSRS) for ratio estimation. Data that consist of weights and bilirubin levels in the blood of 120 babies are used to illustrate the procedure on a real data set. Based on our simulation, SBVRSS for ratio estimation is more efficient than using SBVSRS in all cases. [ABSTRACT FROM AUTHOR]

This paper extends the analysis of the bivariate Seemingly Unrelated Regression (SUN) Tobit model by modeling its nonlinear dependence structure through the Clayton copula. The ability to capture/model the lower tail dependence of the SUN Tobit model where some data are censored (generally, left-censored at zero) is an useful feature of the Clayton copula. We propose a modified version of the (classical) Inference Function for Margins (IFS) method by Joe and XP [H. Joe and J.J. XP,The estimation method of inference functions for margins for multivariate models, Tech. Rep. 166, Department of Statistics, University of British Columbia, 1996], which we refer to as Modified Inference Function for Margins (MIFF) method, to obtain the (point) estimates of the marginal and Clayton copula parameters. More specifically, we employ the (frequenting) data augmentation technique at the second stage of the IFS method (the first stage of the MIFF method is equivalent to the first stage of the IFS method) to generate the censored observations and then estimate the Clayton copula parameter. This process (data augmentation and copula parameter estimation) is repeated until convergence. Such modification at the second stage of the usual estimation method is justified in order to obtain continuous marginal distributions, which ensures the uniqueness of the resulting Clayton copula, as stated by Solar's [A. Solar,Fonctions de répartition à n dimensions et leurs marges, Publ. de l'Institut de Statistique de l'Université de Paris 8 (1959), pp. 229–231] theorem; and also to provide an unbiased estimate of the association parameter (the IFS method provides a biased estimate of the Clayton copula parameter in the presence of censored observations in both margins). Since the usual asymptotic approach, that is the computation of the asymptotic covariance matrix of the parameter estimates, is troublesome in this case, we also propose the use of resampling procedures (bootstrap methods, such as standard normal and percentile, by Efron and Tibshirani [B. Efron and R.J. Tibshirani,An Introduction to the Bootstrap, Chapman & Hall, New York, 1993] to obtain confidence intervals for the model parameters. [ABSTRACT FROM PUBLISHER]

Here we introduce an orderversion of the alternative zero-inflated logarithmic series distribution of Kumar and Riyaz [14] and investigate some of its important properties by deriving an expression for its probability mass function, recurrence relations for its probabilities, raw moments and factorial moments. We discuss the estimation of the parameters of the distribution by the method of maximum likelihood. Certain test procedures are developed for testing the significance of the additional parameters of the model. All these procedures discussed in the paper are illustrated with the help of real life data sets. A simulation study is also considered for assessing the performance of the estimators. [ABSTRACT FROM AUTHOR]

In the context of categorical data analysis, the CATegorical ANalysis Of Variance (CATANOVA) has been proposed to analyse the scheme variable-factor, both for nominal and ordinal variables. This method is based on theCstatistic and allows to test the statistical significance of the tau index using its relationship with theCstatistic. Through Emerson orthogonal polynomials (EOP) a useful decomposition ofCstatistic into bivariate moments (location, dispersion and higher order components) has been developed. In the construction of EOP the categories are replaced by scores, typically natural scores. In the paper, we provide an overview of the main scoring schemes focusing on the advantages and the statistical properties; we pay special attention to the impact of the chosen scores on theCstatistic of CATANOVA and the graphical representations of doubly ordered non-symmetrical correspondence analysis. Through a real data example, we show the impact of the scoring schemes and we consider the RV and multidimensional scaling as tools to measure similarity among the results achieved with each method. [ABSTRACT FROM PUBLISHER]

A correction to the article "Discrete and continuous bivariate lifetime models in presence of cure rate: a comparative study under Bayesian approach" is presented.

In this paper, we introduce classical and Bayesian approaches for the Basu–Dhar bivariate geometric distribution in the presence of covariates and censored data. This distribution is considered for the analysis of bivariate lifetime as an alternative to some existing bivariate lifetime distributions assuming continuous lifetimes as the Block and Basu or Marshall and Olkin bivariate distributions. Maximum likelihood and Bayesian estimators are presented. Two examples are considered to illustrate the proposed methodology: an example with simulated data and an example with medical bivariate lifetime data. [ABSTRACT FROM PUBLISHER]

We investigate the problem of estimating the association between two related survival variables when they follow a copula model and bivariate left-truncated and right-censored data are available. By expressing truncation probability as the functional of marginal survival functions, we propose a two-stage estimation procedure for estimating the parameters of Archimedean copulas. The asymptotic properties of the proposed estimators are established. Simulation studies are conducted to investigate the finite sample properties of the proposed estimators. The proposed method is applied to a bivariate RNA data. [ABSTRACT FROM PUBLISHER]

The academic success of students is a priority for all universities. We analyze the students' success at university by considering their performance in terms of both ‘qualitative performance’, measured by their mean grade, and ‘quantitative performance’, measured by university credits accumulated. These data come from an Italian University and concern a cohort of students enrolled at the Faculty of Economics. To jointly model both the marginal relationships and the association structure with covariates, we fit a bivariate ordered logistic model by penalized maximum likelihood estimation. The penalty term we use allows us to smooth the association structure and enlarge the range of possible parameterizations beyond that provided by the usual Dale model. The advantages of our approach are also in terms of parsimony and parameter interpretation, while preserving the goodness of fit. [ABSTRACT FROM PUBLISHER]

In biomedical research, two or more biomarkers may be available for diagnosis of a particular disease. Selecting one single biomarker which ideally discriminate a diseased group from a healthy group is confront in a diagnostic process. Frequently, most of the people use the accuracy measure, area under the receiver operating characteristic (ROC) curve to choose the best diagnostic marker among the available markers for diagnosis. Some authors have tried to combine the multiple markers by an optimal linear combination to increase the discriminatory power. In this paper, we propose an alternative method that combines two continuous biomarkers by direct bivariate modeling of the ROC curve under log-normality assumption. The proposed method is applied to simulated data set and prostate cancer diagnostic biomarker data set. [ABSTRACT FROM AUTHOR]

We investigate the relative performance of stratified bivariate ranked set sampling (SBVRSS), with respect to stratified simple random sampling (SSRS) for estimating the population mean with regression methods. The mean and variance of the proposed estimators are derived with the mean being shown to be unbiased. We perform a simulation study to compare the relative efficiency of SBVRSS to SSRS under various data-generating scenarios. We also compare the two sampling schemes on a real data set from trauma victims in a hospital setting. The results of our simulation study and the real data illustration indicate that using SBVRSS for regression estimation provides more efficiency than SSRS in most cases. [ABSTRACT FROM AUTHOR]

This paper presents a new parametric model for recurrent events, in which the time of each recurrence is associated to one or multiple latent causes and no information is provided about the responsible cause for the event. This model is characterized by a rate function and it is based on the Poisson-exponential distribution, namely the distribution of the maximum among a random number (truncated Poisson distributed) of exponential times. The time of each recurrence is then given by the maximum lifetime value among all latent causes. Inference is based on a maximum likelihood approach. A simulation study is performed in order to observe the frequentist properties of the estimation procedure for small and moderate sample sizes. We also investigated likelihood-based tests procedures. A real example from a gastroenterology study concerning small bowel motility during fasting state is used to illustrate the methodology. Finally, we apply the proposed model to a real data set and compare it with the classical Homogeneous Poisson model, which is a particular case. [ABSTRACT FROM AUTHOR]

Let, be independent copies of bivariate random vectorwith joint cumulative distribution functionand probability density function. For, the vector of order statistics ofand, respectively, is denoted by. Let,, be a new sample from, which is independent from. Letbe the rank of order statisticsin a new sampleandbe the rank of order statisticsin a new sample. We derive the joint distribution of discrete random vectorand a general scheme wherein the distributions of new and old samples are different is considered. Numerical examples for given well-known distribution are also provided. [ABSTRACT FROM AUTHOR]

In real problems, it is usual to have the available data presented as intervals. Therefore, different approaches have been proposed to obtain a regression model for this new type of data. In this paper, we represent the interval-valued response variableas a bivariate random vector and we consider the copula's theory to propose a general bivariate distribution forZ, creating a more flexible random component to the model. Inference techniques and a residual definition based on deviance are considered, as well as applications to synthetic and real data sets that demonstrate the usefulness of the proposed approach. The new method is also compared with other methods reported in the literature. [ABSTRACT FROM PUBLISHER]

This study proposes a simple way to perform a power analysis of Mantel's test applied to squared Euclidean distance matrices. The general statistical aspects of the simple Mantel's test are reviewed. The Monte Carlo method is used to generate bivariate Gaussian variables in order to create squared Euclidean distance matrices. The power of the parametric correlationt-test applied to raw data is also evaluated and compared with that of Mantel's test. The standard procedure for calculating punctual power levels is used for validation. The proposed procedure allows one to draw the power curve by running the test only once, dispensing with the time demanding standard procedure of Monte Carlo simulations. Unlike the standard procedure, it does not depend on a knowledge of the distribution of the raw data. Thesimulated powerfunction has all the properties of the power analysis theory and is in agreement with the results of the standard procedure. [ABSTRACT FROM PUBLISHER]

Internal migration is one of the major components of rapid and unplanned growth of towns and cities especially in the developing countries. This paper describes the transition pattern of internal out migration in Bangladesh and some sociodemographic factors influencing such migration in the country using a covariate-dependent Markov model. Four types of migration behavior namely, rural to rural, rural to urban, urban to rural and urban to urban are under consideration of this paper. Defining two discrete states, urban and rural, each of such transition can be characterized by a stochastic process; hence we use a two-state Markov chain for this purpose. We find that age, sex, division and reason of migration are significantly associated with internal migration in Bangladesh. The major findings include that any type of migration, rural to rural, rural to urban, urban to rural and urban to urban, mostly take place at the ages of 15–30 as well as at the ages of 0–15; females have higher odds than males to make a migration; Dhaka, Rajshahi and Chittagong divisions have remarkably higher migration rate as compared to Barisal and Sylhet division; and the professional reason is the main reason for rural to urban migration. [ABSTRACT FROM AUTHOR]

In medical diagnostic research, it is customary to collect multiple continuous biomarker measures to improve the accuracy of diagnostic tests. A prevalent practice is to combine the measurements of these biomarkers into one single composite score. However, incorporating those biomarker measurements into a single score depends on the combination of methods and may lose vital information needed to make an effective and accurate decision. Furthermore, a diagnostic cut-off is required for such a combined score, and it is difficult to interpret in actual clinical practice. The paper extends the classical biomarkers' accuracy and predictive values from univariate to bivariate markers. Also, we will develop a novel pseudo-measures system to maximize the vital information from multiple biomarkers. We specified these pseudo-and-or classifiers for the true positive rate, true negative rate, false-positive rate, and false-negative rate. We used them to redefine classical measures such as the Youden index, diagnostics odds ratio, likelihood ratios, and predictive values. We provide optimal cut-off point selection based on the modified Youden index with numerical illustrations and real data analysis for this paper's newly developed pseudo measures., Competing Interests: No potential conflict of interest was reported by the author(s)., (© 2022 Informa UK Limited, trading as Taylor & Francis Group.)