Bivariate Situation Research Articles

HIV deathrate prediction by Gaidai multivariate risks assessment method.

HIV is a contagious disease with reportedly high transmissibility, being spread worldwide, with certain mortality, allegedly presenting a burden to public health worldwide. The main objective of this study was to determine excessive HIV death risks at any time within any region or country of interest. Current study presents a novel multivariate public health system bio-risk assessment approach that is particularly applicable to environmental multi-regional, biological, and public health systems, being observed over a representative period of time, yielding reliable long-term HIV deathrate assessment. Hence, the development of a new bio-statistical approach, that is, population-based, multicenter, and medical survey-based. The expansion of extreme value statistics from the univariate to the bivariate situation meets with numerous challenges. Firstly, the univariate extreme value types theorem cannot be directly extended to the bivariate (2D) case, - not to mention challenges with system dimensionality higher than 2D. Existing bio-statistical methods that process spatiotemporal clinical observations of multinational bio-processes often do not have the advantage of efficiently dealing with high regional dimensionalities and complex nonlinear inter-correlations between different national raw datasets. Hence, this study advocates the direct application of the novel bio-statistical Gaidai method to a raw unfiltered clinical data set. This investigation described the successful application of a novel bio-risk assessment approach, yielding reliable long-term HIV mortality risk assessments. The suggested risk assessment methodology may be utilized in various public bio and public health clinical applications based on available raw patient survey datasets.

Future worldwide coronavirus disease 2019 epidemic predictions by Gaidai multivariate risk evaluation method.

Accurate estimation of pandemic likelihood in every US state of interest and at any time. Coronavirus disease 2019 (COVID-19) is an infectious illness with a high potential for global dissemination and low rates of fatality and morbidity, placing some strains on national public health systems. This research intends to benchmark a novel technique, that enables hazard assessment, based on available clinical data, and dynamically observed patient numbers while taking into account pertinent territorial and temporal mapping. Multicentre, population-based, and biostatistical strategies have been utilized to process raw/unfiltered medical survey data. The expansion of extreme value statistics from the univariate to the bivariate situation meets with numerous challenges. First, the univariate extreme value types theorem cannot be directly extended to the bivariate (2D) case,-not to mention challenges with system dimensionality higher than 2D. Assessing outbreak risks of future outbreaks in any nation/region of interest. Existing bio-statistical approaches do not always have the benefits of effectively handling large regional dimensionality and cross-correlation between various regional observations. These methods deal with temporal observations of multi-regional phenomena. Apply contemporary, novel statistical/reliability techniques directly to raw/unfiltered clinical data. The current study outlines a novel bio-system hazard assessment technique that is particularly suited for multi-regional environmental, bio, and public health systems, observed over a representative period. With the use of the Gaidai multivariate hazard assessment approach, epidemic outbreak spatiotemporal risks may be properly assessed. Based on raw/unfiltered clinical survey data, the Gaidai multivariate hazard assessment approach may be applied to a variety of public health applications. The study's primary finding was an assessment of the risks of epidemic outbreaks, along with a matching confidence range. Future global COVID-19/severe acute respiratory syndrome coronavirus 2 (SARS-COV2) epidemic risks have been examined in the current study; however, COVID-19/SARS-COV2 infection transmission mechanisms have not been discussed.

Multivariate Density Estimation Using a Multivariate Weighted Log-Normal Kernel

This paper suggests a multivariate asymmetric kernel density estimation using a multivariate weighted log-normal (LN) kernel for non-negative multivariate data. Asymptotic properties of the multivariate weighted LN kernel density estimator are studied. Simulation studies are also conducted in the bivariate situation.

Trend estimation of multivariate time series with controlled smoothness

ABSTRACTThis paper extends the univariate time series smoothing approach provided by penalized least squares to a multivariate setting, thus allowing for joint estimation of several time series trends. The theoretical results are valid for the general multivariate case, but particular emphasis is placed on the bivariate situation from an applied point of view. The proposal is based on a vector signal-plus-noise representation of the observed data that requires the first two sample moments and specifying only one smoothing constant. A measure of the amount of smoothness of an estimated trend is introduced so that an analyst can set in advance a desired percentage of smoothness to be achieved by the trend estimate. The required smoothing constant is determined by the chosen percentage of smoothness. Closed form expressions for the smoothed estimated vector and its variance-covariance matrix are derived from a straightforward application of generalized least squares, thus providing best linear unbiased estimates for the trends. A detailed algorithm applicable for estimating bivariate time series trends is also presented and justified. The theoretical results are supported by a simulation study and two real applications. One corresponds to Mexican and US macroeconomic data within the context of business cycle analysis, and the other one to environmental data pertaining to a monitored site in Scotland.

Robustifying the multivariate chain-ladder method: A comparison of two methods

The expected result of a non-life insurance company is usually determined for its activity in different business lines as a whole. This implies that the claims reserving problem for a portfolio of several (perhaps correlated) subportfolios is to be solved. A popular technique for studying such a portfolio is the chain-ladder method. However, it is well known that the chain-ladder method is very sensitive to outlying data. For the bivariate situation, we have already developed robust solutions for the chain-ladder method by introducing two techniques for detecting and correcting outliers. In this article we focus on higher dimensions. Being subjected to multiple constraints (no graphical plots available), the goal of our research is to find solutions to detect and smooth the influence of outlying data on the outstanding claims reserve in higher dimensional data sets. The methodologies are illustrated and computed for real examples from the insurance practice.

Penalization of Robin boundary conditions

This paper is devoted to the mathematical analysis of a method based on fictitious domain approach. Boundary conditions of Robin type (also known as Fourier boundary conditions) are enforced using a penalization method. A complete description of the method and a full analysis are provided for univariate elliptic and parabolic problems using finite difference approximation. Numerical evidence of the predicted estimations is provided as well as numerical results for a nonlinear problem and a first extension of the method in the bivariate situation is proposed.

Detection and correction of outliers in the bivariate chain–ladder method

The expected profit or loss of a non-life insurance company is determined for the whole of its multiple business lines. This implies the study of the claims reserving problem for a portfolio consisting of several correlated run-off triangles. A popular technique to deal with such a portfolio is the multivariate chain–ladder method of Merz and Wüthrich (2008). However, it is well known that the chain–ladder method is very sensitive to outlying data. For the univariate case, we have already developed a robust version of the chain–ladder method. In this article we propose two techniques to detect and correct outlying values in a bivariate situation. The methodologies are illustrated and compared on real examples from practice.

A Bayesian Approach to Parameter Estimation for Kernel Density Estimation via Transformations

AbstractIn this paper, we present a Markov chain Monte Carlo (MCMC) simulation algorithm for estimating parameters in the kernel density estimation of bivariate insurance claim data via transformations. Our data set consists of two types of auto insurance claim costs and exhibits a high-level of skewness in the marginal empirical distributions. Therefore, the kernel density estimator based on original data does not perform well. However, the density of the original data can be estimated through estimating the density of the transformed data using kernels. It is well known that the performance of a kernel density estimator is mainly determined by the bandwidth, and only in a minor way by the kernel. In the current literature, there have been some developments in the area of estimating densities based on transformed data, where bandwidth selection usually depends on pre-determined transformation parameters. Moreover, in the bivariate situation, the transformation parameters were estimated for each dimension individually. We use a Bayesian sampling algorithm and present a Metropolis-Hastings sampling procedure to sample the bandwidth and transformation parameters from their posterior density. Our contribution is to estimate the bandwidths and transformation parameters simultaneously within a Metropolis-Hastings sampling procedure. Moreover, we demonstrate that the correlation between the two dimensions is better captured through the bivariate density estimator based on transformed data.

Hotelling's T 2 Method in Multivariate On-Line Surveillance: On the Delay of an Alarm

A system for detecting changes in an on-going process is needed in many situations. On-line monitoring (surveillance) is used in early detection of disease outbreaks, of patients at risk, and of financial instability. By continually monitoring one or several indicators, we can, early, detect a change in the processes of interest. There are several suggested methods for multivariate surveillance, one of which is the Hotelling's T 2. Since one aim in surveillance is quick detection of a change, it is important to use evaluation measures that reflect the timeliness of an alarm. One suggested measure is the expected delay of an alarm, in relation to the time of change (τ) in the process. Here we investigate a delay measure for the bivariate situation. Generally, the measure depends on both change times (i.e. τ1 and τ2). We show that, for a bivariate situation using the T 2 method, the delay only depends on τ1 and τ2 through the distance τ1–τ2.

The lipoprotein subfraction profile: heritability and identification of quantitative trait loci

The HDL and LDL subclass profile is an emerging cardiovascular risk factor. Yet, the biological and genetic mechanisms controlling the lipoprotein subclass distribution are unclear. Therefore, we aimed 1) to determine the heritability of the entire spectrum of LDL and HDL subclass features and 2) to identify gene loci influencing the lipoprotein subfraction pattern. Using NMR spectroscopy, we analyzed the lipoprotein subclass distribution in 1,275 coronary artery disease patients derived from the Regensburg Myocardial Infarction Family Study. We calculated heritabilities, performed a microsatellite genome scan, and calculated linkage. HDL and LDL subclass profiles showed heritabilities ranging from 23% to 67% (all P < 10(-3)) of traits using univariate calculation. After multivariate adjustment, we found heritabilities of 27-48% (all P < 0.05) for HDL and 21-44% for LDL traits. The linkage analysis revealed a significant logarithm of the odds (LOD) score (3.3) for HDL particle concentration on chromosome 18 and a highly suggestive signal for HDL particle size on chromosome 12 (2.9). After multivariate adjustment, we found a significant maximum LOD score of 3.7 for HDL size. Our study is the first to analyze heritability and linkage for the entire spectrum of LDL and HDL subclass features. Our findings may lead to the identification of genes controlling the lipoprotein subclass distribution.

Non-parametric estimation of lifetime distribution of competing risk models when censoring times are missing

There are situations in the analysis of failure time or lifetime data where the censoring times of unfailed units are missing. The non-parametric estimator of the lifetime distribution for such data is available in literature. In this paper we consider an extension of this situation to the univariate and bivariate competing risk setups. The maximum likelihood and simple moment estimators of cause specific distribution functions in both univariate and bivariate situations are developed. A simulation study is carried out to assess the performance of the estimators. Finally, we illustrate the method with real data set.

Modeling Unequally Spaced Bivariate Growth Curve Data Using a Kalman Filter Approach

ABSTRACT In many clinical studies, patients are followed over time with their responses measured longitudinally. Using mixed model theory, one can characterize these data using a wide array of across subject models. A state-space representation of the mixed effects model and use of the Kalman filter allows one to have great flexibility in choosing the within error correlation structure even in the presence of missing or unequally spaced observations. Furthermore, using the state-space approach, one can avoid inverting large matrices resulting in efficient computation. The approach also allows one to make detailed inference about the error correlation structure. We consider a bivariate situation where the longitudinal responses are unequally spaced and assume that the within subject errors follows a continuous first-order autoregressive (CAR(1)) structure. Since a large number of nonlinear parameters need to be estimated, the modeling strategy and numerical techniques are critical in the process. We developed both a Visual Fortran® and a SAS® program for modeling such data. A simulation study was conducted to investigate the robustness of the model assumptions. We also use data from a psychiatric study to demonstrate our model fitting procedure.

Discrete Rayleigh Distribution

Using a general approach for discretization of continuous life distributions in the univariate & bivariate situations, we have proposed a discrete Rayleigh distribution. This distribution has been examined in detail with respect to two measures of failure rate. Characterization results have also been studied to establish a direct link between the discrete Rayleigh distribution, and its continuous counterpart. This discretization approach not only expands the scope of reliability modeling, but also provides a method for approximating probability integrals arising out of a continuous setting. As an example, the reliability value of a complex system has been approximated. This discrete approximation in a nonnormal setting can be of practical use & importance, as it can replace the much relied upon simulation method. While the replication required is minimal, the degree of accuracy remains reasonable for our suggested method when compared with the simulation method.

Some simple corrected confidence intervals following a sequential test

In this paper, we consider the construction of confidence intervals for a secondary variable after a sequential test for a primary variable. Asymptotic moment expansions for randomly stopped averages are used to guide us to correct the naive confidence interval. Three corrected confidence intervals are investigated in terms of their coverage probability via Monte Carlo simulation. All three corrected confidence intervals are easy to calculate and improvements over the naive confidence interval for most of the situations considered. For the bivariate normal situation, one corrected confidence interval has its minimum coverage probability very close to its nominal confidence level and hence is recommended.

The Potential for Conflict Index: A Graphic Approach to Practical Significance of Human Dimensions Research

To facilitate the understanding and applicability of human dimensions findings, this article develops a formula for computing a Potential for Conflict Index (PCI) and a graphic technique for presenting the results. This approach (1) conveys information about a distribution's central tendency, dispersion, and form simultaneously; (2) uses a graphic display that allows easy assimilation of research findings; and (3) places the findings in the context of managerial concern. Computed values for PCI range from 0 to 1, where 0 indicates no conflict and 1 indicates maximum conflict. Data are presented from a recent wildlife values project to illustrate the computation and graphic display of the PCI for univariate and bivariate situations. Researchers are encouraged to adopt this approach or variations of it to improve the understandability of their research results.

Discretization of Continuous Distributions with an Application to Stress-Strength Reliability

A generic approach has been studied for discretization of continuous distributions in the univariate and bivariate situations. In particular, discretization of uniform distribution has been used to develop a bivariate binary model. Characterization results have also been studied to establish a direct link between the discrete Weibull distribution and its continuous counterpart. Attempts have also been made for approximating reliability of complex systems using suitably adjusted discrete concentrations of continuous design variables.

Maximally Selected Rank Statistics for Dose-Response Problems

We consider the bivariate situation of some quantitative, ordinal, binary or censored response variable and some quantitative or ordinal exposure variable (dose) with a hypothetical effect on the response. Data can either be the outcome of a planned dose-response experiment with only few dose levels or of an observational study where, for example, both exposure and response variable are observed within each individual. We are interested in testing the null hypothesis of no effect of the dose variable vs. a dose-response function depending on an unknown ‘threshold’ parameter. The variety of dose-response functions considered ranges from no observed effect level (NOEL) models to umbrella alternatives. Here we discuss generalizations of the method of Lausen & Schumacher (Biometrics, 1992, 48, 73–85)which are based on combinations of two-sample rank statistics and rank statistics for trend. Our approach may be seen as a generalization of a proposal for change-point problems. Using the approach of Davies (Biometrika, 1987, 74, 33–43)we derive and approximate the asymptotic null distribution for a large number of thresholds considered. We use an improved Bonferroni inequality as approximation for a small number of thresholds considered. Moreover, we analyse the small sample behaviour by means of a Monte-Carlo study. Our paper is illustrated by examples from clinical research and epidemiology.

A multivariate mixture of Weibull distributions in reliability modeling

A new class of multivariate distribution is derived where each component is a mixture of Weibull distribution. The approach in this paper is based on the introduction of an exponentially distributed latent random variable. The new class includes several multivariate and bivariate models including Marshall and Olkin type. The moment generating function and, hence, the correlation structure is obtained for the bivariate situation. The distribution of the minimum in a competing risk framework is discussed and various other properties including correlation structures are investigated.

Multiple functional regression—II. Rotation followed by classical regression technique

A method and FORTRAN program is presented for calculating a multivariate functional regression, analogous to the reduced major axis regression for the bivariate situation. The method is based on rotating the coordinates of the experimental points with respect to the axes. The rotation is such that the direction of distances whose sums of squares are to be minimized now are parallel to the “ Y” axis. A classical regression, using matrix expressions, then is performed following which the best-fit line is rotated back to give its equation in the original space. The rotation is performed to give a regression in a direction proportional to the square roots of the total variances of the parameters in the regression (which is the reduced major axis regression for the bivariate situation). Standard errors of the regression coefficients are estimated by a Monte-Carlo method. The program also can perform a classical regression, simply be omitting the rotation phase. The two examples used in Part 1 are repeated. In both examples the program gives the same result for classical regression as other methods including the function minimization method of Part 1. The first example is a bivariate example and the program gives the same answer as analytical expressions for the reduced major axis regression. In the second, the multivariate example, the program gives the same result as the function minimization method of Part 1.

SIAM: Statistics information access method

This paper outlines a new data access method for statistical information. When statistical data is organized using this access method, statistical parametric estimates can be processed asymptotically with respect to time, i.e. the precision of the estimates increases asymptotically with increase in processing time. This structure also enables the estimation of statistical parameters for range-type queries. Estimating the mean value and the second moment of the values of an attribute using SIAM is illustrated. Expressions for precision of the estimates, using up to a certain level of the SIAM index structure, are derived. SIAM structures have been extended to bivariate situation, for calculating covariances. Sampling techniques bases on SIAM organization has been discussed. Performance for computing statistics from SIAM structures has been compared with the present data access methods.