Multiresponse Regression Models Research Articles

Bayesian inference for identifying tumour-specific cancer dependencies through integration of ex-vivo drug response assays and drug-protein profiling

The identification of tumor-specific molecular dependencies is essential for the development of effective cancer therapies. Genetic and chemical perturbations are powerful tools for discovering these dependencies. Even though chemical perturbations can be applied to primary cancer samples at large scale, the interpretation of experiment outcomes is often complicated by the fact that one chemical compound can affect multiple proteins. To overcome this challenge, Batzilla et al. (PLoS Comput Biol 18(8): e1010438, 2022) proposed DepInfeR, a regularized multi-response regression model designed to identify and estimate specific molecular dependencies of individual cancers from their ex-vivo drug sensitivity profiles. Inspired by their work, we propose a Bayesian extension to DepInfeR. Our proposed approach offers several advantages over DepInfeR, including e.g. the ability to handle missing values in both protein-drug affinity and drug sensitivity profiles without the need for data pre-processing steps such as imputation. Moreover, our approach uses Gaussian Processes to capture more complex molecular dependency structures, and provides probabilistic statements about whether a protein in the protein-drug affinity profiles is informative to the drug sensitivity profiles. Simulation studies demonstrate that our proposed approach achieves better prediction accuracy, and is able to discover unreported dependency structures.

Reproducing Kernel Hilbert Space Approach to Multiresponse Smoothing Spline Regression Function

In statistical analyses, especially those using a multiresponse regression model approach, a mathematical model that describes a functional relationship between more than one response variables and one or more predictor variables is often involved. The relationship between these variables is expressed by a regression function. In the multiresponse nonparametric regression (MNR) model that is part of the multiresponse regression model, estimating the regression function becomes the main problem, as there is a correlation between the responses such that it is necessary to include a symmetric weight matrix into a penalized weighted least square (PWLS) optimization during the estimation process. This is, of course, very complicated mathematically. In this study, to estimate the regression function of the MNR model, we developed a PWLS optimization method for the MNR model proposed by a previous researcher, and used a reproducing kernel Hilbert space (RKHS) approach based on a smoothing spline to obtain the solution to the developed PWLS optimization. Additionally, we determined the symmetric weight matrix and optimal smoothing parameter, and investigated the consistency of the regression function estimator. We provide an illustration of the effects of the smoothing parameters for the estimation results using simulation data. In the future, the theory generated from this study can be developed within the scope of statistical inference, especially for the purpose of testing hypotheses involving multiresponse nonparametric regression models and multiresponse semiparametric regression models, and can be used to estimate the nonparametric component of a multiresponse semiparametric regression model used to model Indonesian toddlers’ standard growth charts.

Quality management of the chemical-technological process for continuous synthesis of pharmaceutical substances of medicinal compounds in flow microreactors

Objectives. The introduction of digital tools for the development of medicines, intelligent management systems, and quality control is stipulated not only by modern requirements for the chemical and pharmaceutical industry but also by strict regulatory requirements for manufactured products. This principle ensures the release of a quality product on the first attempt. The aim of this study is to develop information support for the intelligent quality management system for the production of active pharmaceutical substances (APSs) for medicines using a fundamentally new technology: continuous synthesis in flow microreactors. To develop the necessary information support, we developed appropriate systemic, informational, and mathematical models; algorithms for the online management of the experiment; and techniques and algorithms to qualitatively assess whether the product meets official regulatory documents.Methods. System analysis techniques, information and mathematical modeling techniques with multireference regression models, and online optimization using the Hook–Jeevs algorithm (a method of expert evaluation based on the concordance factor) were used to solve the problems formulated.Results. To manage the quality of the process of continuous APS synthesis in the flow microreactor, we developed theoretic multiple system models that were designed to build the digital information environment for the process of experimental research. We developed algorithms for mathematical modeling and optimization of the control process based on multiresponse regression models and an online optimization algorithm that allows the process to be managed step by step, taking into account the limitations. Our results show that the degree of conversion is higher in reactions that contain bromodiphenylmethan.Conclusions. Based on mathematical modeling method algorithms for the quality control of the process of continuous APS synthesis on a fundamentally new microreactor system, Qmix were developed. The applicability of the proposed methods and algorithms in the production of the drug diphenhydramine from chlorobenzohydrol and bromobenzohydrol as initial substances was proven by an experimental study. The built models were statistically adequate and valid.

Practical method of vector optimization on the example of optimization of thermal conditions

The practical method of vector optimization is described by the example of optimization of thermal conditions in industrial premises during their design based on the construction of a multi-response regression model. A practical algorithm is proposed for determining the discrete set of Pareto optimal thermal parameters.

R-optimal designs for multi-response regression models with multi-factors

We investigate R-optimal designs for multi-response regression models with multi-factors, where the random errors in these models are correlated. Several theoretical results are derived for R-optimal designs, including scale invariance, reflection symmetry, line and plane symmetry, and dependence on the covariance matrix of the errors. All the results can be applied to linear and non-linear models. In addition, an efficient algorithm based on an interior point method is developed for finding R-optimal designs on discrete design spaces. The algorithm is very flexible, and can be applied to any multi-response regression model.

Minimax D-optimal designs for multivariate regression models with multi-factors

In multi-response regression models, the error covariance matrix is never known in practice. Thus, there is a need for optimal designs which are robust against possible misspecification of the error covariance matrix. In this paper, we approximate the error covariance matrix with a neighborhood of covariance matrices, in order to define minimax D-optimal designs that are robust against small departures from an assumed error covariance matrix. It is well known that the optimization problems associated with robust designs are non-convex, which makes it challenging to construct robust designs analytically or numerically, even for one-response regression models. We show that the objective function for the minimax D-optimal design is a difference of two convex functions, and develop a flexible algorithm for computing minimax D-optimal designs, which can be applied to any multi-response model with a discrete design space. We also derive several theoretical results for minimax D-optimal designs.

Estimation of covariance matrix using multi-response local polynomial estimator for designing children growth charts: A theoretically discussion

In statistical analysis for instance regression analysis we always be faced a estimation problem of regression function which draws relationship between variables in the regression model. In the real cases we frequently meet the relationship between one or more response variables and one or more predictor variables where there are correlations between responses that is called a multi-response regression model. There are two approaches to estimate the multi-response regression model, i.e., parametric and nonparametric. One of estimators in nonparametric regression model is local polynomial estimator for estimating the regression function. Since there are correlations between responses then in the estimating of regression function we need a weight matrix that is to be inverse of covariance matrix of error. Therefore, the main objective of this research is to estimate of covariance matrix of error by using multi-response local polinomial estimator. The result of this research is a covariance matrix estimator that is in the future can be used to design children growth charts.

Robust feature screening for multi-response trans-elliptical regression model with ultrahigh-dimensional covariates

In this paper, we innovatively propose an extremely flexible semi-parametric regression model called Multi-response Trans-Elliptical Regression (MTER) Model, which can capture the heavy-tail characteristic and tail dependence of both responses and covariates. We investigate the feature screening procedure for the MTER model, in which Kendall’ tau-based canonical correlation estimators are proposed to characterize the correlation between each transformed predictor and the multivariate transformed responses. The main idea is to substitute the classical canonical correlation ranking index in [X. B. Kong, Z. Liu, Y. Yao and W. Zhou, Sure screening by ranking the canonical correlations, TEST 26 (2017) 1–25] by a carefully constructed non-parametric version. The sure screening property and ranking consistency property are established for the proposed procedure. Simulation results show that the proposed method is much more powerful to distinguish the informative features from the unimportant ones than some state-of-the-art competitors, especially for heavy-tailed distributions and high-dimensional response. At last, a real data example is given to illustrate the effectiveness of the proposed procedure.

Perceiving Reconciliation: Child Care Policies and Gendered Time Conflicts

In recent decades, many studies have examined gender-related differences in paid employment and the reconciliation of family and employment. Considering perceptions of time conflicts with regards to work at home and leisure activities, this article contributes to a more encompassing understanding of attitudes toward reconciliation problems. Special attention is given to the role of external child care services. The use of an original data set from 60 Swiss municipalities and hierarchical multiresponse regression models enable an analysis of the various aspects of time conflicts simultaneously, and a consideration of how different policy contexts shape these attitudes. This study provides evidence that the communal provision of external child care is related to gender-specific perceptions of time conflicts. Most interestingly, men seem to be affected most strongly by communal policy conditions, whereby the provision of external child care is related to systematically higher levels of time conflicts.

Diagnostics of a Multiresponse Regression Model with Autocorrelated Errors

In this paper we study the diagnostics of a multiresponse regression model with a first-order autoregressive error sequence. The deletion technique is used to identify the outliers taking account of the dependence structure of the errors. Besides the usual measures, some scalar measures to gauge the impact of the ouliers on the regression are suggested.

Accuracy increase of temperature measurement on thermal images

Multiresponse regression model is used for dependence of thermal image pixel amplitudes from temperature to increase accuracy of remote indirect method of temperature measurement. Obtained model allows to calculate integral estimation of temperature and its dispersion on all pixels taking into account correlation relationships of amplitude observation errors.

MATRIKS KOVARIANSI DALAM REGRESI NONPARAMETRIK MULTIRESPON PADA KASUS KORELASI SAMA DAN KORELASI TIDAK SAMA

In the real cases, we are frequently faced the problem in which two or more dependent variables are observed at several values of the independent variables, such as at multiple time points. Multi-response nonparametric regression model, especially smoothing spline model, provides powerful tools to model the function which represents association of among the variables. The problem is how to estimate nonparametric regression curve of the multi-response nonparametric regression model. The nonparametric regression curve can be estimated using spline estimator approach, that is by carrying out penalized weighted least-squares optimation. Therefore, we need a covariance matrix which will be used as a weight of the optimation. In this paper, we determine the construction of covariance matrix for both equal and unequal of correlations cases. The results show that the covariance matrices have quite similar construction of diagonal elements but the elements outside the diagonal have very different construction that depend on the construction of the Jordan matrix.

A note on $$R$$ -optimal designs for multiresponse models

This paper considers the optimal design problem for multiresponse regression models. The $$R$$ -optimality introduced by Dette (J R Stat Soc B 59:97–110, 1997) for single response experiments is extended to the case of multiresponse parameter estimation. A general equivalence theorem for the $$R$$ -optimality is provided for multiresponse models. Illustrative examples of the $$R$$ -optimal designs for two multiresponse models are presented based on the general equivalence theorem.

Designing of Child Growth Chart Based on Multi-Response Local Polynomial Modeling

Problem statements: Anthropometry measures used to measure physical children growth are not onlyweight but also height and head circumference. In this study we develop the estimation of multi-response localpolynomial regression and apply it to design growth chart for children up to five years old based on three responsevariables i.e., weight, height and head circumference. Approach: Based on local polynomial estimator, wedescribe the estimation of multi-response nonparametric regression model by using weighted least squared. Themodel is applied to design health card of children up to five years old by using children data in Surabaya, Indonesia. Generalized Cross Validation (GCV) method is used to determine the order of local polynomial fit and the bandwidthfor each response variable. Results: We formulate the multi-response local polynomial modeling and give a design of health card of children up to five years old in Surabayacity, Indonesia. Conclusion: The child growth chart based on multi-response local polynomial modeling showsincreasing of children nutrition in Surabaya 2010.Because of the strong correlations among all three response variables,the simultaneosly approach for model estimationis better than partly single response approach. The result of simultaneosly model estimation based on multi-response local polynomial modeling satisfies goodness of fit criterion i.e., mean squared error value tend to zero and determination coefficient value tend to one.

Spline Estimator in Multi-Response Nonparametric Regression Model with Unequal Correlation of Errors

Problem statement: In many applications two or more dependent variables are observed at several values of the independent variables, such as at time points. The statistical problems are to estimate functions that model their dependences on the independent variables and to investigate relationships between these functions. Nonparametric regression model, especially smoothing splines provide powerful tools to model the functions which draw association of these variables. Approach: Penalized weighted least-squares was used to jointly estimate nonparametric functions from contemporaneously correlated data. We apply Generalized Maximum Likelihood (GML), Generalized Cross Validation (GCV) and leaving-out-one-pair Cross Validation (CV) for estimating the smoothing parameters, the weighting parameters and the correlation parameter Results: In this study we formulated the multi-response nonparametric regression model with unequal correlation of errors and give a theoretical method for both obtaining distribution of the response and estimating the nonparametric function in the model. We also estimate the smoothing parameters, the weighting parameters and the correlation parameter simultaneously by applying three methods GML, GCV and CV. Conclusion: Distribution of responses is normal. With multiple correlated responses it is better to estimate these functions jointly using the penalized weighted least-squares.

A goodness-of-fit test for parametric and semi-parametric models in multiresponse regression

We propose an empirical likelihood test that is able to test the goodness of fit of a class of parametric and semi-parametric multiresponse regression models. The class includes as special cases fully parametric models; semi-parametric models, like the multiindex and the partially linear models; and models with shape constraints. Another feature of the test is that it allows both the response variable and the covariate be multivariate, which means that multiple regression curves can be tested simultaneously. The test also allows the presence of infinite-dimensional nuisance functions in the model to be tested. It is shown that the empirical likelihood test statistic is asymptotically normally distributed under certain mild conditions and permits a wild bootstrap calibration. Despite the large size of the class of models to be considered, the empirical likelihood test enjoys good power properties against departures from a hypothesized model within the class.

Parametric sensitivity: A case study comparison

This article presents a comparative analysis of three derivative-based parametric sensitivity approaches in multi-response regression estimation: marginal sensitivity, profile-based approach developed by [Sulieman, H., McLellan, P.J., Bacon, D.W., 2004, A Profile-based approach to parametric sensitivity in multiresponse regression models, Computational Statistics & Data Analysis, 45, 721–740] and the commonly used approach of the Fourier Amplitude Sensitivity Test (FAST). We apply the classical formulation of FAST in which Fourier sine coefficients are utilized as sensitivity measures. Contrary to marginal sensitivity, profile-based and FAST approaches provide sensitivity measures that account for model nonlinearity and are pertinent to linear and nonlinear regression models. However, the primary difference between FAST and profile-based sensitivity is that traditional FAST fails to account for parameter dependencies in the model system while these dependencies are considered in the analysis procedure of profile-based sensitivity through the re-estimation of the remaining model parameters conditional on the values of the parameter of interest. An example is discussed to illustrate the comparisons by applying the three sensitivity methods to a model described by set of non-linear differential equations. Some computational aspects are also explored.

A profile-based approach to parametric sensitivity in multiresponse regression models

The profile-based sensitivity measure proposed by Sulieman et al. (Technometrics 43(4) (2001) 425) for single-response nonlinear models is extended to the case of multiresponse parameter estimation based on the Box–Draper estimation criterion. The profile-based sensitivity measure for the parameters in the multiresponse case is a vector-valued measure which simultaneously provides complete insight on the sensitivity behaviours of the M predicted responses in the model with respect to a parameter of interest. While providing first-order sensitivity information, the profile-based sensitivity coefficients, unlike the conventional sensitivity coefficients, also account for nonlinear parameter estimate co-dependencies derived from the Hessian of the determinant criterion, and are thus valid over broader ranges of parameter uncertainties. Two examples are discussed to illustrate applications of the extended measure.

A profile-based approach to parametric sensitivity in multiresponse regression models

A profile-based approach to parametric sensitivity in multiresponse regression models

Multiresponse Models for Calibrating Scanners

A method of calibrating scanners based on multiresponse regression models which connect the color parameters of color images of a calibrated light target with the results of the scanning of this target is proposed. A procedure and the results of an analysis of the covariance matrices of the errors of observation of the color parameters for different types of scanners are presented. Estimates of the prediction capability of the proposed calibration method are given and comparative results of its use are presented.