A Nonrecursive Estimator for the Cox Model

The Cox regression model is one of the most widely used models to incorporate covariates. The frequently used partial likelihood estimator of the regression parameter has to be computed iteratively. In this paper we propose a noniterative estimator for the regression parameter and show that under certain conditions it dominates another noniterative estimator derived by Kalbfleish and Prentice. The new estimator is demonstrated on lifetime data of rats having been subject to insult with a carcinogen.     

Independent contrasts and PGLS regression estimators are equivalent

We prove that the slope parameter of the ordinary least squares regression of phylogenetically independent contrasts (PICs) conducted through the origin is identical to the slope parameter of the method of generalized least squares (GLSs) regression under a Brownian motion model of evolution. This equivalence has several implications: 1. Understanding the structure of the linear model for GLS regression provides insight into when and why phylogeny is important in comparative studies. 2. The limitations of the PIC regression analysis are the same as the limitations of the GLS model. In particular, phylogenetic covariance applies only to the response variable in the regression and the explanatory variable should be regarded as fixed. Calculation of PICs for explanatory variables should be treated as a mathematical idiosyncrasy of the PIC regression algorithm. 3. Since the GLS estimator is the best linear unbiased estimator (BLUE), the slope parameter estimated using PICs is also BLUE. 4. If the slope is estimated using different branch lengths for the explanatory and response variables in the PIC algorithm, the estimator is no longer the BLUE, so this is not recommended. Finally, we discuss whether or not and how to accommodate phylogenetic covariance in regression analyses, particularly in relation to the problem of phylogenetic uncertainty. This discussion is from both frequentist and Bayesian perspectives.     

A novel force field parameter optimization method based on LSSVR for ECEPP

In this paper, we propose a novel force field parameter optimization method based on LSSVR and optimize the torsion energy parameters of ECEPP force field. In this method force field parameter optimization problem is turned into a support vector regression problem. Protein samples for regression model training are chosen from Protein Data Bank. The experiments show that the optimized force-field parameters make both α-helix and β-hairpin structures more consistent with the experimental implications than the original parameters.     

Analysis of Colony-Forming Ability of Human Fibroblast Strains by Linear Regression

A linear regression approach is presented for the statistical analysis of dose-response curves obtained by measuring the colony-forming ability of human fibroblast strains. The crucial determination of the dose range in which the linear model can be assumed is achieved by a combination of statistical criteria and biological claims. As a basic quantitative parameter we investigate the slope of the regression line and, by taking reciprocals, we retransform it into the biologically established parameter D₀. Several methods for the combination of estimates are presented.     

Inference on Collapsibility in Generalized Linear Models

GREENLAND and MICKEY (1988) derived a closed-form collapsibility test and confidence interval for IxJxK contingency tables with qualitative factors, and presented a small simulation study of its performance. We show how their method can be extended to regression models linear in the natural parameter of a one-parameter exponential family, in which the parameter of interest is the difference of “crude” and “adjusted” regression coefficients. A simplification of the method yields a generalization of the test for omitted covariates given by HAUSMAN (1978) for ordinary linear regression. We present an application to a study of coffee use and myocardial infarction, and a simulation study which indicates that the simplified test performs adequately in typical epidemiologic settings.     

Regression Modeling of a Physiological Parameter Affected by Both Intrinsic and Extrinsic Factors

We discuss regression modeling of a physiological parameter affected by both intrinsic and extrinsic factors. Such parameter commonly exists in our daily life (e.g., the sleeping quality of human beings or other animals). An additive regression model is suggested which consists of two parts. The first part is for explaining the effect of intrinsic factors and the second part is for describing the effect of extrinsic factors. The fitted model is proved to be statistically consistent. Hypothesis tests about the model coefficients are also discussed. Some simulation results are presented and the modeling procedure is applied to a rat sleep data set.     

Quantifying nonlinear anisotropic elastic material properties of biological tissue by use of membrane inflation

Determination of material parameters for soft tissue frequently involves regression of material parameters for nonlinear, anisotropic constitutive models against experimental data from heterogeneous tests. Here, parameter estimation based on membrane inflation is considered. A four parameter nonlinear, anisotropic hyperelastic strain energy function was used to model the material, in which the parameters are cast in terms of key response features. The experiment was simulated using finite element (FE) analysis in order to predict the experimental measurements of pressure versus profile strain. Material parameter regression was automated using inverse FE analysis; parameter values were updated by use of both local and global techniques, and the ability of these techniques to efficiently converge to a best case was examined. This approach provides a framework in which additional experimental data, including surface strain measurements or local structural information, may be incorporated in order to quantify heterogeneous nonlinear material properties.     

Proportional Hazards Regression for the Analysis of Clustered Survival Data from Case–Cohort Studies

Summary Case–cohort sampling is a commonly used and efficient method for studying large cohorts. Most existing methods of analysis for case–cohort data have concerned the analysis of univariate failure time data. However, clustered failure time data are commonly encountered in public health studies. For example, patients treated at the same center are unlikely to be independent. In this article, we consider methods based on estimating equations for case–cohort designs for clustered failure time data. We assume a marginal hazards model, with a common baseline hazard and common regression coefficient across clusters. The proposed estimators of the regression parameter and cumulative baseline hazard are shown to be consistent and asymptotically normal, and consistent estimators of the asymptotic covariance matrices are derived. The regression parameter estimator is easily computed using any standard Cox regression software that allows for offset terms. The proposed estimators are investigated in simulation studies, and demonstrated empirically to have increased efficiency relative to some existing methods. The proposed methods are applied to a study of mortality among Canadian dialysis patients.     

Iterative Integral Parameter Identification of a Respiratory Mechanics Model

ABSTRACT: BACKGROUND: Patient-specific respiratory mechanics models can support the evaluation of optimal lung protective ventilator settings during ventilation therapy. Clinical application requires that the individual's model parameter values must be identified with information available at the bedside. Multiple linear regression or gradient-based parameter identification methods are highly sensitive to noise and initial parameter estimates. Thus, they are difficult to apply at the bedside to support therapeutic decisions. METHODS: An iterative integral parameter identification method is applied to a second order respiratory mechanics model. The method is compared to the commonly used regression methods and error-mapping approaches using simulated and clinical data. The clinical potential of the method was evaluated on data from 13 Acute Respiratory Distress Syndrome (ARDS) patients. RESULTS: The iterative integral method converged to error minima 350 times faster than the Simplex Search Method using simulation data sets and 50 times faster using clinical data sets. Established regression methods reported erroneous results due to sensitivity to noise. In contrast, the iterative integral method was effective independent of initial parameter estimations, and converged successfully in each case tested. CONCLUSION: These investigations reveal that the iterative integral method is beneficial with respect to computing time, operator independence and robustness, and thus applicable at the bedside for this clinical application.     

Quantile regression models with multivariate failure time data

As an alternative to the mean regression model, the quantile regression model has been studied extensively with independent failure time data. However, due to natural or artificial clustering, it is common to encounter multivariate failure time data in biomedical research where the intracluster correlation needs to be accounted for appropriately. For right-censored correlated survival data, we investigate the quantile regression model and adapt an estimating equation approach for parameter estimation under the working independence assumption, as well as a weighted version for enhancing the efficiency. We show that the parameter estimates are consistent and asymptotically follow normal distributions. The variance estimation using asymptotic approximation involves nonparametric functional density estimation. We employ the bootstrap and perturbation resampling methods for the estimation of the variance-covariance matrix. We examine the proposed method for finite sample sizes through simulation studies, and illustrate it with data from a clinical trial on otitis media.     

Applications of multiple imputation to the analysis of censored regression data.

The first part of the article reviews the Data Augmentation algorithm and presents two approximations to the Data Augmentation algorithm for the analysis of missing-data problems: the Poor Man's Data Augmentation algorithm and the Asymptotic Data Augmentation algorithm. These two algorithms are then implemented in the context of censored regression data to obtain semiparametric methodology. The performances of the censored regression algorithms are examined in a simulation study. It is found, up to the precision of the study, that the bias of both the Poor Man's and Asymptotic Data Augmentation estimators, as well as the Buckley-James estimator, does not appear to differ from zero. However, with regard to mean squared error, over a wide range of settings examined in this simulation study, the two Data Augmentation estimators have a smaller mean squared error than does the Buckley-James estimator. In addition, associated with the two Data Augmentation estimators is a natural device for estimating the standard error of the estimated regression parameters. It is shown how this device can be used to estimate the standard error of either Data Augmentation estimate of any parameter (e.g., the correlation coefficient) associated with the model. In the simulation study, the estimated standard error of the Asymptotic Data Augmentation estimate of the regression parameter is found to be congruent with the Monte Carlo standard deviation of the corresponding parameter estimate. The algorithms are illustrated using the updated Stanford heart transplant data set.     

Model choice and influential cases for survival studies

Deletion diagnostics are developed for identifying observations that influence the estimates of regression parameters and the mixture parameter in the families of relative risk functions for failure time data. The diagnostic for the regression parameters is a generalization of Cain and Lange's (1984, Biometrics 40, 493-499) measure of individual influence. The generalizations of martingale residuals, Schoenfeld's partial residuals (1982, Biometrika 69, 239-241), and score residuals by Therneau, Grambsch, and Fleming (1990, Biometrika 77, 147-160) are also obtained. The influence of some observations on regression parameters can be drastically modified as the mixture parameter changes, even for a very small change. In addition, adding or deleting some observations might result in choosing different models. The diagnostics are applied to a family proposed by Guerrero and Johnson (1982, Biometrika 69, 309-314). One illustrative example is presented.     

Penalized local polynomial regression for spatial data

When performing spatial regression analysis in environmental data applications, spatial heterogeneity in the regression coefficients is often observed. Spatially varying coefficient models, including geographically weighted regression and spline models, are standard tools for quantifying such heterogeneity. In this paper, we propose a spatially varying coefficient model that represents the spatially varying parameters as a mixture of local polynomials at selected locations. The local polynomial parameters have attractive interpretations, indicating various types of spatial heterogeneity. Instead of estimating the spatially varying regression coefficients directly, we develop a penalized least squares regression procedure for the local polynomial parameter estimation, which both shrinks the parameter estimation and penalizes the differences among parameters that are associated with neighboring locations. We develop confidence intervals for the varying regression coefficients and prediction intervals for the response. We apply the proposed method to characterize the spatially varying association between particulate matter concentrations ( ${\text{PM}}_{2.5}$) and pollutant gases related to the secondary aerosol formulation in China. The identified regression coefficients show distinct spatial patterns for nitrogen dioxide, sulfur dioxide, and carbon monoxide during different seasons.     

Estimation of the Spirometric Residual Volume (RV) by a Regression Built from Gower Distances

We estimate the Residual Volume, a spirometric parameter, by use of four continuous and four categorical variables. The estimation is done using distance-based regression, which allows to construct the predicting regression equation from mixed-type explanatory variables. The additionally introduced categorical variables improve essentially the goodness of fit of the regression equation.     

Regression models for convex ROC curves

The performance of a diagnostic test is summarized by its receiver operating characteristic (ROC) curve. Under quite natural assumptions about the latent variable underlying the test, the ROC curve is convex. Empirical data on a test's performance often comes in the form of observed true positive and false positive relative frequencies under varying conditions. This paper describes a family of regression models for analyzing such data. The underlying ROC curves are specified by a quality parameter delta and a shape parameter mu and are guaranteed to be convex provided delta > 1. Both the position along the ROC curve and the quality parameter delta are modeled linearly with covariates at the level of the individual. The shape parameter mu enters the model through the link functions log(p mu) - log(1 - p mu) of a binomial regression and is estimated either by search or from an appropriate constructed variate. One simple application is to the meta-analysis of independent studies of the same diagnostic test, illustrated on some data of Moses, Shapiro, and Littenberg (1993). A second application, to so-called vigilance data, is given, where ROC curves differ across subjects and modeling of the position along the ROC curve is of primary interest.     

On an Efficient Regression Type Estimator

The regression type estimator proposed by KAUR (1985) is considered. Another expression for the approximated mean square error (AMSE), to a first degree of approximation, is obtained. This AMSE is also minimized with respect to a parameter α. Three numerical examples are included. These numerical examples show that this estimator is not significantly more efficient than regression estimator and with respect to ratio and sample mean estimators, it does not always exhibit a high efficiency, as was contended by KAUR (1985). Moreover, an upper bound for the relative precision of the proposed estimator with respect to linear regression estimator is derived.     

Boosting distributional copula regression

Capturing complex dependence structures between outcome variables (e.g., study endpoints) is of high relevance in contemporary biomedical data problems and medical research. Distributional copula regression provides a flexible tool to model the joint distribution of multiple outcome variables by disentangling the marginal response distributions and their dependence structure. In a regression setup, each parameter of the copula model, that is, the marginal distribution parameters and the copula dependence parameters, can be related to covariates via structured additive predictors. We propose a framework to fit distributional copula regression via model-based boosting, which is a modern estimation technique that incorporates useful features like an intrinsic variable selection mechanism, parameter shrinkage and the capability to fit regression models in high-dimensional data setting, that is, situations with more covariates than observations. Thus, model-based boosting does not only complement existing Bayesian and maximum-likelihood based estimation frameworks for this model class but rather enables unique intrinsic mechanisms that can be helpful in many applied problems. The performance of our boosting algorithm for copula regression models with continuous margins is evaluated in simulation studies that cover low- and high-dimensional data settings and situations with and without dependence between the responses. Moreover, distributional copula boosting is used to jointly analyze and predict the length and the weight of newborns conditional on sonographic measurements of the fetus before delivery together with other clinical variables.     

Flexible cloglog links for binomial regression models as an alternative for imbalanced medical data

The complementary log-log link was originally introduced in 1922 to R. A. Fisher, long before the logit and probit links. While the last two links are symmetric, the complementary log-log link is an asymmetrical link without a parameter associated with it. Several asymmetrical links with an extra parameter were proposed in the literature over last few years to deal with imbalanced data in binomial regression (when one of the classes is much smaller than the other); however, these do not necessarily have the cloglog link as a special case, with the exception of the link based on the generalized extreme value distribution. In this paper, we introduce flexible cloglog links for modeling binomial regression models that include an extra parameter associated with the link that explains some unbalancing for binomial outcomes. For all cases, the cloglog is a special case or the reciprocal version loglog link is obtained. A Bayesian Markov chain Monte Carlo inference approach is developed. Simulations study to evaluate the performance of the proposed algorithm is conducted and prior sensitivity analysis for the extra parameter shows that a uniform prior is the most convenient for all models. Additionally, two applications in medical data (age at menarche and pulmonary infection) illustrate the advantages of the proposed models.     

Optimality assessment in the enzyme-linked immunosorbent assay (ELISA)

An optimality criterion is proposed for evaluating the precision of alternative designs in the enzyme-linked immunosorbent assay. Assay profiles are represented as four-parameter logistic functions with parameter estimation based on either a weighted nonlinear regression or a simple nonlinear regression after a logarithmic transformation. Assay design changes are characterized in terms of their effects on parameters in the four-parameter logistic model. General optimality results are derived for the variance of relative potency estimates in routine assay applications.