Covariate-adjusted varying coefficient models

Covariate-adjusted regression was recently proposed for situations where both predictors and response in a regression model are not directly observed, but are observed after being contaminated by unknown functions of a common observable covariate. The method has been appealing because of its flexibility in targeting the regression coefficients under different forms of distortion. We extend this methodology proposed for regression into the framework of varying coefficient models, where the goal is to target the covariate-adjusted relationship between longitudinal variables. The proposed method of covariate-adjusted varying coefficient model (CAVCM) is illustrated with an analysis of a longitudinal data set containing calcium absorbtion and intake measurements on 188 subjects. We estimate the age-dependent relationship between these two variables adjusted for the covariate body surface area. Simulation studies demonstrate the flexibility of CAVCM in handling different forms of distortion in the longitudinal setting.     

A goodness-of-fit test for multinomial logistic regression

This article presents a score test to check the fit of a logistic regression model with two or more outcome categories. The null hypothesis that the model fits well is tested against the alternative that residuals of samples close to each other in covariate space tend to deviate from the model in the same direction. We propose a test statistic that is a sum of squared smoothed residuals, and show that it can be interpreted as a score test in a random effects model. By specifying the distance metric in covariate space, users can choose the alternative against which the test is directed, making it either an omnibus goodness-of-fit test or a test for lack of fit of specific model variables or outcome categories.     

Adjusting for regression effect in uncontrolled studies

When clinical studies require enrolled patients to have abnormal assays, the natural tendency of repeat measurements to regress toward the mean can lead to a false assessment of effectiveness of therapy. We propose a method to more accurately estimate the true effect of therapy by adjusting for a component of improvement that can be attributed to regression effect. The model we use allows for a combination of additive and/or multiplicative effects of the therapy.     

Generalized varying coefficient models for longitudinal data

We propose a generalization of the varying coefficient modelfor longitudinal data to cases where not only current but alsorecent past values of the predictor process affect current response.More precisely, the targeted regression coefficient functionsof the proposed model have sliding window supports around currenttime t. A variant of a recently proposed two-step estimationmethod for varying coefficient models is proposed for estimationin the context of these generalized varying coefficient models,and is found to lead to improvements, especially for the caseof additive measurement errors in both response and predictors.The proposed methodology for estimation and inference is alsoapplicable for the case of additive measurement error in thecommon versions of varying coefficient models that relate onlycurrent observations of predictor and response processes toeach other. Asymptotic distributions of the proposed estimatorsare derived, and the model is applied to the problem of predictingprotein concentrations in a longitudinal study. Simulation studiesdemonstrate the efficacy of the proposed estimation procedure.     

Estimation of regression models under linear restrictions

The variance-covariance matrices of restricted regression and mixed regression estimators are compared and the consequences of introducing variability in the restrictions are examined.     

Model checking for ROC regression analysis

Summary .   The receiver operating characteristic (ROC) curve is a prominent tool for characterizing the accuracy of a continuous diagnostic test. To account for factors that might influence the test accuracy, various ROC regression methods have been proposed. However, as in any regression analysis, when the assumed models do not fit the data well, these methods may render invalid and misleading results. To date, practical model-checking techniques suitable for validating existing ROC regression models are not yet available. In this article, we develop cumulative residual-based procedures to graphically and numerically assess the goodness of fit for some commonly used ROC regression models, and show how specific components of these models can be examined within this framework. We derive asymptotic null distributions for the residual processes and discuss resampling procedures to approximate these distributions in practice. We illustrate our methods with a dataset from the cystic fibrosis registry.     

Bootstrap tests for overdispersion in a zero-inflated Poisson regression model

Ridout, Hinde, and Demétrio (2001, Biometrics 57, 219-223) derived a score test for testing a zero-inflated Poisson (ZIP) regression model against zero-inflated negative binomial (ZINB) alternatives. They mentioned that the score test using the normal approximation might underestimate the nominal significance level possibly for small sample cases. To remedy this problem, a parametric bootstrap method is proposed. It is shown that the bootstrap method keeps the significance level close to the nominal one and has greater power uniformly than the existing normal approximation for testing the hypothesis.     

Estimating severity of sideways fall using a generic multi linear regression model based on kinematic input variables

Many research groups have studied fall impact mechanics to understand how fall severity can be reduced to prevent hip fractures. Yet, direct impact force measurements with force plates are restricted to a very limited repertoire of experimental falls. The purpose of this study was to develop a generic model for estimating hip impact forces (i.e. fall severity) in in vivo sideways falls without the use of force plates.Twelve experienced judokas performed sideways Martial Arts (MA) and Block (‘natural’) falls on a force plate, both with and without a mat on top. Data were analyzed to determine the hip impact force and to derive 11 selected (subject-specific and kinematic) variables. Falls from kneeling height were used to perform a stepwise regression procedure to assess the effects of these input variables and build the model.The final model includes four input variables, involving one subject-specific measure and three kinematic variables: maximum upper body deceleration, body mass, shoulder angle at the instant of ‘maximum impact’ and maximum hip deceleration. The results showed that estimated and measured hip impact forces were linearly related (explained variances ranging from 46 to 63%). Hip impact forces of MA falls onto the mat from a standing position (3650 ± 916 N) estimated by the final model were comparable with measured values (3698 ± 689 N), even though these data were not used for training the model. In conclusion, a generic linear regression model was developed that enables the assessment of fall severity through kinematic measures of sideways falls, without using force plates.     

Functional regression analysis of fluorescence curves

Summary .  Fluorescence curves are useful for monitoring changes in photosynthesis activity. Various summary measures have been used to quantify differences among fluorescence curves corresponding to different treatments, but these approaches may forfeit valuable information. As each individual fluorescence curve is a functional observation, it is natural to consider a functional regression model. The proposed model consists of a nonparametric component capturing the general form of the curves and a semiparametric component describing the differences among treatments and allowing comparisons of treatments. Several graphical model-checking approaches are introduced. Both approximate, asymptotic confidence intervals as well as simulation-based confidence intervals are available. Analysis of data from a crop experiment using the proposed model shows that the salient features in the fluorescence curves are captured adequately. The proposed functional regression model is useful for analysis of high throughput fluorescence curve data from regular monitoring or screening of plant growth.     

On nonlinear beta regression residuals

We proposed a new residual to be used in linear and nonlinear beta regressions. Unlike the residuals that had already been proposed, the derivation of the new residual takes into account not only information relative to the estimation of the mean submodel but also takes into account information obtained from the precision submodel. This is an advantage of the residual we introduced. Additionally, the new residual is computationally less intensive than the weighted residual. Recall that the computation of the latter involves an matrix, where n is the sample size. Obviously, that can be a problem when the sample size is very large. In contrast, our residual does not suffer from that. It can be easily computed even in large samples. Finally, our residual proved to be able to identify atypical observations as well as the weighted residual. We also propose new thresholds for residual plots and a scheme for the choice of starting values to be used in maximum likelihood point estimation in the class of nonlinear beta regression models. We report Monte Carlo simulation results on the behavior of different residuals. We also present and discuss two empirical applications; one uses the proportion of killed grasshoppers in an assay on the grasshopper Melanopus sanguinipes with the insecticide carbofuran and the synergist piperonyl butoxide, which enhances the toxicity of the insecticide, and the other uses simulated data. The results favor the new methodology we introduce.