Optimal designs for a multiresponse Emax model and efficient parameter estimation

The aim of dose finding studies is sometimes to estimate parameters in a fitted model. The precision of the parameter estimates should be as high as possible. This can be obtained by increasing the number of subjects in the study, N, choosing a good and efficient estimation approach, and by designing the dose finding study in an optimal way. Increasing the number of subjects is not always feasible because of increasing cost, time limitations, etc. In this paper, we assume fixed N and consider estimation approaches and study designs for multiresponse dose finding studies. We work with diabetes dose–response data and compare a system estimation approach that fits a multiresponse Emax model to the data to equation‐by‐equation estimation that fits uniresponse Emax models to the data. We then derive some optimal designs for estimating the parameters in the multi‐ and uniresponse Emax model and study the efficiency of these designs.     

Bayesian experimental design for nonlinear mixed-effects models with application to HIV dynamics

Bayesian experimental design is investigated for Bayesian analysis of nonlinear mixed-effects models. Existence of the posterior risk for parameter estimation is shown. When the same prior distribution is used for both design and inference, existence of the preposterior risk for design is also proven. If the prior distribution used in design is different from that used for inference, sufficient conditions are established for existence of the preposterior risk for design. A case study of design for an experiment in population HIV dynamics is provided.     

On estimation and prediction for spatial generalized linear mixed models

We use spatial generalized linear mixed models (GLMM) to model non-Gaussian spatial variables that are observed at sampling locations in a continuous area. In many applications, prediction of random effects in a spatial GLMM is of great practical interest. We show that the minimum mean-squared error (MMSE) prediction can be done in a linear fashion in spatial GLMMs analogous to linear kriging. We develop a Monte Carlo version of the EM gradient algorithm for maximum likelihood estimation of model parameters. A by-product of this approach is that it also produces the MMSE estimates for the realized random effects at the sampled sites. This method is illustrated through a simulation study and is also applied to a real data set on plant root diseases to obtain a map of disease severity that can facilitate the practice of precision agriculture.     

An estimation method for the semiparametric mixed effects model

A semiparametric mixed effects regression model is proposed for the analysis of clustered or longitudinal data with continuous, ordinal, or binary outcome. The common assumption of Gaussian random effects is relaxed by using a predictive recursion method (Newton and Zhang, 1999) to provide a nonparametric smooth density estimate. A new strategy is introduced to accelerate the algorithm. Parameter estimates are obtained by maximizing the marginal profile likelihood by Powell's conjugate direction search method. Monte Carlo results are presented to show that the method can improve the mean squared error of the fixed effects estimators when the random effects distribution is not Gaussian. The usefulness of visualizing the random effects density itself is illustrated in the analysis of data from the Wisconsin Sleep Survey. The proposed estimation procedure is computationally feasible for quite large data sets.     

Coarse‐ and fine‐grained models for proteins: Evaluation by decoy discrimination

Coarse‐grained models for protein structure are increasingly used in simulations and structural bioinformatics. In this study, we evaluated the effectiveness of three granularities of protein representation based on their ability to discriminate between correctly folded native structures and incorrectly folded decoy structures. The three levels of representation used one bead per amino acid (coarse), two beads per amino acid (medium), and all atoms (fine). Multiple structure features were compared at each representation level including two‐body interactions, three‐body interactions, solvent exposure, contact numbers, and angle bending. In most cases, the all‐atom level was most successful at discriminating decoys, but the two‐bead level provided a good compromise between the number of model parameters which must be estimated and the accuracy achieved. The most effective feature type appeared to be two‐body interactions. Considering three‐body interactions increased accuracy only marginally when all atoms were used and not at all in medium and coarse representations. Though two‐body interactions were most effective for the coarse representations, the accuracy loss for using only solvent exposure or contact number was proportionally less at these levels than in the all‐atom representation. We propose an optimization method capable of selecting bead types of different granularities to create a mixed representation of the protein. We illustrate its behavior on decoy discrimination and discuss implications for data‐driven protein model selection. Proteins 2013. © 2012 Wiley Periodicals, Inc.     

Extending conventional priors for testing general hypotheses in linear models

We consider that observations come from a general normal linearmodel and that it is desirable to test a simplifying null hypothesisabout the parameters. We approach this problem from an objectiveBayesian, model-selection perspective. Crucial ingredients forthis approach are ‘proper objective priors’ to beused for deriving the Bayes factors. Jeffreys-Zellner-Siow priorshave good properties for testing null hypotheses defined byspecific values of the parameters in full-rank linear models.We extend these priors to deal with general hypotheses in generallinear models, not necessarily of full rank. The resulting priors,which we call ‘conventional priors’, are expressedas a generalization of recently introduced ‘partiallyinformative distributions’. The corresponding Bayes factorsare fully automatic, easily computed and very reasonable. Themethodology is illustrated for the change-point problem andthe equality of treatments effects problem. We compare the conventionalpriors derived for these problems with other objective Bayesianproposals like the intrinsic priors. It is concluded that bothpriors behave similarly although interesting subtle differencesarise. We adapt the conventional priors to deal with nonnestedmodel selection as well as multiple-model comparison. Finally,we briefly address a generalization of conventional priors tononnormal scenarios.     

Conditional estimation for generalized linear models when covariates are subject-specific parameters in a mixed model for longitudinal measurements

The relationship between a primary endpoint and features of longitudinal profiles of a continuous response is often of interest, and a relevant framework is that of a generalized linear model with covariates that are subject-specific random effects in a linear mixed model for the longitudinal measurements. Naive implementation by imputing subject-specific effects from individual regression fits yields biased inference, and several methods for reducing this bias have been proposed. These require a parametric (normality) assumption on the random effects, which may be unrealistic. Adapting a strategy of Stefanski and Carroll (1987, Biometrika74, 703-716), we propose estimators for the generalized linear model parameters that require no assumptions on the random effects and yield consistent inference regardless of the true distribution. The methods are illustrated via simulation and by application to a study of bone mineral density in women transitioning to menopause.     

Maximum likelihood estimation of generalized linear models for adaptive designs: Applications and asymptotics

Due to increasing discoveries of biomarkers and observed diversity among patients, there is growing interest in personalized medicine for the purpose of increasing the well‐being of patients (ethics) and extending human life. In fact, these biomarkers and observed heterogeneity among patients are useful covariates that can be used to achieve the ethical goals of clinical trials and improving the efficiency of statistical inference. Covariate‐adjusted response‐adaptive (CARA) design was developed to use information in such covariates in randomization to maximize the well‐being of participating patients as well as increase the efficiency of statistical inference at the end of a clinical trial. In this paper, we establish conditions for consistency and asymptotic normality of maximum likelihood (ML) estimators of generalized linear models (GLM) for a general class of adaptive designs. We prove that the ML estimators are consistent and asymptotically follow a multivariate Gaussian distribution. The efficiency of the estimators and the performance of response‐adaptive (RA), CARA, and completely randomized (CR) designs are examined based on the well‐being of patients under a logit model with categorical covariates. Results from our simulation studies and application to data from a clinical trial on stroke prevention in atrial fibrillation (SPAF) show that RA designs lead to ethically desirable outcomes as well as higher statistical efficiency compared to CARA designs if there is no treatment by covariate interaction in an ideal model. CARA designs were however more ethical than RA designs when there was significant interaction.     

Nonparametric and parametric estimation for a linear germination-growth model

Seeds are planted on the interval [0, L] at various locations. Each seed has a location x and a potential germination time t epsilon [0, infinity), and it is assumed that the collection of such (x, t) pairs forms a Poisson process in [0, L] x [0, infinity) with intensity measure dxd lambda(t). From each seed that germinates, an inhibiting region grows bidirectionally at rate 2v. These regions inhibit germination of any seed in the region with a later potential germination time. Thus, seeds only germinate in the uninhibited part of [0, L]. We want to estimate lambda on the basis of one or more realizations of the process, the data being the locations and germination times of the germinated seeds. We derive the maximum likelihood estimator of v and a nonparametric estimator of lambda and describe methods of obtaining parametric estimates from it, illustrating these with reference to gamma densities. Simulation results are described and the methods applied to some neurobiological data. An Appendix outlines the S-PLUS code used.     

Fixed and random effects selection in linear and logistic models

We address the problem of selecting which variables should be included in the fixed and random components of logistic mixed effects models for correlated data. A fully Bayesian variable selection is implemented using a stochastic search Gibbs sampler to estimate the exact model-averaged posterior distribution. This approach automatically identifies subsets of predictors having nonzero fixed effect coefficients or nonzero random effects variance, while allowing uncertainty in the model selection process. Default priors are proposed for the variance components and an efficient parameter expansion Gibbs sampler is developed for posterior computation. The approach is illustrated using simulated data and an epidemiologic example.