Structured additive regression for categorical space-time data: a mixed model approach

Motivated by a space-time study on forest health with damage state of trees as the response, we propose a general class of structured additive regression models for categorical responses, allowing for a flexible semiparametric predictor. Nonlinear effects of continuous covariates, time trends, and interactions between continuous covariates are modeled by penalized splines. Spatial effects can be estimated based on Markov random fields, Gaussian random fields, or two-dimensional penalized splines. We present our approach from a Bayesian perspective, with inference based on a categorical linear mixed model representation. The resulting empirical Bayes method is closely related to penalized likelihood estimation in a frequentist setting. Variance components, corresponding to inverse smoothing parameters, are estimated using (approximate) restricted maximum likelihood. In simulation studies we investigate the performance of different choices for the spatial effect, compare the empirical Bayes approach to competing methodology, and study the bias of mixed model estimates. As an application we analyze data from the forest health survey.     

Estimating data transformations in nonlinear mixed effects models

A routine practice in the analysis of repeated measurement data is to represent individual responses by a mixed effects model on some transformed scale. For example, for pharmacokinetic, growth, and other data, both the response and the regression model are typically transformed to achieve approximate within-individual normality and constant variance on the new scale; however, the choice of transformation is often made subjectively or by default, with adoption of a standard choice such as the log. We propose a mixed effects framework based on the transform-both-sides model, where the transformation is represented by a monotone parametric function and is estimated from the data. For this model, we describe a practical fitting strategy based on approximation of the marginal likelihood. Inference is complicated by the fact that estimation of the transformation requires modification of the usual standard errors for estimators of fixed effects; however, we show that, under conditions relevant to common applications, this complication is asymptotically negligible, allowing straightforward implementation via standard software.     

Statistical analysis of amounts and ratios in pheromone composition: a mixed model approach

Analysis of variation in pheromone amounts and ratios between individuals is usually performed separately for amounts and ratios of the different components. Non-parametric tests are regularly applied. This way of analysis is statistically correct, yet, limited for several reasons. The use of a parametric linear mixed model approach to analyze both amounts and ratios of different components at the same time is proposed. This method appears to be very flexible and may facilitate the analysis of pheromone data.     

Assessing non-specificity of resistance in wheat to head blight caused by inoculation with European strains of Fusarium culmorum,F. graminearum and F. nivale using a multiplicative model for interaction

To determine whether resistance to Fusarium head blight in winter wheat is horizontal and non-species specific, 25 genotypes from five European countries were tested at six locations across Europe in the years 1990, 1991, and 1992. The five genotypes from each country had to cover the range from resistant to susceptible. The locations involved were Wageningen, Vienna, Rennes, Hohenheim, Oberer Lindenhof, and Szeged. In total, 17 local strains of Fusarium culmorum, F. graminearum, and F. nivale were used for experimental inoculation. One strain, F. culmorum IPO 39-01, was used at all locations. Best linear unbiased predictions (BLUPs) for the head blight ratings of the genotypes were formed within each particular location for each combination of year and strain. The BLUPs over all locations were collected in a genotype-by environment table in which the genotypic dimension consisted of the 25 genotypes, while the environmental dimension was made up of 59 year-by-strain-by-location combinations. A multiplicative model was fitted to the genotype by-environment interaction in this table. The inverses of the variances of the genotype-by-environment BLUPs were used as weights. Interactions between genotypes and environments were written as sums of products between genotypic scores and environmental scores. After correction for year-by-location influence very little variation in environmental scores could be ascribed to differences between strains. This provided the basis for the conclusion that the resistance to Fusarium head blight in winter wheat was of the horizontal and non-species specific type. There was no indication for any geographical pattern in virulence genes. Any reasonable aggressive strain, a F. culmorum strain for the cool climates and a F. graminearum strain for the warmer humid areas, should be satisfactory for screening purposes.     

Two-stage functional mixed models for evaluating the effect of longitudinal covariate profiles on a scalar outcome

The Daily Hormone Study, a substudy of the Study of Women's Health Across the Nation (SWAN) consisting of more than 600 pre- and perimenopausal women, includes a scalar measure of total hip bone mineral density (BMD) together with repeated measures of creatinine-adjusted follicle stimulating hormone (FSH) assayed from daily urine samples collected over one menstrual cycle. It is of scientific interest to investigate the effect of the FSH time profile during a menstrual cycle on total hip BMD, adjusting for age and body mass index. The statistical analysis is challenged by several features of the data: (1) the covariate FSH is measured longitudinally and its effect on the scalar outcome BMD may be complex; (2) due to varying menstrual cycle lengths, subjects have unbalanced longitudinal measures of FSH; and (3) the longitudinal measures of FSH are subject to considerable among- and within-subject variations and measurement errors. We propose a measurement error partial functional linear model, where repeated measures of FSH are modeled using a functional mixed effects model and the effect of the FSH time profile on BMD is modeled using a partial functional linear model by treating the unobserved true subject-specific FSH time profile as a functional covariate. We develop a two-stage nonparametric regression calibration method using period smoothing splines. Using the connection between smoothing splines and mixed models, we show that a key feature of our approach is that estimation at both stages can be conveniently cast into a unified mixed model framework. A simple testing procedure for constant functional covariate effect is also proposed. The proposed methods are evaluated using simulation studies and applied to the SWAN data.     

kakusan: a computer program to automate the selection of a nucleotide substitution model and the configuration of a mixed model on multilocus data

The application of different substitution models to each gene (a.k.a. mixed model) should be considered in model‐based phylogenetic analysis of multigene sequences. However, a single molecular evolution model is still usually applied. There are no computer programs able to conduct model selection for multiple loci at the same time, though several recently developed types of software for phylogenetic inference can handle mixed model. Here, I have developed computer software named ‘kakusan’ that enables us to solve the above problems. Major running steps are briefly described, and an analysis of results with kakusan is compared to that obtained with other program.     

The importance of phenotypic data analysis for genomic prediction - a case study comparing different spatial models in rye

Background

Genomic prediction is becoming a daily tool for plant breeders. It makes use of genotypic information to make predictions used for selection decisions. The accuracy of the predictions depends on the number of genotypes used in the calibration; hence, there is a need of combining data across years. A proper phenotypic analysis is a crucial prerequisite for accurate calibration of genomic prediction procedures. We compared stage-wise approaches to analyse a real dataset of a multi-environment trial (MET) in rye, which was connected between years only through one check, and used different spatial models to obtain better estimates, and thus, improved predictive abilities for genomic prediction. The aims of this study were to assess the advantage of using spatial models for the predictive abilities of genomic prediction, to identify suitable procedures to analyse a MET weakly connected across years using different stage-wise approaches, and to explore genomic prediction as a tool for selection of models for phenotypic data analysis.

Results

Using complex spatial models did not significantly improve the predictive ability of genomic prediction, but using row and column effects yielded the highest predictive abilities of all models. In the case of MET poorly connected between years, analysing each year separately and fitting year as a fixed effect in the genomic prediction stage yielded the most realistic predictive abilities. Predictive abilities can also be used to select models for phenotypic data analysis. The trend of the predictive abilities was not the same as the traditionally used Akaike information criterion, but favoured in the end the same models.

Conclusions

Making predictions using weakly linked datasets is of utmost interest for plant breeders. We provide an example with suggestions on how to handle such cases. Rather than relying on checks we show how to use year means across all entries for integrating data across years. It is further shown that fitting of row and column effects captures most of the heterogeneity in the field trials analysed.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2164-15-646) contains supplementary material, which is available to authorized users.     

Semiparametric transformation models for interval‐censored data in the presence of a cure fraction

Mixed case interval‐censored data arise when the event of interest is known only to occur within an interval induced by a sequence of random examination times. Such data are commonly encountered in disease research with longitudinal follow‐up. Furthermore, the medical treatment has progressed over the last decade with an increasing proportion of patients being cured for many types of diseases. Thus, interest has grown in cure models for survival data which hypothesize a certain proportion of subjects in the population are not expected to experience the events of interest. In this article, we consider a two‐component mixture cure model for regression analysis of mixed case interval‐censored data. The first component is a logistic regression model that describes the cure rate, and the second component is a semiparametric transformation model that describes the distribution of event time for the uncured subjects. We propose semiparametric maximum likelihood estimation for the considered model. We develop an EM type algorithm for obtaining the semiparametric maximum likelihood estimators (SPMLE) of regression parameters and establish their consistency, efficiency, and asymptotic normality. Extensive simulation studies indicate that the SPMLE performs satisfactorily in a wide variety of settings. The proposed method is illustrated by the analysis of the hypobaric decompression sickness data from National Aeronautics and Space Administration.     

Exposing the confounding in experimental designs to understand and evaluate them,and formulating linear mixed models for analyzing the data from a designed experiment

Comparative experiments involve the allocation of treatments to units, ideally by randomization. This necessarily confounds treatment information with unit information, which we distinguish from the other forms of information blending, in particular aliasing and marginality. We outline a factor-allocation paradigm for describing experimental designs with the aim of (i) exhibiting the confounding in a design, using analysis-of-variance-like tables, so as to understand and evaluate the design and (ii) formulating a linear mixed model based on the factor allocation that the design involves. The approach exhibits the dispersal of treatments information between units sources, allows designers a choice in the strategy that they adopt for including block-treatment interactions, clarifies differences between experiments, accommodates systematic allocation of factors, and provides a consolidated analysis of nonorthogonal designs. It provides insights into the process of designing experiments and issues that commonly arise with designs. The paradigm has pedagogical advantages and is implemented using the R package dae .     

The exponential‐Poisson model for recurrent event data: An application to a set of data on malaria in Brazil

In this paper, we introduce a new model for recurrent event data characterized by a baseline rate function fully parametric, which is based on the exponential‐Poisson distribution. The model arises from a latent competing risk scenario, in the sense that there is no information about which cause was responsible for the event occurrence. Then, the time of each recurrence is given by the minimum lifetime value among all latent causes. The new model has a particular case, which is the classical homogeneous Poisson process. The properties of the proposed model are discussed, including its hazard rate function, survival function, and ordinary moments. The inferential procedure is based on the maximum likelihood approach. We consider an important issue of model selection between the proposed model and its particular case by the likelihood ratio test and score test. Goodness of fit of the recurrent event models is assessed using Cox‐Snell residuals. A simulation study evaluates the performance of the estimation procedure in the presence of a small and moderate sample sizes. Applications on two real data sets are provided to illustrate the proposed methodology. One of them, first analyzed by our team of researchers, considers the data concerning the recurrence of malaria, which is an infectious disease caused by a protozoan parasite that infects red blood cells.