Fitting a regression model for genotype-by-environment data on heading dates in grasses by methods for nonlinear mixed models

The analysis of agricultural crop variety trials is usually complicated by the presence of genotype-by-environment interaction. A number of methods and models have been proposed to tackle this problem. One of the most common methods is the regression approach due to Yates and Cochran (1938, Journal of Agricultural Science 28, 556-580), in which performances of genotypes in the environments are regressed onto environmental means. The underlying regression model contains a multiplicative term with two unknown parameters (one for genotypes and one for environments). In the present paper, the model is modified by exchanging the role of genotypes and environments. Various diagnostic plots show that this modified model is adequate for a data set on heading dates in the grass species Dactylis glomerata. If environments are considered as a random factor while genotypes are taken as fixed, the model falls into the class of nonlinear mixed models. Recently, a number of procedures have been suggested for this class of models, which are based on first-order Taylor series expansion. Alternatively, the model can be estimated by maximum likelihood. This paper discusses the application of these methods for estimating parameters of the model.     

干旱区生态系统健康评价的指标、模型及应用

采用生态系统健康的理论与方法分析干旱地区生态环境问题具有较强的理论和现实意义。本研究以沙坡头地区荒漠景观为背景,着重探讨干旱区生态系统健康评价方法,建立评价指标体系及模型。研究结果表明：单种时,以密度为2500株／hm^2的油蒿样地最为健康;混种时,以样地5最为健康,其密度为5000株／hm^2,覆盖率亦最大。该结果说明适当的种植密度和方式是一种值得提倡的经营管理模式。     

A discrete latent factor model for smoking,cancer and mortality

This paper investigates the relationship between smoking and ill-health, with a focus on the onset of cancer. A discrete latent factor model for smoking and health outcomes, allowing for these to be commonly affected by unobserved factors, is jointly estimated, using the British Health and Lifestyle Survey (HALS) dataset. Post-estimation predictions suggest the reduction in time-to-cancer to be 5.7 years for those with an exposure of 30 pack-years, compared to never-smokers. Estimation of posterior probabilities for class membership shows that individuals in certain classes exhibit similar observables but highly divergent health outcomes, suggesting that unobserved factors influence outcomes. The use of a joint model changes the results substantially. The results show that failure to account for unobserved heterogeneity leads to differences in survival times between those with different smoking exposures to be overestimated by more than 50% (males, with 30 pack-years of exposure).     

A multistate model for bivariate interval-censored failure time data

SUMMARY: Interval-censored life-history data arise when the events of interest are only detectable at periodic assessments. When interest lies in the occurrence of two such events, bivariate-interval censored event time data are obtained. We describe how to fit a four-state Markov model useful for characterizing the association between two interval-censored event times when the assessment times for the two events may be generated by different inspection processes. The approach treats the two events symmetrically and enables one to fit multiplicative intensity models that give estimates of covariate effects as well as relative risks characterizing the association between the two events. An expectation-maximization (EM) algorithm is described for estimation in which the maximization step can be carried out with standard software. The method is illustrated by application to data from a trial of HIV patients where the events are the onset of viral shedding in the blood and urine among individuals infected with cytomegalovirus.     

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.     

A spatial simulation model for vegetation dynamics

A fine-resolution, spatially explicit, stochastic model was developed to simulate the dynamics of species cover abundance and pattern in a single vegetation layer wherein neighbouring individuals are assumed to compete for growing space. Each species in the model is characterized by a small number of morphological and life-history parameters, which enter into equations that stand for a minimal set of vegetation processes. The model performed well in reproducing post-fire successional trends among the three codominant dwarf shrubs in a Dutch heathland community as recorded in an annually mapped permanent quadrat. Program inputs, outputs and an example of sensitivity analysis are illustrated. With suitable changes, the model could potentially describe any plant community in which the vertical structure is simple and community dynamics are determined by spatial interactions among neighbouring plants.Jacques de Smidt provided data, information and stimulus for this project. The model was developed during ICP's visit to Utrecht, arranged by Marinus Werger and financed by The Netherlands Science Research Council (ZWO). We also thank David Glenn-Lewin and Ernst Lippe for discussion and cooperation.     

Analyzing Variety by Environment Data Using Multiplicative Mixed Models and Adjustments for Spatial Field Trend

The recommendation of new plant varieties for commercial use requires reliable and accurate predictions of the average yield of each variety across a range of target environments and knowledge of important interactions with the environment. This information is obtained from series of plant variety trials, also known as multi-environment trials (MET). Cullis, Gogel, Verbyla, and Thompson (1998) presented a spatial mixed model approach for the analysis of MET data. In this paper we extend the analysis to include multiplicative models for the variety effects in each environment. The multiplicative model corresponds to that used in the multivariate technique of factor analysis. It allows a separate genetic variance for each environment and provides a parsimonious and interpretable model for the genetic covariances between environments. The model can be regarded as a random effects analogue of AMMI (additive main effects and multiplicative interactions). We illustrate the method using a large set of MET data from a South Australian barley breeding program.     

A new software for measuring leaf area, and area damaged by Tetranychus urticae Koch

Abstract:  Measuring leaf area manually is a tedious and time-consuming process and it is inaccurate. In an attempt to make this process easier and more accurate, a new software namely 'Compu Eye, Leaf & Symptom Area' was developed. A standard green shape with a known area of 1.5 cm² was used to evaluate the accuracy of the software. The measurements obtained were of high accuracy. Measurements varied between 1.4771 and 1.5095 cm². Probabilities of t values were usually <0.01 and did not exceed 0.023. It was also observed that accuracy could be enhanced either by increasing scanner resolution and/or by decreasing measurement unit area. In order to evaluate the performance of the software, leaves with symptoms of mite injury were collected from six different plant species (squash, cucumber, green bean, vigna, dahlia and rose). Symptom area of each leaf was assessed manually and by the software. It was observed that the software was able to assess the symptom area accurately with no significant difference compared with manual measurement.     

Stochastic model for analysis of longitudinal data on aging and mortality

Aging-related changes in a human organism follow dynamic regularities, which contribute to the observed age patterns of incidence and mortality curves. An organism's 'optimal' (normal) physiological state changes with age, affecting the values of risks of disease and death. The resistance to stresses, as well as adaptive capacity, declines with age. An exposure to improper environment results in persisting deviation of individuals' physiological (and biological) indices from their normal state (due to allostatic adaptation), which, in turn, increases chances of disease and death. Despite numerous studies investigating these effects, there is no conceptual framework, which would allow for putting all these findings together, and analyze longitudinal data taking all these dynamic connections into account. In this paper we suggest such a framework, using a new version of stochastic process model of aging and mortality. Using this model, we elaborated a statistical method for analyses of longitudinal data on aging, health and longevity and tested it using different simulated data sets. The results show that the model may characterize complicated interplay among different components of aging-related changes in humans and that the model parameters are identifiable from the data.     

A random effects model for multivariate failure time data from multicenter clinical trials

A random effects model for analyzing multivariate failure time data is proposed. The work is motivated by the need for assessing the mean treatment effect in a multicenter clinical trial study, assuming that the centers are a random sample from an underlying population. An estimating equation for the mean hazard ratio parameter is proposed. The proposed estimator is shown to be consistent and asymptotically normally distributed. A variance estimator, based on large sample theory, is proposed. Simulation results indicate that the proposed estimator performs well in finite samples. The proposed variance estimator effectively corrects the bias of the naive variance estimator, which assumes independence of individuals within a group. The methodology is illustrated with a clinical trial data set from the Studies of Left Ventricular Dysfunction. This shows that the variability of the treatment effect is higher than found by means of simpler models.     

Integrating stable isotopes,parasite, and ring‐reencounter data to quantify migratory connectivity—A case study with Barn Swallows breeding in Switzerland,Germany, Sweden,and Finland

Ecosystems around the world are connected by seasonal migration. The migrant animals themselves are influenced by migratory connectivity through effects on the individual and the population level. Measuring migratory connectivity is notoriously difficult due to the simple requirement of data conveying information about the nonbreeding distribution of many individuals from several breeding populations. Explicit integration of data derived from different methods increases the precision and the reliability of parameter estimates. We combine ring‐reencounter, stable isotope, and blood parasite data of Barn Swallows Hirundo rustica in a single integrated model to estimate migratory connectivity for three large scale breeding populations across a latitudinal gradient from Central Europe to Scandinavia. To this end, we integrated a non‐Markovian multistate mark‐recovery model for the ring‐reencounter data with normal and binomial mixture models for the stable isotope and parasite data. The integration of different data sources within a mark‐recapture modeling framework enables the most precise quantification of migratory connectivity on the given broad spatial scale. The results show that northern‐breeding populations and Southern Africa as well as southern‐breeding populations and Western–Central Africa are more strongly connected through Barn Swallow migration than central European breeding populations with any of the African wintering areas. The nonbreeding distribution of Barn Swallows from central European breeding populations seems to be a mixture of those populations breeding further north and south, indicating a migratory divide.     

A class of latent Markov models for capture-recapture data allowing for time, heterogeneity, and behavior effects

We propose an extension of the latent class model for the analysis of capture-recapture data which allows us to take into account the effect of a capture on the behavior of a subject with respect to future captures. The approach is based on the assumption that the variable indexing the latent class of a subject follows a Markov chain with transition probabilities depending on the previous capture history. Several constraints are allowed on these transition probabilities and on the parameters of the conditional distribution of the capture configuration given the latent process. We also allow for the presence of discrete explanatory variables, which may affect the parameters of the latent process. To estimate the resulting models, we rely on the conditional maximum likelihood approach and for this aim we outline an EM algorithm. We also give some simple rules for point and interval estimation of the population size. The approach is illustrated by applying it to two data sets concerning small mammal populations.     

Genetic model for longitudinal studies of aging, health, and longevity and its potential application to incomplete data

Many longitudinal studies of aging collect genetic information only for a sub-sample of participants of the study. These data also do not include recent findings, new ideas and methodological concepts developed by distinct groups of researchers. The formal statistical analyses of genetic data ignore this additional information and therefore cannot utilize the entire research potential of the data. In this paper, we present a stochastic model for studying such longitudinal data in joint analyses of genetic and non-genetic sub-samples. The model incorporates several major concepts of aging known to date and usually studied independently. These include age-specific physiological norms, allostasis and allostatic load, stochasticity, and decline in stress resistance and adaptive capacity with age. The approach allows for studying all these concepts in their mutual connection, even if respective mechanisms are not directly measured in data (which is typical for longitudinal data available to date). The model takes into account dependence of longitudinal indices and hazard rates on genetic markers and permits evaluation of all these characteristics for carriers of different alleles (genotypes) to address questions concerning genetic influence on aging-related characteristics. The method is based on extracting genetic information from the entire sample of longitudinal data consisting of genetic and non-genetic sub-samples. Thus it results in a substantial increase in the accuracy of statistical estimates of genetic parameters compared to methods that use only information from a genetic sub-sample. Such an increase is achieved without collecting additional genetic data. Simulation studies illustrate the increase in the accuracy in different scenarios for datasets structurally similar to the Framingham Heart Study. Possible applications of the model and its further generalizations are discussed.     

A flexible B-spline model for multiple longitudinal biomarkers and survival

Often when jointly modeling longitudinal and survival data, we are interested in a multivariate longitudinal measure that may not fit well by linear models. To overcome this problem, we propose a joint longitudinal and survival model that has a nonparametric model for the longitudinal markers. We use cubic B-splines to specify the longitudinal model and a proportional hazards model to link the longitudinal measures to the hazard. To fit the model, we use a Markov chain Monte Carlo algorithm. We select the number of knots for the cubic B-spline model using the Conditional Predictive Ordinate (CPO) and the Deviance Information Criterion (DIC). The method and model selection approach are validated in a simulation. We apply this method to examine the link between viral load, CD4 count, and time to event in data from an AIDS clinical trial. The cubic B-spline model provides a good fit to the longitudinal data that could not be obtained with simple parametric models.     

A flexible cure rate model for spatially correlated survival data based on generalized extreme value distribution and Gaussian process priors

Our present work proposes a new survival model in a Bayesian context to analyze right‐censored survival data for populations with a surviving fraction, assuming that the log failure time follows a generalized extreme value distribution. Many applications require a more flexible modeling of covariate information than a simple linear or parametric form for all covariate effects. It is also necessary to include the spatial variation in the model, since it is sometimes unexplained by the covariates considered in the analysis. Therefore, the nonlinear covariate effects and the spatial effects are incorporated into the systematic component of our model. Gaussian processes (GPs) provide a natural framework for modeling potentially nonlinear relationship and have recently become extremely powerful in nonlinear regression. Our proposed model adopts a semiparametric Bayesian approach by imposing a GP prior on the nonlinear structure of continuous covariate. With the consideration of data availability and computational complexity, the conditionally autoregressive distribution is placed on the region‐specific frailties to handle spatial correlation. The flexibility and gains of our proposed model are illustrated through analyses of simulated data examples as well as a dataset involving a colon cancer clinical trial from the state of Iowa.