How much variance is explained by ecologists? Additional perspectives

Oecologia - A recent meta-analysis of meta-analyses by Møller and Jennions (2002, Oecologia 132:492–500) suggested that ecologists using statistical models are explaining between 2.5%...     

A new dose-finding design for bivariate outcomes

For some drugs, toxicity events lead to early termination of treatment before a therapeutic response is observed. That is, there are three possible outcomes: toxicity (therapeutic response unknown), therapeutic response without toxicity, and no response with no toxicity. The optimal dose is the dose that maximizes the probability of the joint event, response, and no toxicity. The optimal safe dose is the dose, from among the doses with toxicity rate less than the maximum tolerable level, that maximizes the probability of response and no toxicity. We present a new sequential design to maximize the number of subjects assigned in the neighborhood of the optimal safe dose in a dose-finding trial with two outcomes.     

Shrinkage estimation for functional principal component scores with application to the population kinetics of plasma folate

We present the application of a nonparametric method to performing functional principal component analysis for functional curve data that consist of measurements of a random trajectory for a sample of subjects. This design typically consists of an irregular grid of time points on which repeated measurements are taken for a number of subjects. We introduce shrinkage estimates for the functional principal component scores that serve as the random effects in the model. Scatterplot smoothing methods are used to estimate the mean function and covariance surface of this model. We propose improved estimation in the neighborhood of and at the diagonal of the covariance surface, where the measurement errors are reflected. The presence of additive measurement errors motivates shrinkage estimates for the functional principal component scores. Shrinkage estimates are developed through best linear prediction and in a generalized version, aiming at minimizing one-curve-leave-out prediction error. The estimation of individual trajectories combines data obtained from that individual as well as all other individuals. We apply our methods to new data regarding the analysis of the level of 14C-folate in plasma as a function of time since dosing of healthy adults with a small tracer dose of 14C-folic acid. A time transformation was incorporated to handle design irregularity concerning the time points on which the measurements were taken. The proposed methodology, incorporating shrinkage and data-adaptive features, is seen to be well suited for describing population kinetics of 14C-folate-specific activity and random effects, and can also be applied to other functional data analysis problems.     

Testing the correlation for clustered categorical and censored discrete time-to-event data when covariates are measured without/with errors

In the analysis of clustered categorical data, it is of common interest to test for the correlation within clusters, and the heterogeneity across different clusters. We address this problem by proposing a class of score tests for the null hypothesis that the variance components are zero in random effects models, for clustered nominal and ordinal categorical responses. We extend the results to accommodate clustered censored discrete time-to-event data. We next consider such tests in the situation where covariates are measured with errors. We propose using the SIMEX method to construct the score tests for the null hypothesis that the variance components are zero. Key advantages of the proposed score tests are that they can be easily implemented by fitting standard polytomous regression models and discrete failure time models, and that they are robust in the sense that no assumptions need to be made regarding the distributions of the random effects and the unobserved covariates. The asymptotic properties of the proposed tests are studied. We illustrate these tests by analyzing two data sets and evaluate their performance with simulations.     

Multivariate approach for selecting sets of differentially expressed genes

An important problem addressed using cDNA microarray data is the detection of genes differentially expressed in two tissues of interest. Currently used approaches ignore the multidimensional structure of the data. However it is well known that correlation among covariates can enhance the ability to detect less pronounced differences. We use the Mahalanobis distance between vectors of gene expressions as a criterion for simultaneously comparing a set of genes and develop an algorithm for maximizing it. To overcome the problem of instability of covariance matrices we propose a new method of combining data from small-scale random search experiments. We show that by utilizing the correlation structure the multivariate method, in addition to the genes found by the one-dimensional criteria, finds genes whose differential expression is not detectable marginally.     

Chromosome Inversion Polymorphisms Influence Morphological Traits in <Emphasis Type="Italic">Trimerotropis Pallidipennis</Emphasis> (Orthoptera)

Trimerotropis pallidipennis is a New World grasshopper whose South-American populations are polymorphic for six pericentric inversions. Previous work has demonstrated that the frequences of these inversions correlate with climatic variables, and hence a possible adaptive pattern was put forward. In the present work we analysed a sample of a natural population of T. pallidipennis to ascertain whether the chromosomal inversions have effects on exophenotypes. Two hundred and sixty-eight males coming from a natural population at Uspallata, Mendoza Province, Argentina were analysed, and it was observed that most inversions had significant effects on phenotypes. Furthermore, some body size-related characteristics (such as tegmina length) were correlated with the number of inversions. Individuals from populations at higher altitude or latitude (i.e., at lower minimum temperatures), along with higher frequencies of standard sequences, were significantly smaller, and this coherence between interpopulational with intrapopulational results may indicate that the diminished body size of the standard sequence-carrying individuals may be caused by an effect of the inversions, or genes within the inversions, on body size. We finally put forward the hypothesis that reduced body size in a context of reduced minimum temperature may be a response to shortened development season, and so smaller individuals may be advantageous.     

A study on relations of vegetation,climate and soils in Shanxi province,China

Relationships of vegetation, climate and soils in Shanxi plateau wereanalyzed by use of Canonical Correspondence Analysis (CCA). Shanxi province,located at 34°35–40°43 N, 110°15–114°33 E, was divided into a series of rectangular districts of30 latitude by 20 longitude. Areas of vegetation formations and soil types ineach district were measured carefully using fine grain on the vegetation andsoil maps of Shanxi. Climatic data were mean values of 25 years records in eachdistrict. Three data matrices of climate, vegetation and soil were combined byCCA. The results showed that the distribution of vegetation is closely relatedto the variety of climates and to soils distribution.     

Modeling multivariate survival data by a semiparametric random effects proportional odds model

In this article, the focus is on the analysis of multivariate survival time data with various types of dependence structures. Examples of multivariate survival data include clustered data and repeated measurements from the same subject, such as the interrecurrence times of cancer tumors. A random effect semiparametric proportional odds model is proposed as an alternative to the proportional hazards model. The distribution of the random effects is assumed to be multivariate normal and the random effect is assumed to act additively to the baseline log-odds function. This class of models, which includes the usual shared random effects model, the additive variance components model, and the dynamic random effects model as special cases, is highly flexible and is capable of modeling a wide range of multivariate survival data. A unified estimation procedure is proposed to estimate the regression and dependence parameters simultaneously by means of a marginal-likelihood approach. Unlike the fully parametric case, the regression parameter estimate is not sensitive to the choice of correlation structure of the random effects. The marginal likelihood is approximated by the Monte Carlo method. Simulation studies are carried out to investigate the performance of the proposed method. The proposed method is applied to two well-known data sets, including clustered data and recurrent event times data.     

A semiparametric model for the analysis of recurrent-event panel data

In many longitudinal studies, interest focuses on the occurrence rate of some phenomenon for the subjects in the study. When the phenomenon is nonterminating and possibly recurring, the result is a recurrent-event data set. Examples include epileptic seizures and recurrent cancers. When the recurring event is detectable only by an expensive or invasive examination, only the number of events occurring between follow-up times may be available. This article presents a semiparametric model for such data, based on a multiplicative intensity model paired with a fully flexible nonparametric baseline intensity function. A random subject-specific effect is included in the intensity model to account for the overdispersion frequently displayed in count data. Estimators are determined from quasi-likelihood estimating functions. Because only first- and second-moment assumptions are required for quasi-likelihood, the method is more robust than those based on the specification of a full parametric likelihood. Consistency of the estimators depends only on the assumption of the proportional intensity model. The semiparametric estimators are shown to be highly efficient compared with the usual parametric estimators. As with semiparametric methods in survival analysis, the method provides useful diagnostics for specific parametric models, including a quasi-score statistic for testing specific baseline intensity functions. The techniques are used to analyze cancer recurrences and a pheromone-based mating disruption experiment in moths. A simulation study confirms that, for many practical situations, the estimators possess appropriate small-sample characteristics.     

A unified parametric regression model for recapture studies with random removals in continuous time

Conditional likelihood based on counting processes are combined with a Horvitz-Thompson estimator to yield a population size estimator that is more efficient than the existing ones. Random removals are allowed in the recapturing process. Simulation studies are shown to assess the performance of the proposed estimators. Examples on a bird banding and a small mammal recapturing study are given.