Statistical design and analysis of pharmacogenetic trials

Pharmacogenetic trials investigate the effect of genotype on treatment response. When there are two or more treatment groups and two or more genetic groups, investigation of gene-treatment interactions is of key interest. However, calculation of the power to detect such interactions is complicated because this depends not only on the treatment effect size within each genetic group, but also on the number of genetic groups, the size of each genetic group, and the type of genetic effect that is both present and tested for. The scale chosen to measure the magnitude of an interaction can also be problematic, especially for the binary case. Elston et al. proposed a test for detecting the presence of gene-treatment interactions for binary responses, and gave appropriate power calculations. This paper shows how the same approach can also be used for normally distributed responses. We also propose a method for analysing and performing sample size calculations based on a generalized linear model (GLM) approach. The power of the Elston et al. and GLM approaches are compared for the binary and normal case using several illustrative examples. While more sensitive to errors in model specification than the Elston et al. approach, the GLM approach is much more flexible and in many cases more powerful. Copyright © 2005 John Wiley & Sons, Ltd.

CAMCR: Computer assisted mixture model analysis for capture-recapture count data

Population size estimation with discrete or nonparametric mixture models is considered, and reliable ways of construction of the nonparametric mixture model estimator are reviewed and set into perspective. Construction of the maximum likelihood estimator of the mixing distribution is done for any number of components up to the global nonparametric maximum likelihood bound using the EM algorithm. In addition, the estimators of Chao and Zelterman are considered with some generalisations of Zelterman’s estimator. All computations are done with CAMCR, a special software developed for population size estimation with mixture models. Several examples and data sets are discussed and the estimators illustrated. Problems using the mixture model-based estimators are highlighted.

Statistical inferences in phylogeography

In conventional phylogeographic studies, historical demographic processes are elucidated from the geographical distribution of individuals represented on an inferred gene tree. However, the interpretation of gene trees in this context can be difficult as the same demographic/geographical process can randomly lead to multiple different genealogies. Likewise, the same gene trees can arise under different demographic models. This problem has led to the emergence of many statistical methods for making phylogeographic inferences. A popular phylogeographic approach based on nested clade analysis is challenged by the fact that a certain amount of the interpretation of the data is left to the subjective choices of the user, and it has been argued that the method performs poorly in simulation studies. More rigorous statistical methods based on coalescence theory have been developed. However, these methods may also be challenged by computational problems or poor model choice. In this review, we will describe the development of statistical methods in phylogeographic analysis, and discuss some of the challenges facing these methods.

Statistical evaluation of alternative models of human evolution

An appropriate model of recent human evolution is not only important to understand our own history, but it is necessary to disentangle the effects of demography and selection on genome diversity. Although most genetic data support the view that our species originated recently in Africa, it is still unclear if it completely replaced former members of the Homo genus, or if some interbreeding occurred during its range expansion. Several scenarios of modern human evolution have been proposed on the basis of molecular and paleontological data, but their likelihood has never been statistically assessed. Using DNA data from 50 nuclear loci sequenced in African, Asian and Native American samples, we show here by extensive simulations that a simple African replacement model with exponential growth has a higher probability (78%) as compared with alternative multiregional evolution or assimilation scenarios. A Bayesian analysis of the data under this best supported model points to an origin of our species approximate to 141 thousand years ago (Kya), an exit out-of-Africa approximate to 51 Kya, and a recent colonization of the Americas approximate to 10.5 Kya. We also find that the African replacement model explains not only the shallow ancestry of mtDNA or Y-chromosomes but also the occurrence of deep lineages at some autosomal loci, which has been formerly interpreted as a sign of interbreeding with Homo erectus.

Assembly rules for protein networks derived from phylogenetic-statistical analysis of whole genomes

Background: We report an analysis of a protein network of functionally linked proteins, identified from a phylogenetic statistical analysis of complete eukaryotic genomes. Phylogenetic methods identify pairs of proteins that co-evolve on a phylogenetic tree, and have been shown to have a high probability of correctly identifying known functional links. Results: The eukaryotic correlated evolution network we derive displays the familiar power law scaling of connectivity. We introduce the use of explicit phylogenetic methods to reconstruct the ancestral presence or absence of proteins at the interior nodes of a phylogeny of eukaryote species. We find that the connectivity distribution of proteins at the point they arise on the tree and join the network follows a power law, as does the connectivity distribution of proteins at the time they are lost from the network. Proteins resident in the network acquire connections over time, but we find no evidence that 'preferential attachment' - the phenomenon of newly acquired connections in the network being more likely to be made to proteins with large numbers of connections - influences the network structure. We derive a 'variable rate of attachment' model in which proteins vary in their propensity to form network interactions independently of how many connections they have or of the total number of connections in the network, and show how this model can produce apparent power-law scaling without preferential attachment. Conclusion: A few simple rules can explain the topological structure and evolutionary changes to protein-interaction networks: most change is concentrated in satellite proteins of low connectivity and small phenotypic effect, and proteins differ in their propensity to form attachments. Given these rules of assembly, power law scaled networks naturally emerge from simple principles of selection, yielding protein interaction networks that retain a high-degree of robustness on short time scales and evolvability on longer evolutionary time scales.

Three-level main-effects designs exploiting prior information about model uncertainty

To explore the projection efficiency of a design, Tsai, et al [2000. Projective three-level main effects designs robust to model uncertainty. Biometrika 87, 467-475] introduced the Q criterion to compare three-level main-effects designs for quantitative factors that allow the consideration of interactions in addition to main effects. In this paper, we extend their method and focus on the case in which experimenters have some prior knowledge, in advance of running the experiment, about the probabilities of effects being non-negligible. A criterion which incorporates experimenters' prior beliefs about the importance of each effect is introduced to compare orthogonal, or nearly orthogonal, main effects designs with robustness to interactions as a secondary consideration. We show that this criterion, exploiting prior information about model uncertainty, can lead to more appropriate designs reflecting experimenters' prior beliefs. (c) 2006 Elsevier B.V. All rights reserved.

Predicting functional gene links from phylogenetic-statistical analyses of whole genomes

An important element of the developing field of proteomics is to understand protein-protein interactions and other functional links amongst genes. Across-species correlation methods for detecting functional links work on the premise that functionally linked proteins will tend to show a common pattern of presence and absence across a range of genomes. We describe a maximum likelihood statistical model for predicting functional gene linkages. The method detects independent instances of the correlated gain or loss of pairs of proteins on phylogenetic trees, reducing the high rates of false positives observed in conventional across-species methods that do not explicitly incorporate a phylogeny. We show, in a dataset of 10,551 protein pairs, that the phylogenetic method improves by up to 35% on across-species analyses at identifying known functionally linked proteins. The method shows that protein pairs with at least two to three correlated events of gain or loss are almost certainly functionally linked. Contingent evolution, in which one gene's presence or absence depends upon the presence of another, can also be detected phylogenetically, and may identify genes whose functional significance depends upon its interaction with other genes. Incorporating phylogenetic information improves the prediction of functional linkages. The improvement derives from having a lower rate of false positives and from detecting trends that across-species analyses miss. Phylogenetic methods can easily be incorporated into the screening of large-scale bioinformatics datasets to identify sets of protein links and to characterise gene networks.

Design and analysis of climate model experiments for the efficient estimation of anthropogenic signals

Presented herein is an experimental design that allows the effects of several radiative forcing factors on climate to be estimated as precisely as possible from a limited suite of atmosphere-only general circulation model (GCM) integrations. The forcings include the combined effect of observed changes in sea surface temperatures, sea ice extent, stratospheric (volcanic) aerosols, and solar output, plus the individual effects of several anthropogenic forcings. A single linear statistical model is used to estimate the forcing effects, each of which is represented by its global mean radiative forcing. The strong colinearity in time between the various anthropogenic forcings provides a technical problem that is overcome through the design of the experiment. This design uses every combination of anthropogenic forcing rather than having a few highly replicated ensembles, which is more commonly used in climate studies. Not only is this design highly efficient for a given number of integrations, but it also allows the estimation of (nonadditive) interactions between pairs of anthropogenic forcings. The simulated land surface air temperature changes since 1871 have been analyzed. The changes in natural and oceanic forcing, which itself contains some forcing from anthropogenic and natural influences, have the most influence. For the global mean, increasing greenhouse gases and the indirect aerosol effect had the largest anthropogenic effects. It was also found that an interaction between these two anthropogenic effects in the atmosphere-only GCM exists. This interaction is similar in magnitude to the individual effects of changing tropospheric and stratospheric ozone concentrations or to the direct (sulfate) aerosol effect. Various diagnostics are used to evaluate the fit of the statistical model. For the global mean, this shows that the land temperature response is proportional to the global mean radiative forcing, reinforcing the use of radiative forcing as a measure of climate change. The diagnostic tests also show that the linear model was suitable for analyses of land surface air temperature at each GCM grid point. Therefore, the linear model provides precise estimates of the space time signals for all forcing factors under consideration. For simulated 50-hPa temperatures, results show that tropospheric ozone increases have contributed to stratospheric cooling over the twentieth century almost as much as changes in well-mixed greenhouse gases.

Simple general method of generating non-oxo, non-amavadine model octacoordinated vanadium(IV) complexes of some tetradentate ONNO chelating ligands from various oxovanadium(IV/V) compounds and structural characterization of one of them

A simple general route of obtaining very stable octacoordinated non-oxovanadium( IV) complexes of the general formula VL2 (where H2L is a tetradentate ONNO donor) is presented. Six such complexes (1-6) are adequately characterized by elemental analysis, mass spectrometry, and various spectroscopic techniques. One of these compounds (1) has been structurally characterized. The molecule has crystallographic 4 symmetry and has a dodecahedral structure existing in a tetragonal space group P4n2. The non-oxo character and VL2 stoichiometry for all of the complexes are established from analytical and mass spectrometric data. In addition, the non-oxo character is clearly indicated by the complete absence of the strong nu(v=o) band in the 925-1025 cm(-1) region, which is a signature of all oxovanadium species. The complexes are quite stable in open air in the solid state and in solution, a phenomenon rarely observed in non-oxovanadium(IV) or bare vanadium(IV) complexes.

Effect of internal partitioning on room air quality with mixing ventilation-statistical analysis

In designing modern office buildings, building spaces are frequently zoned by introducing internal partitioning, which may have a significant influence on the room air environment. This internal partitioning was studied by means of model test, numerical simulation, and statistical analysis as the final stage. In this paper, the results produced from the statistical analysis are summarized and presented.

Backward elimination model construction for regression and classification using leave-one-out criteria

A fundamental principle in practical nonlinear data modeling is the parsimonious principle of constructing the minimal model that explains the training data well. Leave-one-out (LOO) cross validation is often used to estimate generalization errors by choosing amongst different network architectures (M. Stone, "Cross validatory choice and assessment of statistical predictions", J. R. Stast. Soc., Ser. B, 36, pp. 117-147, 1974). Based upon the minimization of LOO criteria of either the mean squares of LOO errors or the LOO misclassification rate respectively, we present two backward elimination algorithms as model post-processing procedures for regression and classification problems. The proposed backward elimination procedures exploit an orthogonalization procedure to enable the orthogonality between the subspace as spanned by the pruned model and the deleted regressor. Subsequently, it is shown that the LOO criteria used in both algorithms can be calculated via some analytic recursive formula, as derived in this contribution, without actually splitting the estimation data set so as to reduce computational expense. Compared to most other model construction methods, the proposed algorithms are advantageous in several aspects; (i) There are no tuning parameters to be optimized through an extra validation data set; (ii) The procedure is fully automatic without an additional stopping criteria; and (iii) The model structure selection is directly based on model generalization performance. The illustrative examples on regression and classification are used to demonstrate that the proposed algorithms are viable post-processing methods to prune a model to gain extra sparsity and improved generalization.

CAMCR: Computer-Assisted Mixture model analysis for Capture–Recapture count data

Population size estimation with discrete or nonparametric mixture models is considered, and reliable ways of construction of the nonparametric mixture model estimator are reviewed and set into perspective. Construction of the maximum likelihood estimator of the mixing distribution is done for any number of components up to the global nonparametric maximum likelihood bound using the EM algorithm. In addition, the estimators of Chao and Zelterman are considered with some generalisations of Zelterman’s estimator. All computations are done with CAMCR, a special software developed for population size estimation with mixture models. Several examples and data sets are discussed and the estimators illustrated. Problems using the mixture model-based estimators are highlighted.

Model car-exhaust catalyst studied by TPD and TP-RAIRS: Surface reactions of NO on clean and O-covered Ir{100}

The adsorption of NO on Ir{100} has been studied as a function of NO coverage and temperature using temperature programmed reflection absorption infrared spectroscopy (TP-RAIRS), low energy electron diffraction (LEED) and temperature programmed desorption (TPD). After saturating the clean (1 x 5)-reconstructed surface with NO at 95 K. two N-2, desorption peaks are observed upon heating. The first N-2 peak at 346 K results from the decomposition of bridge-bonded NO, and the second at 475 K from the decomposition of atop-bonded NO molecules. NO decomposition is proposed to be the rate limiting step for both N-2 desorption states. For high NO coverages on the (1 x 5) surface, the narrow width of the first N-2 desorption peak is indicative of an autocatalytic process for which the parallel formation of N2O appears to be the crucial step. When NO is adsorbed on the metastable unreconstructed (1 x 1) phase of clean Ir{100} N-2 desorption starts at lower temperatures, indicating that this surface modification is more reactive. When a high coverage of oxygen, near 0.5 ML, is pre-adsorbed on the surface, the decomposition of NO is inhibited and mainly desorption of intact NO is observed.

A statistical mechanical approach for the computation of the climatic response to general forcings

The climate belongs to the class of non-equilibrium forced and dissipative systems, for which most results of quasi-equilibrium statistical mechanics, including the fluctuation-dissipation theorem, do not apply. In this paper we show for the first time how the Ruelle linear response theory, developed for studying rigorously the impact of perturbations on general observables of non-equilibrium statistical mechanical systems, can be applied with great success to analyze the climatic response to general forcings. The crucial value of the Ruelle theory lies in the fact that it allows to compute the response of the system in terms of expectation values of explicit and computable functions of the phase space averaged over the invariant measure of the unperturbed state. We choose as test bed a classical version of the Lorenz 96 model, which, in spite of its simplicity, has a well-recognized prototypical value as it is a spatially extended one-dimensional model and presents the basic ingredients, such as dissipation, advection and the presence of an external forcing, of the actual atmosphere. We recapitulate the main aspects of the general response theory and propose some new general results. We then analyze the frequency dependence of the response of both local and global observables to perturbations having localized as well as global spatial patterns. We derive analytically several properties of the corresponding susceptibilities, such as asymptotic behavior, validity of Kramers-Kronig relations, and sum rules, whose main ingredient is the causality principle. We show that all the coefficients of the leading asymptotic expansions as well as the integral constraints can be written as linear function of parameters that describe the unperturbed properties of the system, such as its average energy. Some newly obtained empirical closure equations for such parameters allow to define such properties as an explicit function of the unperturbed forcing parameter alone for a general class of chaotic Lorenz 96 models. We then verify the theoretical predictions from the outputs of the simulations up to a high degree of precision. The theory is used to explain differences in the response of local and global observables, to define the intensive properties of the system, which do not depend on the spatial resolution of the Lorenz 96 model, and to generalize the concept of climate sensitivity to all time scales. We also show how to reconstruct the linear Green function, which maps perturbations of general time patterns into changes in the expectation value of the considered observable for finite as well as infinite time. Finally, we propose a simple yet general methodology to study general Climate Change problems on virtually any time scale by resorting to only well selected simulations, and by taking full advantage of ensemble methods. The specific case of globally averaged surface temperature response to a general pattern of change of the CO2 concentration is discussed. We believe that the proposed approach may constitute a mathematically rigorous and practically very effective way to approach the problem of climate sensitivity, climate prediction, and climate change from a radically new perspective.

A spectral performance model for the High Resolution Dynamics Limb Sounder (6-18µm)

A spectral performance model, designed to simulate the system spectral throughput for each of the 21 channels in the HIRDLS radiometer, is described. This model uses the measured spectral characteristics of each of the components in the optical train, appropriately corrected for their optical environment, to determine the end-to-end spectral throughput profile for each channel. This profile is then combined with the predicted thermal emission from the atmosphere, arising from the height of interest, to establish an in-band (wanted) to out-of-band (unwanted) radiance ratio. The results from the use of the model demonstrate that the instrument level radiometric requirements for the instrument will be achieved. The optical arrangement and spectral design requirements for filtering in the HIRDLS instrument are described together with a presentation of the performance achieved for the complete set of manufactured filters. Compliance of the predicted passband throughput model to the spectral positioning requi rements of the instrument is also demonstrated.