C. Barceló-Vidal

Isometric Logratio Transformations for Compositional Data Analysis

Geometry in the simplex has been developed in the last 15 years mainly based on the contributions due to J. Aitchison. The main goal was to develop analytical tools for the statistical analysis of compositional data. Our present aim is to get a further insight into some aspects of this geometry in order to clarify the way for more complex statistical approaches. This is done by way of orthonormal bases, which allow for a straightforward handling of geometric elements in the simplex. The transformation into real coordinates preserves all metric properties and is thus called isometric logratio transformation (ilr). An important result is the decomposition of the simplex, as a vector space, into orthogonal subspaces associated with nonoverlapping subcompositions. This gives the key to join compositions with different parts into a single composition by using a balancing element. The relationship between ilr transformations and the centered-logratio (clr) and additive-logratio (alr) transformations is also studied. Exponential growth or decay of mass is used to illustrate compositional linear processes, parallelism and orthogonality in the simplex.

Dealing with zeros and missing values in compositional data sets using nonparametric imputation

The statistical analysis of compositional data based on logratios of parts is not suitable when zeros are present in a data set. Nevertheless, if there is interest in using this modeling approach, several strategies have been published in the specialized literature which can be used. In particular, substitution or imputation strategies are available for rounded zeros. In this paper, existing nonparametric imputation methods—both for the additive and the multiplicative approach—are revised and essential properties of the last method are given. For missing values a generalization of the multiplicative approach is proposed.

Updated reference ranges for the ductus venosus pulsatility index at 11-13 weeks.

Objective: To update the reference ranges for the ductus venosus pulsatility index (DVPI) at 11+0 to 13+6 gestational weeks. Methods: DVPI was calculated in 14,444 singleton fetuses at 11+0 to 13+6 weeks in two Fetal Medicine Centers, during a 4-year period. Using previously described medians, DVPI evolution was assessed both over the study period on a yearly basis and over gestation, grouping fetuses according to 5-mm crown-rump length (CRL) ranges. Weighted DVPI medians, the 5th and 95th percentiles and distribution parameters for unaffected and trisomy 21 fetuses were newly calculated. Results: A significant DVPI multiple of the median decrease was observed over both the study period (p < 0.01) and over gestation (p < 0.01) using previous medians, in the two centers. Newly calculated weighted medians were lower than those previously described, decreasing with CRL. Distribution parameters calculated using the new medians were different from those previously described. Conclusion: DVPI reference ranges were lower than those previously reported and decreased with CRL. Updated medians and distribution parameters should be considered to include the DVPI as a Gaussian marker in trisomy 21 screening and for quality control purposes.

Cumulative sum plots and retrospective parameters in first-trimester ductus venosus quality assurance.

This study aimed to evaluate the application of two quality assurance methods to the ductus venosus pulsatility index (DVPI), as a first‐trimester aneuploidy marker, including retrospective assessment of distribution parameters and cumulative sum (CUSUM) plots.

The peril of proportions: robust niche indices for categorical data

Indices of niche breadth and niche overlap for categorical data are typically expressed in terms of proportions of resources use. These are unit-sum constrained data; hence, direct application of standard general linear modelling methods to such indices can lead to spurious correlations and misleading inference. To overcome these limitations, we introduce a compositional data analysis (CoDA) approach and derive compositional expressions of niche breadth, niche overlap and specialization. Compositional data analysis is specifically devoted to the analysis of vectors of proportions (i.e. compositions) and represents the appropriate framework for the study of sets of data with unit-sum constraint as those typically used in the calculation of niche indices. We show that compositional indices exhibit suitable statistical properties that make them flexible and robust, allowing downstream application of the full toolbox of multivariate analysis techniques to these estimators, a possibility not available with classical indices. In addition, we find that when characterizing niche breadth, niche overlap and specialization in terms of vectors of proportions, these concepts are naturally integrated in a coherent unifying framework. When data are categorical, we recommend the use of compositional indices for the statistical analysis of specialization metrics, niche breadth and niche overlap. We believe that the unified framework emerging from our compositional approach to niche metrics will allow a more thorough understanding of specialization at multiple levels of biological organization and provide novel insights in complex phenomena such as invasions and niche shifts

Contents Vol. 32, 2012

R. Achiron, Tel Hashomer N.S. Adzick, Philadelphia, Pa. L. Allan, London A.A. Baschat, Baltimore, Md. K.J. Blakemore, Baltimore, Md. T.-H. Bui, Stockholm F.A. Chervenak, New York, N.Y. T. Chiba, Tokyo R. Chmait, Los Angeles, Calif. F. Crispi, Barcelona J.E. De Lia, Milwaukee, Wisc. J.A. Deprest, Leuven G.C. Di Renzo, Perugia J.W. Dudenhausen, Berlin N.M. Fisk, Brisbane, Qld. A.W. Flake, Philadelphia, Pa. U. Gembruch, Bonn M.R. Harrison, San Francisco, Calif. J.C. Hobbins, Denver, Colo. L.K. Hornberger, San Francisco, Calif. E.R.M. Jauniaux, London M.P. Johnson, Philadelphia, Pa. C. Jorgensen, Copenhagen J.-M. Jouannic, Paris P.M. Kyle, London O. Lapaire, Basel S. Lipitz, Tel-Hashomer G. Malinger, Holon G. Mari, Detroit, Mich. M. Martinez-Ferro, Buenos Aires K.J. Moise, Houston, Tex. F. Molina, Granada K.H. Nicolaides, London D. Oepkes, Leiden L. Otaño, Buenos Aires Z. Papp, Budapest R.A. Quintero, Miami, Fla. G. Ryan, Toronto J. Rychik, Philadelphia, Pa. H. Sago, Tokyo W. Sepulveda, Santiago P. Stone, Auckland D.V. Surbek, Bern B.J. Trudinger, Westmead, N.S.W. J.M.G. van Vugt, Amsterdam Y. Ville, Paris Clinical Advances and Basic Research