Understanding Variation in Sets of N-of-1 Trials.

A recent paper in this journal by Chen and Chen has used computer simulations to examine a number of approaches to analysing sets of n-of-1 trials. We have examined such designs using a more theoretical approach based on considering the purpose of analysis and the structure as regards randomisation that the design uses. We show that different purposes require different analyses and that these in turn may produce quite different results. Our approach to incorporating the randomisation employed when the purpose is to test a null hypothesis of strict equality of the treatment makes use of Nelder's theory of general balance. However, where the purpose is to make inferences about the effects for individual patients, we show that a mixed model is needed. There are strong parallels to the difference between fixed and random effects meta-analyses and these are discussed

Ellipsoidal analysis of coordination polyhedra

The idea of the coordination polyhedron is essential to understanding chemical structure. Simple polyhedra in crystalline compounds are often deformed due to structural complexity or electronic instabilities so distortion analysis methods are useful. Here we demonstrate that analysis of the minimum bounding ellipsoid of a coordination polyhedron provides a general method for studying distortion, yielding parameters that are sensitive to various orders in metal oxide examples. Ellipsoidal analysis leads to discovery of a general switching of polyhedral distortions at symmetry-disallowed transitions in perovskites that may evidence underlying coordination bistability, and reveals a weak off-centre ‘d(5) effect' for Fe(3+) ions that could be exploited in multiferroics. Separating electronic distortions from intrinsic deformations within the low temperature superstructure of magnetite provides new insights into the charge and trimeron orders. Ellipsoidal analysis can be useful for exploring local structure in many materials such as coordination complexes and frameworks, organometallics and organic molecules

Female sexual preferences toward conspecific and hybrid male mating calls in two species of polygynous deer, Cervus elaphus and C. nippon

The behavioral processes at the basis of hybridization and introgression are understudied in terrestrial mammals. We use a unique model to test the role of sexual signals as a reproductive barrier to introgression by investigating behavioral responses to male sexual calls in estrous females of two naturally allopatric but reproductively compatible deer species, red deer and sika deer. Previous studies demonstrated asymmetries in acoustic species discrimination between these species: most but not all female red deer prefer conspecific over sika deer male calls while female sika deer exhibit no preference differences. Here, we extend this examination of acoustic species discrimination to the role of male sexual calls in introgression between parent species and hybrids. Using two-speaker playback experiments, we compared the preference responses of estrous female red and sika deer to male sexual calls from conspecifics versus red × sika hybrids. These playbacks simulate early secondary contact between previously allopatric species after hybridization has occurred. Based on previous conspecific versus heterospecific playbacks, we predicted that most female red deer would prefer conspecific calls while female sika deer would show no difference in their preference behaviors toward conspecific and hybrid calls. However, results show that previous asymmetries did not persist as neither species exhibited more preferences for conspecific over hybrid calls. Thus, vocal behavior is not likely to deter introgression between these species during the early stages of sympatry. On a wider scale, weak discrimination against hybrid sexual signals could substantially contribute to this important evolutionary process in mammals and other taxa

Accounting for centre-effects in multicentre trials with a binary outcome - when, why, and how?

BACKGROUND: It is often desirable to account for centre-effects in the analysis of multicentre randomised trials, however it is unclear which analysis methods are best in trials with a binary outcome. METHODS: We compared the performance of four methods of analysis (fixed-effects models, random-effects models, generalised estimating equations (GEE), and Mantel-Haenszel) using a re-analysis of a previously reported randomised trial (MIST2) and a large simulation study. RESULTS: The re-analysis of MIST2 found that fixed-effects and Mantel-Haenszel led to many patients being dropped from the analysis due to over-stratification (up to 69% dropped for Mantel-Haenszel, and up to 33% dropped for fixed-effects). Conversely, random-effects and GEE included all patients in the analysis, however GEE did not reach convergence. Estimated treatment effects and p-values were highly variable across different analysis methods. The simulation study found that most methods of analysis performed well with a small number of centres. With a large number of centres, fixed-effects led to biased estimates and inflated type I error rates in many situations, and Mantel-Haenszel lost power compared to other analysis methods in some situations. Conversely, both random-effects and GEE gave nominal type I error rates and good power across all scenarios, and were usually as good as or better than either fixed-effects or Mantel-Haenszel. However, this was only true for GEEs with non-robust standard errors (SEs); using a robust ‘sandwich’ estimator led to inflated type I error rates across most scenarios. CONCLUSIONS: With a small number of centres, we recommend the use of fixed-effects, random-effects, or GEE with non-robust SEs. Random-effects and GEE with non-robust SEs should be used with a moderate or large number of centres

Many continuous variables should be analyzed using the relative scale: a case study of β2-agonists for preventing exercise-induced bronchoconstriction

BACKGROUND: The relative scale adjusts for baseline variability and therefore may lead to findings that can be generalized more widely. It is routinely used for the analysis of binary outcomes but only rarely for continuous outcomes. Our objective was to compare relative vs absolute scale pooled outcomes using data from a recently published Cochrane systematic review that reported only absolute effects of inhaled β2-agonists on exercise-induced decline in forced-expiratory volumes in 1 s (FEV1). METHODS: From the Cochrane review, we selected placebo-controlled cross-over studies that reported individual participant data (IPD). Reversal in FEV1 decline after exercise was modeled as a mean uniform percentage point (pp) change (absolute effect) or average percent change (relative effect) using either intercept-only or slope-only, respectively, linear mixed-effect models. We also calculated the pooled relative effect estimates using standard random-effects, inverse-variance-weighting meta-analysis using study-level mean effects. RESULTS: Fourteen studies with 187 participants were identified for the IPD analysis. On the absolute scale, β2-agonists decreased the exercise-induced FEV1 decline by 28 pp., and on the relative scale, they decreased the FEV1 decline by 90%. The fit of the statistical model was significantly better with the relative 90% estimate compared with the absolute 28 pp. estimate. Furthermore, the median residuals (5.8 vs. 10.8 pp) were substantially smaller in the relative effect model than in the absolute effect model. Using standard study-level meta-analysis of the same 14 studies, β2-agonists reduced exercise-induced FEV1 decline on the relative scale by a similar amount: 83% or 90%, depending on the method of calculating the relative effect. CONCLUSIONS: Compared with the absolute scale, the relative scale captures more effectively the variation in the effects of β2-agonists on exercise-induced FEV1-declines. The absolute scale has been used in the analysis of FEV1 changes and may have led to sub-optimal statistical analysis in some cases. The choice between the absolute and relative scale should be determined based on biological reasoning and empirical testing to identify the scale that leads to lower heterogeneity.Peer reviewe

Demographic and spatial predictors of anemia in women of reproductive age in Timor-Leste: Implications for health program prioritization

10.1371/journal.pone.0091252PLoS ONE93-POLN

Identifying source populations for the reintroduction of the Eurasian beaver, Castor fiber L. 1758, into Britain: evidence from ancient DNA

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