Effect of training-sample size and classification difficulty on the accuracy of genomic predictors.

Introduction: As part of the MicroArray Quality Control (MAQC)-II project, this analysis examines how the choice of univariate feature-selection methods and classification algorithms may influence the performance of genomic predictors under varying degrees of prediction difficulty represented by three clinically relevant endpoints. Methods: We used gene-expression data from 230 breast cancers (grouped into training and independent validation sets), and we examined 40 predictors (five univariate feature-selection methods combined with eight different classifiers) for each of the three endpoints. Their classification performance was estimated on the training set by using two different resampling methods and compared with the accuracy observed in the independent validation set. Results: A ranking of the three classification problems was obtained, and the performance of 120 models was estimated and assessed on an independent validation set. The bootstrapping estimates were closer to the validation performance than were the cross-validation estimates. The required sample size for each endpoint was estimated, and both gene-level and pathway-level analyses were performed on the obtained models. Conclusions: We showed that genomic predictor accuracy is determined largely by an interplay between sample size and classification difficulty. Variations on univariate feature-selection methods and choice of classification algorithm have only a modest impact on predictor performance, and several statistically equally good predictors can be developed for any given classification problem.

Sample size and statistical power in the hierarchical analysis of variance: applications in morphometry of the nervous system.

Analysis of variance is commonly used in morphometry in order to ascertain differences in parameters between several populations. Failure to detect significant differences between populations (type II error) may be due to suboptimal sampling and lead to erroneous conclusions; the concept of statistical power allows one to avoid such failures by means of an adequate sampling. Several examples are given in the morphometry of the nervous system, showing the use of the power of a hierarchical analysis of variance test for the choice of appropriate sample and subsample sizes. In the first case chosen, neuronal densities in the human visual cortex, we find the number of observations to be of little effect. For dendritic spine densities in the visual cortex of mice and humans, the effect is somewhat larger. A substantial effect is shown in our last example, dendritic segmental lengths in monkey lateral geniculate nucleus. It is in the nature of the hierarchical model that sample size is always more important than subsample size. The relative weight to be attributed to subsample size thus depends on the relative magnitude of the between observations variance compared to the between individuals variance.

A program for the computation of power and determination of sample size in hierarchical experimental designs.

We have devised a program that allows computation of the power of F-test, and hence determination of appropriate sample and subsample sizes, in the context of the one-way hierarchical analysis of variance with fixed effects. The power at a fixed alternative is an increasing function of the sample size and of the subsample size. The program makes it easy to obtain the power of F-test for a range of values of sample and subsample sizes, and therefore the appropriate sizes based on a desired power. The program can be used for the 'ordinary' case of the one-way analysis of variance, as well as for hierarchical analysis of variance with two stages of sampling. Examples are given of the practical use of the program.

Effects of sample size on the performance of species distribution models

A wide range of modelling algorithms is used by ecologists, conservation practitioners, and others to predict species ranges from point locality data. Unfortunately, the amount of data available is limited for many taxa and regions, making it essential to quantify the sensitivity of these algorithms to sample size. This is the first study to address this need by rigorously evaluating a broad suite of algorithms with independent presence-absence data from multiple species and regions. We evaluated predictions from 12 algorithms for 46 species (from six different regions of the world) at three sample sizes (100, 30, and 10 records). We used data from natural history collections to run the models, and evaluated the quality of model predictions with area under the receiver operating characteristic curve (AUC). With decreasing sample size, model accuracy decreased and variability increased across species and between models. Novel modelling methods that incorporate both interactions between predictor variables and complex response shapes (i.e. GBM, MARS-INT, BRUTO) performed better than most methods at large sample sizes but not at the smallest sample sizes. Other algorithms were much less sensitive to sample size, including an algorithm based on maximum entropy (MAXENT) that had among the best predictive power across all sample sizes. Relative to other algorithms, a distance metric algorithm (DOMAIN) and a genetic algorithm (OM-GARP) had intermediate performance at the largest sample size and among the best performance at the lowest sample size. No algorithm predicted consistently well with small sample size (n < 30) and this should encourage highly conservative use of predictions based on small sample size and restrict their use to exploratory modelling.

EEG-based functional brain networks: does the network size matter?

Functional connectivity in human brain can be represented as a network using electroencephalography (EEG) signals. These networks--whose nodes can vary from tens to hundreds--are characterized by neurobiologically meaningful graph theory metrics. This study investigates the degree to which various graph metrics depend upon the network size. To this end, EEGs from 32 normal subjects were recorded and functional networks of three different sizes were extracted. A state-space based method was used to calculate cross-correlation matrices between different brain regions. These correlation matrices were used to construct binary adjacency connectomes, which were assessed with regards to a number of graph metrics such as clustering coefficient, modularity, efficiency, economic efficiency, and assortativity. We showed that the estimates of these metrics significantly differ depending on the network size. Larger networks had higher efficiency, higher assortativity and lower modularity compared to those with smaller size and the same density. These findings indicate that the network size should be considered in any comparison of networks across studies.

Sensitivity of predictive species distribution models to change in grain size

Predictive species distribution modelling (SDM) has become an essential tool in biodiversity conservation and management. The choice of grain size (resolution) of environmental layers used in modelling is one important factor that may affect predictions. We applied 10 distinct modelling techniques to presence-only data for 50 species in five different regions, to test whether: (1) a 10-fold coarsening of resolution affects predictive performance of SDMs, and (2) any observed effects are dependent on the type of region, modelling technique, or species considered. Results show that a 10 times change in grain size does not severely affect predictions from species distribution models. The overall trend is towards degradation of model performance, but improvement can also be observed. Changing grain size does not equally affect models across regions, techniques, and species types. The strongest effect is on regions and species types, with tree species in the data sets (regions) with highest locational accuracy being most affected. Changing grain size had little influence on the ranking of techniques: boosted regression trees remain best at both resolutions. The number of occurrences used for model training had an important effect, with larger sample sizes resulting in better models, which tended to be more sensitive to grain. Effect of grain change was only noticeable for models reaching sufficient performance and/or with initial data that have an intrinsic error smaller than the coarser grain size.

X-ray microtomography of Larger Foraminifera

X-ray microtomography has become a new tool in earth sciences to obtain non-destructive 3D-image data from geological objects in which variations in mineralogy, chemical composition and/or porosity create sufficient x-ray density contrasts.We present here first, preliminary results of an application to the external and internal morphology of Permian to Recent Larger Foraminifera. We use a SkyScan-1072 high-resolution desk-top micro-CT system. The system has a conical x-ray source with a spot size of about 5µm that runs at 20-100kV, 0-250µA, resulting in a maximal resolution of 5µm. X-ray transmission images are captured by a scintillator coupled via fibre optics to a 1024x1024 pixel 12-bit CCD. The object is placed between the x-ray source and the scintillator on a stub that rotates 360°around its vertical axis in steps as small as 0.24 degrees. Sample size is limited to 2 cm due to the absorption of geologic material for x-rays. The transmission images are back projected using a Feldkamp algorithm into a vertical stack of up to 1000 1Kx1K images that represent horizontal cuts of the object. This calculation takes 2 to several hours on a Double-Processor 2.4GHz PC. The stack of images (.bmp) can be visualized with any 3D-imaging software, used to produce cuts of Larger Foraminifera. Among other applications, the 3D-imaging software furnished by SkyScan can produce 3D-models by defining a threshold density value to distinguish "solid" from "void. Several models with variable threshold values and colors can be imbricated, rotated and cut together. The best results were obtained with microfossils devoid of chamber-filling cements (Permian, Eocene, Recent). However, even slight differences in cement mineralogy/composition can result in surprisingly good x-ray density contrasts.X-ray microtomography may develop into a powerful tool for larger microfossils with a complex internal structure, because it is non-destructive, requires no preparation of the specimens, and produces a true 3D-image data set. We will use these data sets in the future to produce cuts in any direction to compare them with arbitrary cuts of complex microfossils in thin sections. Many groups of benthic and planktonic foraminifera may become more easily determinable in thin section by this way.

What spatial data do we need to develop global mammal conservation strategies?

Spatial data on species distributions are available in two main forms, point locations and distribution maps (polygon ranges and grids). The first are often temporally and spatially biased, and too discontinuous, to be useful (untransformed) in spatial analyses. A variety of modelling approaches are used to transform point locations into maps. We discuss the attributes that point location data and distribution maps must satisfy in order to be useful in conservation planning. We recommend that before point location data are used to produce and/or evaluate distribution models, the dataset should be assessed under a set of criteria, including sample size, age of data, environmental/geographical coverage, independence, accuracy, time relevance and (often forgotten) representation of areas of permanent and natural presence of the species. Distribution maps must satisfy additional attributes if used for conservation analyses and strategies, including minimizing commission and omission errors, credibility of the source/assessors and availability for public screening. We review currently available databases for mammals globally and show that they are highly variable in complying with these attributes. The heterogeneity and weakness of spatial data seriously constrain their utility to global and also sub-global scale conservation analyses.

Effectiveness of cladribine therapy in patients with pulmonary Langerhans cell histiocytosis.

BackgroundPulmonary Langerhans cell histiocytosis (PLCH) is a rare disorder characterised by granulomatous proliferation of CD1a-positive histiocytes forming granulomas within lung parenchyma, in strong association with tobacco smoking, and which may result in chronic respiratory failure. Smoking cessation is considered to be critical in management, but has variable effects on outcome. No drug therapy has been validated. Cladribine (chlorodeoxyadenosine, 2-CDA) down-regulates histiocyte proliferation and has been successful in curbing multi-system Langerhans cell histiocytosis and isolated PLCH.Methods and patientsWe retrospectively studied 5 patients (aged 37¿55 years, 3 females) with PLCH who received 3 to 4 courses of cladribine therapy as a single agent (0.1 mg/kg per day for 5 consecutive days at monthly intervals). One patient was treated twice because of relapse at 1 year. Progressive pulmonary disease with obstructive ventilatory pattern despite smoking cessation and/or corticosteroid therapy were indications for treatment. Patients were administered oral trimethoprim/sulfamethoxazole and valaciclovir to prevent opportunistic infections. They gave written consent to receive off-label cladribine in the absence of validated treatment.ResultsFunctional class dyspnea improved with cladribine therapy in 4 out of 5 cases, and forced expiratory volume in 1 second (FEV1) increased in all cases by a mean of 387 ml (100¿920 ml), contrasting with a steady decline prior to treatment. Chest high-resolution computed tomography (HRCT) features improved with cladribine therapy in 4 patients. Hemodynamic improvement was observed in 1 patient with pre-capillary pulmonary hypertension. The results suggested a greater treatment effect in subjects with nodular lung lesions and/or thick-walled cysts on chest HRCT, with diffuse hypermetabolism of lung lesions on positron emission tomography (PET)-scan, and with progressive disease despite smoking cessation. Infectious pneumonia developed in 1 patient, with later grade 4 neutrocytopenia but without infection.DiscussionData interpretation was limited by the retrospective, uncontrolled study design and small sample size.ConclusionCladribine as a single agent may be effective therapy in patients with progressive PLCH.

Swain: Stata module to correct the SEM chi-square overidentification test in small sample sizes or complex models. Statistical Software Components S457617, Boston College Department of Economics.

Swain corrects the chi-square overidentification test (i.e., likelihood ratio test of fit) for structural equation models whethr with or without latent variables. The chi-square statistic is asymptotically correct; however, it does not behave as expected in small samples and/or when the model is complex (cf. Herzog, Boomsma, & Reinecke, 2007). Thus, particularly in situations where the ratio of sample size (n) to the number of parameters estimated (p) is relatively small (i.e., the p to n ratio is large), the chi-square test will tend to overreject correctly specified models. To obtain a closer approximation to the distribution of the chi-square statistic, Swain (1975) developed a correction; this scaling factor, which converges to 1 asymptotically, is multiplied with the chi-square statistic. The correction better approximates the chi-square distribution resulting in more appropriate Type 1 reject error rates (see Herzog & Boomsma, 2009; Herzog, et al., 2007).

Genes mirror geography within Europe.

Understanding the genetic structure of human populations is of fundamental interest to medical, forensic and anthropological sciences. Advances in high-throughput genotyping technology have markedly improved our understanding of global patterns of human genetic variation and suggest the potential to use large samples to uncover variation among closely spaced populations. Here we characterize genetic variation in a sample of 3,000 European individuals genotyped at over half a million variable DNA sites in the human genome. Despite low average levels of genetic differentiation among Europeans, we find a close correspondence between genetic and geographic distances; indeed, a geographical map of Europe arises naturally as an efficient two-dimensional summary of genetic variation in Europeans. The results emphasize that when mapping the genetic basis of a disease phenotype, spurious associations can arise if genetic structure is not properly accounted for. In addition, the results are relevant to the prospects of genetic ancestry testing; an individual's DNA can be used to infer their geographic origin with surprising accuracy-often to within a few hundred kilometres.

Random measurement error and regression dilution bias.

Summary points: - The bias introduced by random measurement error will be different depending on whether the error is in an exposure variable (risk factor) or outcome variable (disease) - Random measurement error in an exposure variable will bias the estimates of regression slope coefficients towards the null - Random measurement error in an outcome variable will instead increase the standard error of the estimates and widen the corresponding confidence intervals, making results less likely to be statistically significant - Increasing sample size will help minimise the impact of measurement error in an outcome variable but will only make estimates more precisely wrong when the error is in an exposure variable

Gait and foot clearance parameters obtained using shoe-worn inertial sensors in a large-population sample of older adults

In order to distinguish dysfunctional gait; clinicians require a measure of reference gait parameters for each population. This study provided normative values for widely used parameters in more than 1400 able-bodied adults over the age of 65. We also measured the foot clearance parameters (i.e., height of the foot above ground during swing phase) that are crucial to understand the complex relationship between gait and falls as well as obstacle negotiation strategies. We used a shoe-worn inertial sensor on each foot and previously validated algorithms to extract the gait parameters during 20 m walking trials in a corridor at a self-selected pace. We investigated the difference of the gait parameters between male and female participants by considering the effect of age and height factors. Besides; we examined the inter-relation of the clearance parameters with the gait speed. The sample size and breadth of gait parameters provided in this study offer a unique reference resource for the researchers.

Renal transplantation following aorto-iliac reconstruction is a safe a strategy

Introduction: Renal transplantation is considered the treatment of choice for end-stage renal disease. However, the association of occlusive aorto-iliac disease and chronic renal failure is frequent and aorto-iliac reconstruction may be necessary prior to renal transplantation. This retrospective study reviews the results of this operative strategy.Material and Methods: Between January 2001 and June 2010, 309 patients underwent renal transplantation at our institution and 8 patients had prior aorto-iliac reconstruction using prosthetic material. There were 6 men and 2 women with a median age of 62 years (range 51-70). Five aorto-bifemoral and 2 aorto-bi-iliac bypasses were performed for stage II (n=5), stage IV (n=1) and aortic aneurysm (n=1). In one patient, iliac kissing stents and an ilio-femoral bypass were implanted. 4 cadaveric and 4 living donor renal transplantations were performed with an interval of 2 months to 10 years after revascularization.The results were analysed with respect of graft and patients survival. Differences between groups were tested by the log rank method.Results: No complications and no death occurred in the post-operative period. All bypasses remained patent during follow-up. The median time of post transplantation follow-up was 46 months for all patients and 27 months for patients with prior revascularization. In the revascularized group and control group, the graft and patient survival at 1 year were respectively 100%/96%, 100%/99% and at 5 years 86%/86%, 86%/94%, without significant differences between both groups.Discussion: Our results suggest that renal transplantation following prior aorto-iliac revascularisation with prosthetic material is safe and effective. Patients with end-stage renal disease and concomitant aorto-iliac disease should therefore be considered for renal transplantation. However, caution in the interpretation of the results is indicated due to the small sample size of our study.