A two-stage strategy to accommodate general patterns of confounding in the design of observational studies

Accommodating general patterns of confounding in sample size/power calculations for observational studies is extremely challenging, both technically and scientifically. While employing previously implemented sample size/power tools is appealing, they typically ignore important aspects of the design/data structure. In this paper, we show that sample size/power calculations that ignore confounding can be much more unreliable than is conventionally thought; using real data from the US state of North Carolina, naive calculations yield sample size estimates that are half those obtained when confounding is appropriately acknowledged. Unfortunately, eliciting realistic design parameters for confounding mechanisms is difficult. To overcome this, we propose a novel two-stage strategy for observational study design that can accommodate arbitrary patterns of confounding. At the first stage, researchers establish bounds for power that facilitate the decision of whether or not to initiate the study. At the second stage, internal pilot data are used to estimate key scientific inputs that can be used to obtain realistic sample size/power. Our results indicate that the strategy is effective at replicating gold standard calculations based on knowing the true confounding mechanism. Finally, we show that consideration of the nature of confounding is a crucial aspect of the elicitation process; depending on whether the confounder is positively or negatively associated with the exposure of interest and outcome, naive power calculations can either under or overestimate the required sample size. Throughout, simulation is advocated as the only general means to obtain realistic estimates of statistical power; we describe, and provide in an R package, a simple algorithm for estimating power for a case-control study.     

Sample size determination

Scientists who use animals in research must justify the number of animals to be used, and committees that review proposals to use animals in research must review this justification to ensure the appropriateness of the number of animals to be used. This article discusses when the number of animals to be used can best be estimated from previous experience and when a simple power and sample size calculation should be performed. Even complicated experimental designs requiring sophisticated statistical models for analysis can usually be simplified to a single key or critical question so that simple formulae can be used to estimate the required sample size. Approaches to sample size estimation for various types of hypotheses are described, and equations are provided in the Appendix. Several web sites are cited for more information and for performing actual calculations     

Effects of grain size and niche breadth on species distribution modeling

Scale is a vital component to consider in ecological research, and spatial resolution or grain size is one of its key facets. Species distribution models (SDMs) are prime examples of ecological research in which grain size is an important component. Despite this, SDMs rarely explicitly examine the effects of varying the grain size of the predictors for species with different niche breadths. To investigate the effect of grain size and niche breadth on SDMs, we simulated four virtual species with different grain sizes/niche breadths using three environmental predictors (elevation, aspect, and percent forest) across two real landscapes of differing heterogeneity in predictor values. We aggregated these predictors to seven different grain sizes and modeled the distribution of each of our simulated species using MaxEnt and GLM techniques at each grain size. We examined model accuracy using the AUC statistic, Pearson's correlations of predicted suitability with the true suitability, and the binary area of presence determined from suitability above the maximum true skill statistic (TSS) threshold. Habitat specialists were more accurately modeled than generalist species, and the models constructed at the grain size from which a species was derived generally performed the best. The accuracy of models in the homogenous landscape deteriorated with increasing grain size to a greater degree than models in the heterogenous landscape. Variable effects on the model varied with grain size, with elevation increasing in importance as grain size increased while aspect lost importance. The area of predicted presence was drastically affected by grain size, with larger grain sizes over predicting this value by up to a factor of 14. Our results have implications for species distribution modeling and conservation planning, and we suggest more studies include analysis of grain size as part of their protocol.     

暴露评估中样本采集量的模拟研究

选择暴露评估常用的4种右偏分布,就评估关注的高百分位数估计与采样量的关系进行模拟研究;又以对数正态分布为代表,从分布形态和变异的角度做了细致探讨.结果表明：（1）对右偏分布来说,百分位数越高,准确估计所需的采样容量就越大.而其估计值都随采样量的增大而趋近理论值,精度也随之增大,采样量500时,本文考察的4种右偏分布除P99.9外的其它百分位数都得到了较为准确的估计.（2）估计相同的百分位数,对数正态分布所需的样本容量要比正态分布大得多;而其分布变异越大,所需的采样量也就越大.本研究可为暴露评估中数据的采样调查提供借鉴.     

Polymorphism and size-pairing in the harvester antPogonomyrmex badius: a test of the ecological release hypothesis

Summary The role of caste polymorphism in the foraging strategy ofPogonomyrmex badius was studied in the field by measuring food items collected by foragers, and correlating food item size variables with forager size variables. The diet ofP. badius included seeds and insects. In two colonies examined, these food types comprised different proportions of the diet sample.Although some forager size variables showed close or significant correlations with food item size variables, we could identify no overall significant relationship between worker size and seed or prey size. Polymorphism inP. badius may be associated with omnivory. However, since minor workers serve as foragers and represent a portion of the total worker size variation, dietary expansion through caste proliferation appears to be only one aspect of the functional significance of polymorphism in this species.     

An efficient sample size adaptation strategy with adjustment of randomization ratio

In clinical trials, sample size reestimation is a useful strategy for mitigating the risk of uncertainty in design assumptions and ensuring sufficient power for the final analysis. In particular, sample size reestimation based on unblinded interim effect size can often lead to sample size increase, and statistical adjustment is usually needed for the final analysis to ensure that type I error rate is appropriately controlled. In current literature, sample size reestimation and corresponding type I error control are discussed in the context of maintaining the original randomization ratio across treatment groups, which we refer to as “proportional increase.” In practice, not all studies are designed based on an optimal randomization ratio due to practical reasons. In such cases, when sample size is to be increased, it is more efficient to allocate the additional subjects such that the randomization ratio is brought closer to an optimal ratio. In this research, we propose an adaptive randomization ratio change when sample size increase is warranted. We refer to this strategy as “nonproportional increase,” as the number of subjects increased in each treatment group is no longer proportional to the original randomization ratio. The proposed method boosts power not only through the increase of the sample size, but also via efficient allocation of the additional subjects. The control of type I error rate is shown analytically. Simulations are performed to illustrate the theoretical results.     

Towards an optimal sampling strategy for assessing genetic variation within and among white clover (Trifolium repens L.) cultivars using AFLP

Cost reduction in plant breeding and conservation programs depends largely on correctly defining the minimal sample size required for the trustworthy assessment of intra- and inter-cultivar genetic variation. White clover, an important pasture legume, was chosen for studying this aspect. In clonal plants, such as the aforementioned, an appropriate sampling scheme eliminates the redundant analysis of identical genotypes. The aim was to define an optimal sampling strategy, i.e., the minimum sample size and appropriate sampling scheme for white clover cultivars, by using AFLP data (283 loci) from three popular types. A grid-based sampling scheme, with an interplant distance of at least 40 cm, was sufficient to avoid any excess in replicates. Simulations revealed that the number of samples substantially influenced genetic diversity parameters. When using less than 15 per cultivar, the expected heterozygosity (He) and Shannon diversity index (I) were greatly underestimated, whereas with 20, more than 95% of total intra-cultivar genetic variation was covered. Based on AMOVA, a 20-cultivar sample was apparently sufficient to accurately quantify individual genetic structuring. The recommended sampling strategy facilitates the efficient characterization of diversity in white clover, for both conservation and exploitation.     

Oligoelements and isotopic geochemistry: a multidisciplinary approach to the reconstruction of the paleodiet

Man's biological evolution, state of health and lifestyle are closely associated with dietary changes. The methods for acquiring useful information on the diet of our ancestors are an important aspect of anthropological research; hence it was retained interesting to apply the oligoelement and isotopic techniques in parallel on the same sample, in order to compare the two methodologies, construct a complete nutritional picture, and compare the analytical results with the ancient literary sources and with the findings from archaeological excavations.     

The size distribution of protein families within different types of folds

It is well known that the structure is currently available only for a small fraction of known protein sequences. It is urgent to discover the important features of known protein sequences based on present protein structures. Here, we report a study on the size distribution of protein families within different types of folds. The fold of a protein means the global arrangement of its main secondary structures, both in terms of their relative orientations and their topological connections, which specify a certain biochemical and biophysical aspect. We first search protein families in the structural database SCOP against the sequence-based database Pfam, and acquire a pool of corresponding Pfam families whose structures can be deemed as known. This pool of Pfam families is called the sample space for short. Then the size distributions of protein families involving the sample space, the Pfam database and the SCOP database are obtained. The results indicate that the size distributions of protein families under different kinds of folds abide by similar power-law. Specially, the largest families scatter evenly in different kinds of folds. This may help better understand the relationship of protein sequence, structure and function. We also show that the total of proteins with known structures can be considered a random sample from the whole space of protein sequences, which is an essential but unsettled assumption for related predictions, such as, estimating the number of protein folds in nature. Finally we conclude that about 2957 folds are needed to cover the total Pfam families by a simple method.     

Reexamining Sample Size Requirements for Multivariate,Abundance-Based Community Research: When Resources are Limited,the Research Does Not Have to Be

Community ecologists commonly perform multivariate techniques (e.g., ordination, cluster analysis) to assess patterns and gradients of taxonomic variation. A critical requirement for a meaningful statistical analysis is accurate information on the taxa found within an ecological sample. However, oversampling (too many individuals counted per sample) also comes at a cost, particularly for ecological systems in which identification and quantification is substantially more resource consuming than the field expedition itself. In such systems, an increasingly larger sample size will eventually result in diminishing returns in improving any pattern or gradient revealed by the data, but will also lead to continually increasing costs. Here, we examine 396 datasets: 44 previously published and 352 created datasets. Using meta-analytic and simulation-based approaches, the research within the present paper seeks (1) to determine minimal sample sizes required to produce robust multivariate statistical results when conducting abundance-based, community ecology research. Furthermore, we seek (2) to determine the dataset parameters (i.e., evenness, number of taxa, number of samples) that require larger sample sizes, regardless of resource availability. We found that in the 44 previously published and the 220 created datasets with randomly chosen abundances, a conservative estimate of a sample size of 58 produced the same multivariate results as all larger sample sizes. However, this minimal number varies as a function of evenness, where increased evenness resulted in increased minimal sample sizes. Sample sizes as small as 58 individuals are sufficient for a broad range of multivariate abundance-based research. In cases when resource availability is the limiting factor for conducting a project (e.g., small university, time to conduct the research project), statistically viable results can still be obtained with less of an investment.     

Obstetric dimensions of the true pelvis in a medieval population from Sudanese Nubia.

Functional analysis of the true pelvis (defined as that portion lying below and including the pelvic brim) was undertaken on a sample of 36 females from the Medieval site of Kulubnarti in Sudanese Nubia. Standard obstetric measurements were taken and compared to four additional prehistoric skeletal samples and to modern American standards for the same obstetric dimensions. Relative to the other prehistoric populations, the Kulubnarti pelves are smaller in most dimensions and, when compared to modern American standards, from one-third to one-half would be diagnosed as contracted in one or more planes. Given the meager, fluctuating resources of these Medieval Nubians' harsh desert environment, pelvic size reduction is a likely result of body size reduction as one biological response to nutritional stress (Mittler and Van Gerven, 1989; Moore et al., 1986; Van Gerven et al., 1981). It is argued, however, that size reduction created a high potential for either maternal-neonatal morbidity and mortality due to fetopelvic disproportion or neonatal loss due to low birth weight. In either case, it is suggested that the Kulubnarti population paid a significant biological price for this aspect of size reduction.     

太白红杉径向生长的预测模型

采用多元回归的方法构建了太白红杉的生长模型,模型中主要考虑了植株自身大小(胸径和冠幅比)、竞争状况和立地因子(海拔、坡度和坡向)三类因子的作用。结果发现,太白红杉近2年生长量与植株自身大小、竞争状况和海拔因子有较高的相关性;坡度、坡向与生长量的相关性较小,但其综合作用在一定程度上影响着太白红杉的生长。所构建的生长模型充分考虑了太白红杉自身的生物学特性,具有较高的回归优度(r=0.938,P<0.001),能很好地预测其生长动态。     

Pore-Scale Modeling of Pore Structure Effects on P-Wave Scattering Attenuation in Dry Rocks

Underground rocks usually have complex pore system with a variety of pore types and a wide range of pore size. The effects of pore structure on elastic wave attenuation cannot be neglected. We investigated the pore structure effects on P-wave scattering attenuation in dry rocks by pore-scale modeling based on the wave theory and the similarity principle. Our modeling results indicate that pore size, pore shape (such as aspect ratio), and pore density are important factors influencing P-wave scattering attenuation in porous rocks, and can explain the variation of scattering attenuation at the same porosity. From the perspective of scattering attenuation, porous rocks can safely suit to the long wavelength assumption when the ratio of wavelength to pore size is larger than 15. Under the long wavelength condition, the scattering attenuation coefficient increases as a power function as the pore density increases, and it increases exponentially with the increase in aspect ratio. For a certain porosity, rocks with smaller aspect ratio and/or larger pore size have stronger scattering attenuation. When the pore aspect ratio is larger than 0.5, the variation of scattering attenuation at the same porosity is dominantly caused by pore size and almost independent of the pore aspect ratio. These results lay a foundation for pore structure inversion from elastic wave responses in porous rocks.     

Publication Bias in Psychology: A Diagnosis Based on the Correlation between Effect Size and Sample Size

Background

The p value obtained from a significance test provides no information about the magnitude or importance of the underlying phenomenon. Therefore, additional reporting of effect size is often recommended. Effect sizes are theoretically independent from sample size. Yet this may not hold true empirically: non-independence could indicate publication bias.

Methods

We investigate whether effect size is independent from sample size in psychological research. We randomly sampled 1,000 psychological articles from all areas of psychological research. We extracted p values, effect sizes, and sample sizes of all empirical papers, and calculated the correlation between effect size and sample size, and investigated the distribution of p values.

Results

We found a negative correlation of r = −.45 [95% CI: −.53; −.35] between effect size and sample size. In addition, we found an inordinately high number of p values just passing the boundary of significance. Additional data showed that neither implicit nor explicit power analysis could account for this pattern of findings.

Conclusion

The negative correlation between effect size and samples size, and the biased distribution of p values indicate pervasive publication bias in the entire field of psychology.     

An instrument for sorting of magnetic microparticles in a magnetic field gradient.

BACKGROUND: The goal of our bioassay technique is to demonstrate high throughput, highly parallel, and high sensitivity quantitative molecular analysis that will expand current biomedical research capabilities. To this end, we have built and characterized a magnetophoresis instrument using a flow chamber in a magnetic field gradient to sort magnetic microparticles by their magnetic moment for eventual use as biological labels. METHODS: The flow chamber consists of a sample inlet, differential sheath streams, and eight outlets for collecting the microparticles after they have traversed the chamber. Magnetic microparticles are injected into the flow chamber that is positioned in a linear magnetic field gradient. The trajectory for each microparticle is determined by its total magnetic moment and size. The resulting populations of monodispersed magnetic microparticles in the different outlet bins are sorted by their magnetic moment; with the highest magnetic moments being deflected the furthest. RESULTS: We have characterized the system for sorting both superparamagnetic and ferromagnetic microparticles with approximate diameters of 8 microm and 4.0-4.9 microm, respectively. To characterize the instrument, we used microparticles with a known size distribution and varied the transit time through the chamber. This is equivalent to varying the magnetic moment, while allowing us to hold the particle properties constant from run-to-run. We demonstrated the ability to reproducibly change the distribution of the particles in the collection bins by varying transit time in good agreement with theory. We identified hydrodynamic instabilities responsible for causing dispersion in the flow. Improvements to the flow chamber hydrodynamics such as reducing the aspect ratio between the sample inlet and the chamber depth and stabilizing the sheath flow resulted in narrow sorting distributions. We measured a sorting reproducibility (percentage of particles returning to their original bin upon resorting individual populations) of 84-89%. CONCLUSIONS: We have developed a simple magnetophoresis system for reproducibly sorting magnetic microparticles. This technique will permit the use of microparticles with a wide range of magnetic moments to create a wide range of magnetic labels. Careful consideration of system design and operational parameters enables reliable and reproducible sorting of microparticles with varying size and magnetic content.     

Paired versus two-group experimental design for rheological studies of vocal fold tissues

Vibratory function of the vocal folds is largely determined by the rheological properties or viscoelastic shear properties of the vocal fold lamina propria. To date, investigation of the sample size estimation and statistical experimental design for vocal fold rheological studies is nonexistent. The current work provides the closed-form sample size formulas for two major study designs (i.e. paired and two-group designs) in vocal fold research. Our results demonstrated that the paired design could greatly increase the statistical power compared to the two-group design. By comparing the variance of estimated treatment effect, this study also confirms that ignoring within-subject and within-vocal fold correlations during rheological data analysis will likely increase type I errors. Finally, viscoelastic shear properties of intact and scarred rabbit vocal fold lamina propria were measured and used to illustrate theoretical findings in a realistic scenario and project sample size requirement for future studies.     

How much confidence do we need in animal experiments? Statistical assumptions in sample size estimation

Statistical sample size calculation is a crucial part of planning nonhuman animal experiments in basic medical research. The 3R principle intends to reduce the number of animals to a sufficient minimum. When planning experiments, one may consider the impact of less rigorous assumptions during sample size determination as it might result in a considerable reduction in the number of required animals. Sample size calculations conducted for 111 biometrical reports were repeated. The original effect size assumptions remained unchanged, but the basic properties (type 1 error 5%, two-sided hypothesis, 80% power) were varied. The analyses showed that a less rigorous assumption on the type 1 error level (one-sided 5% instead of two-sided 5%) was associated with a savings potential of 14% regarding the original number of required animals. Animal experiments are predominantly exploratory studies. In light of the demonstrated potential reduction in the numbers of required animals, researchers should discuss whether less rigorous assumptions during the process of sample size calculation may be reasonable for the purpose of optimizing the number of animals in experiments according to the 3R principle.     

Territory tenure in song sparrows is related to song sharing with neighbours, but not to repertoire size

Song repertoires may be a product of sexual selection and several studies have reported correlations of repertoire size and reproductive success in male songbirds. This hypothesis and the reported correlations, however, are not sufficient to explain the observation that most species have small song repertoire sizes (usually fewer than 10, often fewer than five song types). We examined a second important aspect of a male's song repertoire, the extent to which he shares songs with his neighbours. Song sharing has not been measured in previous studies and it may be partially confounded with repertoire size. We hypothesized that in song sparrows, Melospiza melodia, song sharing rather than repertoire size per se is crucial for male territorial success. Our longitudinal study of 45 song sparrows followed from their first year on territory showed that the number of songs a bird shares with his neighbourhood group is a better predictor of lifetime territory tenure than is his repertoire size. We also found that song sharing increases with repertoire size up to but not beyond eight to nine song types, which are the most common repertoire sizes in the population (range in our sample 5-13). This partial confound of song sharing and repertoire size may account for some earlier findings of territory tenure-repertoire size correlations in this species and other species having small- or medium-sized repertoires. Copyright 2000 The Association for the Study of Animal Behaviour.