Sample size estimation: an overview with applications to orthodontic clinical trial designs

Proper sample size estimation is an important part of clinical trial methodology and closely related to the precision and power of the trial's results. Trials with sufficient sample sizes are scientifically and ethically justified and more credible compared with trials with insufficient sizes. Planning clinical trials with inadequate sample sizes might be considered as a waste of time and resources, as well as unethical, since patients might be enrolled in a study in which the expected results will not be trusted and are unlikely to have an impact on clinical practice. Because of the low emphasis of sample size calculation in clinical trials in orthodontics, it is the objective of this article to introduce the orthodontic clinician to the importance and the general principles of sample size calculations for randomized controlled trials to serve as guidance for study designs and as a tool for quality assessment when reviewing published clinical trials in our specialty. Examples of calculations are shown for 2-arm parallel trials applicable to orthodontics. The working examples are analyzed, and the implications of design or inherent complexities in each category are discussed.

A brief update on lung stereology

Lung stereology has a long and successful tradition. From mice to men, the application of new stereological methods at several levels (alveoli, parenchymal cells, organelles, proteins) has led to new insights into normal lung architecture, parenchymal remodelling in emphysema-like pathology, alveolar type II cell hyperplasia and hypertrophy and intracellular surfactant alterations as well as distribution of surfactant proteins. The Euler number of the network of alveolar openings, estimated using physical disectors at the light microscopic level, is an unbiased and direct estimate of alveolar number. Surfactant-producing alveolar type II cells can be counted and sampled for local size estimation with physical disectors at a high magnification light microscopic level. The number of their surfactant storage organelles, lamellar bodies, can be estimated using physical disectors at the EM level. By immunoelectron microscopy, surfactant protein distribution can be analysed with the relative labelling index. Together with the well-established classical stereological methods, these design-based methods now allow for a complete quantitative phenotype analysis in lung development and disease, including the structural characterization of gene-manipulated mice, at the light and electron microscopic level.

Effective population size of an indigenous Swiss cattle breed estimated from linkage disequilibrium

Effective population size is an important parameter for the assessment of genetic diversity within a livestock population and its development over time. If pedigree information is not available, linkage disequilibrium (LD) analysis might offer an alternative perspective for the estimation of effective population size. In this study, 128 individuals of the Swiss Eringer breed were genotyped using the Illumina BovineSNP50 beadchip. We set bin size at 50 kb for LD analysis, assuming that LD for proximal single nucleotide polymorphism (SNP)-pairs reflects distant breeding history while LD from distal SNP-pairs would reflect near history. Recombination rates varied among different regions of the genome. The use of physical distances as an approximation of genetic distances (e.g. setting 1 Mb = 0.01 Morgan) led to an upward bias in LD-based estimates of effective population size for generations beyond 50, while estimates for recent history were unaffected. Correction for restricted sample size did not substantially affect these results. LD-based actual effective population size was estimated in the range of 87-149, whereas pedigree-based effective population size resulted in 321 individuals. For conservation purposes, requiring knowledge of recent history (<50 generations), approximation assuming constant recombination rate seemed adequate.

Long-distance photogrammetric trait estimation in free-ranging animals: A new approach

The acquisition of accurate information on the size of traits in animals is fundamental for the study of animal ecology and evolution and their management. We demonstrate how morphological traits of free-ranging animals can reliably be estimated on very large observation distances of several hundred meters by the use of ordinary digital photographic equipment and simple photogrammetric software. In our study, we estimated the length of horn annuli in free-ranging male Alpine ibex (Capra ibex) by taking already measured horn annuli of conspecifics on the same photographs as scaling units. Comparisons with hand-measured horn annuli lengths and repeatability analyses revealed a high accuracy of the photogrammetric estimates. If length estimations of specific horn annuli are based on multiple photographs measurement errors of <5.5 mm can be expected. In the current study the application of the described photogrammetric procedure increased the sample size of animals with known horn annuli length by an additional 104%. The presented photogrammetric procedure is of broad applicability and represents an easy, robust and cost-efficient method for the measuring of individuals in populations where animals are hard to capture or to approach.

Optimized aperture shapes for depth estimation

The finite depth of field of a real camera can be used to estimate the depth structure of a scene. The distance of an object from the plane in focus determines the defocus blur size. The shape of the blur depends on the shape of the aperture. The blur shape can be designed by masking the main lens aperture. In fact, aperture shapes different from the standard circular aperture give improved accuracy of depth estimation from defocus blur. We introduce an intuitive criterion to design aperture patterns for depth from defocus. The criterion is independent of a specific depth estimation algorithm. We formulate our design criterion by imposing constraints directly in the data domain and optimize the amount of depth information carried by blurred images. Our criterion is a quadratic function of the aperture transmission values. As such, it can be numerically evaluated to estimate optimized aperture patterns quickly. The proposed mask optimization procedure is applicable to different depth estimation scenarios. We use it for depth estimation from two images with different focus settings, for depth estimation from two images with different aperture shapes as well as for depth estimation from a single coded aperture image. In this work we show masks obtained with this new evaluation criterion and test their depth discrimination capability using a state-of-the-art depth estimation algorithm.