Differentiating gold nanorod samples using particle size and shape distributions from transmission electron microscope images.

Size and shape distributions of gold nanorod samples are critical to their physico-chemical properties, especially their longitudinal surface plasmon resonance. This interlaboratory comparison study developed methods for measuring and evaluating size and shape distributions for gold nanorod samples using transmission electron microscopy (TEM) images. The objective was to determine whether two different samples, which had different performance attributes in their application, were different with respect to their size and/or shape descriptor distributions. Touching particles in the captured images were identified using a ruggedness shape descriptor. Nanorods could be distinguished from nanocubes using an elongational shape descriptor. A non-parametric statistical test showed that cumulative distributions of an elongational shape descriptor, that is, the aspect ratio, were statistically different between the two samples for all laboratories. While the scale parameters of size and shape distributions were similar for both samples, the width parameters of size and shape distributions were statistically different. This protocol fulfills an important need for a standardized approach to measure gold nanorod size and shape distributions for applications in which quantitative measurements and comparisons are important. Furthermore, the validated protocol workflow can be automated, thus providing consistent and rapid measurements of nanorod size and shape distributions for researchers, regulatory agencies, and industry.

On the analysis of very small samples of Gaussian repeated measurements: an alternative approach.

The analysis of very small samples of Gaussian repeated measurements can be challenging. First, due to a very small number of independent subjects contributing outcomes over time, statistical power can be quite small. Second, nuisance covariance parameters must be appropriately accounted for in the analysis in order to maintain the nominal test size. However, available statistical strategies that ensure valid statistical inference may lack power, whereas more powerful methods may have the potential for inflated test sizes. Therefore, we explore an alternative approach to the analysis of very small samples of Gaussian repeated measurements, with the goal of maintaining valid inference while also improving statistical power relative to other valid methods. This approach uses generalized estimating equations with a bias-corrected empirical covariance matrix that accounts for all small-sample aspects of nuisance correlation parameter estimation in order to maintain valid inference. Furthermore, the approach utilizes correlation selection strategies with the goal of choosing the working structure that will result in the greatest power. In our study, we show that when accurate modeling of the nuisance correlation structure impacts the efficiency of regression parameter estimation, this method can improve power relative to existing methods that yield valid inference. Copyright © 2017 John Wiley & Sons, Ltd.

Improving power in small-sample longitudinal studies when using generalized estimating equations.

Generalized estimating equations (GEE) are often used for the marginal analysis of longitudinal data. Although much work has been performed to improve the validity of GEE for the analysis of data arising from small-sample studies, little attention has been given to power in such settings. Therefore, we propose a valid GEE approach to improve power in small-sample longitudinal study settings in which the temporal spacing of outcomes is the same for each subject. Specifically, we use a modified empirical sandwich covariance matrix estimator within correlation structure selection criteria and test statistics. Use of this estimator can improve the accuracy of selection criteria and increase the degrees of freedom to be used for inference. The resulting impacts on power are demonstrated via a simulation study and application example. Copyright © 2016 John Wiley & Sons, Ltd.

A Comparison of Correlation Structure Selection Penalties for Generalized Estimating Equations.

Correlated data are commonly analyzed using models constructed using population-averaged generalized estimating equations (GEEs). The specification of a population-averaged GEE model includes selection of a structure describing the correlation of repeated measures. Accurate specification of this structure can improve efficiency, whereas the finite-sample estimation of nuisance correlation parameters can inflate the variances of regression parameter estimates. Therefore, correlation structure selection criteria should penalize, or account for, correlation parameter estimation. In this manuscript, we compare recently proposed penalties in terms of their impacts on correlation structure selection and regression parameter estimation, and give practical considerations for data analysts.

Size and shape distributions of primary crystallites in titania aggregates.

The primary crystallite size of titania powder relates to its properties in a number of applications. Transmission electron microscopy was used in this interlaboratory comparison (ILC) to measure primary crystallite size and shape distributions for a commercial aggregated titania powder. Data of four size descriptors and two shape descriptors were evaluated across nine laboratories. Data repeatability and reproducibility was evaluated by analysis of variance. One-third of the laboratory pairs had similar size descriptor data, but 83% of the pairs had similar aspect ratio data. Scale descriptor distributions were generally unimodal and were well-described by lognormal reference models. Shape descriptor distributions were multi-modal but data visualization plots demonstrated that the Weibull distribution was preferred to the normal distribution. For the equivalent circular diameter size descriptor, measurement uncertainties of the lognormal distribution scale and width parameters were 9.5% and 22%, respectively. For the aspect ratio shape descriptor, the measurement uncertainties of the Weibull distribution scale and width parameters were 7.0% and 26%, respectively. Both measurement uncertainty estimates and data visualizations should be used to analyze size and shape distributions of particles on the nanoscale.