Varying coefficient frailty models with applications in single molecular experiments.

Motivated by an analysis of single molecular experiments in the study of T-cell signaling, a new model called varying coefficient frailty model with local linear estimation is proposed. Frailty models have been extensively studied, but extensions to nonconstant coefficients are limited to spline-based methods that tend to produce estimation bias near the boundary. To address this problem, we introduce a local polynomial kernel smoothing technique with a modified expectation-maximization algorithm to estimate the unknown parameters. Theoretical properties of the estimators, including their unbiased property near the boundary, are derived along with discussions on the asymptotic bias-variance trade-off. The finite sample performance is examined by simulation studies, and comparisons with existing spline-based approaches are conducted to show the potential advantages of the proposed approach. The proposed method is implemented for the analysis of T-cell signaling. The fitted varying coefficient model provides a rigorous quantification of an early and rapid impact on T-cell signaling from the accumulation of bond lifetime, which can shed new light on the fundamental understanding of how T cells initiate immune responses.

Optimizing and Improving the Growth Quality of ZnO Nanowire Arrays Guided by Statistical Design of Experiments.

Controlling the morphology of the as-synthesized nanostructures is usually challenging, and there lacks of a general theoretical guidance in experimental approach. In this study, a novel way of optimizing the aspect ratio of hydrothermally grown ZnO nanowire (NW) arrays is presented by utilizing a systematic statistical design and analysis method. In this work, we use pick-the-winner rule and one-pair-at-a-time main effect analysis to sequentially design the experiments and identify optimal reaction settings. By controlling the hydrothermal reaction parameters (reaction temperature, time, precursor concentration, and capping agent), we improved the aspect ratio of ZnO NWs from around 10 to nearly 23. The effect of noise on the experimental results was identified and successfully reduced, and the statistical design and analysis methods were very effective in reducing the number of experiments performed and in identifying the optimal experimental settings. In addition, the antireflection spectrum of the as-synthesized ZnO NWs clearly shows that higher aspect ratio of the ZnO NW arrays leads to about 30% stronger suppression in the UV-vis range emission. This shows great potential applications as antireflective coating layers in photovoltaic devices.

Statistical approach to quantifying the elastic deformation of nanomaterials.

Quantifying the mechanical properties of nanomaterials is challenged by its small size, difficulty of manipulation, lack of reliable measurement techniques, and grossly varying measurement conditions and environment. A recently proposed approach is to estimate the elastic modulus from a force-deflection physical model based on the continuous bridged-deformation of a nanobelt/nanowire using an atomic force microscope tip under different contact forces. However, the nanobelt may have some initial bending, surface roughness and imperfect physical boundary conditions during measurement, leading to large systematic errors and uncertainty in data quantification. In this article, a statistical modeling technique, sequential profile adjustment by regression (SPAR), is proposed to account for and eliminate the various experimental errors and artifacts. SPAR can automatically detect and remove the systematic errors and therefore gives more precise estimation of the elastic modulus. This research presents an innovative approach that can potentially have a broad impact in quantitative nanomechanics and nanoelectronics.

Binary Time Series Modeling with Application to Adhesion Frequency Experiments.

Repeated adhesion frequency assay is the only published method for measuring the kinetic rates of cell adhesion. Cell adhesion plays an important role in many physiological and pathological processes. Traditional analysis of adhesion frequency experiments assumes that the adhesion test cycles are independent Bernoulli trials. This assumption can often be violated in practice. Motivated by the analysis of repeated adhesion tests, a binary time series model incorporating random effects is developed in this paper. A goodness-of-fit statistic is introduced to assess the adequacy of distribution assumptions on the dependent binary data with random effects. The asymptotic distribution of the goodness-of-fit statistic is derived and its finite-sample performance is examined via a simulation study. Application of the proposed methodology to real data from a T-cell experiment reveals some interesting information, including the dependency between repeated adhesion tests.

Identifying promising compounds in drug discovery: genetic algorithms and some new statistical techniques.

Throughout the drug discovery process, discovery teams are compelled to use statistics for making decisions using data from a variety of inputs. For instance, teams are asked to prioritize compounds for subsequent stages of the drug discovery process, given results from multiple screens. To assist in the prioritization process, we propose a desirability function to account for a priori scientific knowledge; compounds can then be prioritized based on their desirability scores. In addition to identifying existing desirable compounds, teams often use prior knowledge to suggest new, potentially promising compounds to be created in the laboratory. Because the chemistry space to search can be dauntingly large, we propose the sequential elimination of level combinations (SELC) method for identifying new optimal compounds. We illustrate this method on a combinatorial chemistry example.

A smooth response surface algorithm for constructing a gene regulatory network.

A smooth response surface (SRS) algorithm is developed as an elaborate data mining technique for analyzing gene expression data and constructing a gene regulatory network. A three-dimensional SRS is generated to capture the biological relationship between the target and activator-repressor. This new technique is applied to functionally describe triplets of activators, repressors, and targets, and their regulations in gene expression data. A diagnostic strategy is built into the algorithm to evaluate the scores of the triplets so that those with low scores are kept and a regulatory network is constructed based on this information and existing biological knowledge. The predictions based on the identified triplets in two yeast gene expression data sets agree with some experimental data in the literature. It provides a novel model with attractive mathematical and statistical features that make the algorithm valuable for mining expression or concentration information, assist in determining the function of uncharacterized proteins, and can lead to a better understanding of coherent pathways.