Confidence interval of difference of proportions in logistic regression in presence of covariates

Comparison of treatment differences in incidence rates is an important objective of many clinical trials. However, often the proportion is affected by covariates, and the adjustment of the predicted proportion is made using logistic regression. It is desirable to estimate the treatment differences in proportions adjusting for the covariates, similarly to the comparison of adjusted means in analysis of variance. Because of the correlation between the point estimates in the different treatment groups, the standard methods for constructing confidence intervals are inadequate. The problem is more difficult in the binary case, as the comparison is not uniquely defined, and the sampling distribution more difficult to analyze. Four procedures for analyzing the data are presented, which expand upon existing methods and generalize the link function. It is shown that, among the four methods studied, the resampling method based on the exact distribution function yields a coverage rate closest to the nominal.

EVALUATING MEAN INTRINSIC CURVATURE OF DISORDERED SEMIFLEXIBLE BIOPOLYMERS

We study two-dimensional disordered semiflexible biopolymers with finite mean intrinsic curvature (MIC). We find exact distribution function of orientational angle for the system with short-range correlation (SRC) in intrinsic curvatures. We show that with a finite MIC, our theoretical end-to-end distances can be fitted well to some experimental data of DNA with long-range correlation (LRC) in sequences. Moreover, we find that the variance of the orientational angle has the same power-law behavior as that of the bending profile for DNA with LRC in sequences. Our results provide a way to evaluate MIC and suggest that the LRC in sequences can result in a SRC in intrinsic curvatures.

DARK MATTER ANNIHILATION IN THE GRAVITATIONAL FIELD OF A BLACK HOLE

In this paper we consider dark matter particle annihilation in the gravitational field of black holes. We obtain the exact distribution function of the infalling dark matter particles, and compute the resulting flux and spectra of gamma rays coming from the objects. It is shown that the dark matter density significantly increases near a black hole. Particle collision energy becomes very high, affecting relative cross-sections of various annihilation channels. We also discuss possible experimental consequences of these effects.

Validation of a New Closure Model for Flow-Induced Alignment of Fibers

A closure model for flow-induced orientation of short fibers is presented and discussed. The model retains all the six-fold symmetry and contraction properties of the fourth order tensor. A derivation of the model is presented and the conditions required for the model to be realizable are discussed. The model is validated against analytical and numerical solutions of the exact distribution function for the fiber orientation state for different flow fields. Variations of this model and its limitations are also discussed.

The Exact Distribution of Moran's I

In analogy to the exact distribution of the Durbin—Watson d statistic for serial autocorrelation of regression residuals, the exact small sample distribution of Moran's I statistic (or alternatively Geary's c) can be derived. Use of algebraic results by Koerts and Abrahamse and theoretical results by Imhof, allows the authors to determine by numerical integration the exact distribution function of Moran's I for normally distributed variables. For the case in which the explanatory variables have been neglected, an upper and a lower bound can be given within which the exact distribution of Moran's I for regression residuals will lie. Furthermore, the proposed methodology is flexible enough to investigate related topics such as the characteristics of the exact distribution for distinct spatial structures as well as their different specifications, the exact power function under different spatial autocorrelation levels, and the distribution of Moran's I for nonnormal random variables.