Masticophis taeniatus

Number of Pages: 6Integrative BiologyGeological Science

Comparisons Between the Kaplan-Meier Complement and the Cumulative Incidence for Survival Prediction in the Presence of Competing Events

Estimating cumulative event probabilities in time-to-event data can be complicated by competing events. Competing events occur when individuals can experience events other than the primary event of interest. These “other events” are often treated as censored observations. This thesis compares point estimates and relative differences between two cumulative event probability estimators, the Kaplan-Meier complement (KMC) and the cumulative incidence (CI), in the presence of competing events. The KMC does not allow for the possibility of experiencing competing events, whereas the CI does. Consequently, the KMC overestimates the CI in the presence of competing events. In this thesis, data were simulated with different combinations of primary event hazards, competing event hazards, random censoring hazards, and sample sizes. Cumulative event probabilities using the KMC and CI methods were calculated over a time period of 10 years. Several conclusions were drawn. High primary event hazards resulted in high KMC’s and CI’s and slightly narrowed the variability of the relative differences between the two estimates. High competing event hazards did not affect KMC’s but resulted in low CI’s, causing high relative differences. High random censoring hazards did not affect KMC’s, CI’s, or relative differences. Large sample sizes did not affect the median relative differences but did narrow the variability of the relative differences. The public health relevance of this thesis is to help medical clinicians and researchers understand the advantages and disadvantages of different approaches of calculating cumulative event probabilities in situations where competing events occur. This is particularly important in the area of personalized medicine in diseases like cancer where clinicians attempt to predict their patients' mortality or recurrence probabilities over time given certain clinical, pathologic, or demographic characteristics

The equivariant K-theory of isotropy actions

We compute the equivariant K-theory with integer coefficients of an equivariantly formal isotropy action, subject to natural hypotheses which cover the three major classes of known examples. The proof proceeds by constructing a map of spectral sequences from Hodgkin's K\"unneth spectral sequence in equivariant K-theory to that in Borel cohomology. A new characterization of equivariant formality appears as a consequence of this construction, and we are now able to show that weak equivariant formality in the sense of Harada--Landweber is equivalent with integer coefficients to surjectivity of the forgetful map under a standard hypothesis. The main structure theorem is formally similar to that for Borel equivariant cohomology, which appears in the author's dissertation/dormant book project and whose proof is finally made accessible in an appendix. The most generally applicable corollary of the main theorem for rational coefficients depends on a strengthening of the characterization of equivariant formality due to Shiga and Takahashi, which appears as a second appendix.Comment: 22 pages. Comments extremely welcome

Masticophis bilineatus

Number of Pages: 4Integrative BiologyGeological Science

Rule 10b-5 and the Corporation’s Affirmative Duty to Disclose

In order to make responsible investment decisions investors must be adequately informed. In this article Professor Bauman argues that the existing disclosure requirements of the federal securities laws do not meet the informational needs of investors because there is no affirmative duty to disclose all material information. In order to fill this substantial gap in the existing disclosure scheme, Professor Bauman argues that rule lob-5 should be read to require prompt disclosure of all material information subject only to limited exceptions and should be applicable even in the absence of trading or prior inaccurate disclosure

Equivariant formality of isotropic torus actions

Considering the potential equivariant formality of the left action of a connected Lie group $K$ on the homogeneous space $G/K$, we arrive through a sequence of reductions at the case $G$ is compact and simply-connected and $K$ is a torus. We then classify all pairs $(G,S)$ such that $G$ is compact connected Lie and the embedded circular subgroup $S$ acts equivariantly formally on $G/S$. In the process we provide what seems to be the first published proof of the structure (known to Leray and Koszul) of the cohomology rings $H^*(G/S;\mathbb Q)$.Comment: Completely revised. Many proofs simplified, including reduction to toral isotropy and classification of reflected circles. An error in the reduction to the semisimple case is corrected. New: a reduction to the compact case; partial reductions if the groups are disconnected or compact but not Lie. Citations to literature improved. To be published in the Journal of Homotopy and Related Structure

Smoothing-inspired lack-of-fit tests based on ranks

A rank-based test of the null hypothesis that a regressor has no effect on a response variable is proposed and analyzed. This test is identical in structure to the order selection test but with the raw data replaced by ranks. The test is nonparametric in that it is consistent against virtually any smooth alternative, and is completely distribution free for all sample sizes. The asymptotic distribution of the rank-based order selection statistic is obtained and seen to be the same as that of its raw data counterpart. Exact small sample critical values of the test statistic are provided as well. It is shown that the Pitman-Noether efficiency of the proposed rank test compares very favorably with that of the order selection test. In fact, their asymptotic relative efficiency is identical to that of the Wilcoxon signed rank and $t$-tests. An example involving microarray data illustrates the usefulness of the rank test in practice.Comment: Published in at http://dx.doi.org/10.1214/193940307000000103 the IMS Collections (http://www.imstat.org/publications/imscollections.htm) by the Institute of Mathematical Statistics (http://www.imstat.org