ANALYSIS OF NUCLEI FLUORESCENCE HISTOGRAMS USING NON-LINEAR FUNCTIONS OR WAVELETS

Histograms based on 5,000 nuclei from cells (Chinese hamster ovary cells, bone marrow cells) are used to determine the coefficient of variation (CV) of observations surrounding the highest peak. The cells are subjected to various treatments, for example exposure to herbicides. By eyeballing the histogram, an interval under the highest peak is determined. The CV calculated from the histogram on the eyeballed interval is the response variable in an ANOVA. To avoid the subjectivity of eyeballing the histogram, non-linear functions such as the Gaussian density function can be used to model the histogram. The CV may then be determined from the parameter estimates. In many experiments nonlinear functions modeling the histograms smooth away differences in CV s obtained this way, though visually the histograms appear to be different. Then nonlinear functions or wavelets can be used to obtain intervals for calculating CV s of the histograms restricted to these intervals. The nonlinear models require close initial values for each histogram, while the wavelets just require choice of wavelet and level of decomposition

Extensions of Markov Chain Marginal Bootstrap

92 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2003.The Markov chain marginal bootstrap (MCMB) is a new bootstrap method proposed by He and Hu (2002) for constructing confidence intervals or regions based on likelihood equations. It is designed to ease the computational burden of bootstrap in high-dimensional problems. It differs from the usual bootstrap methods in two aspects: a set of p one-dimensional equations is solved in place of a p-dimensional system of equations for each bootstrap estimate of the parameter; the resulting estimates form a Markov chain rather than an independent sequence of realizations. This thesis proposes two modifications to extend the use of MCMB to more general models and estimators. The first modification is a transformation of the parameter space, which reduces high autocorrelation of the resulting MCMB chains, and improves on the efficiency and stability of the procedure. The second is a transformation of the estimating equations, which extends the use of MCMB beyond the likelihood-based estimators. Through examples and Monte Carlo simulations, the transformations proposed in this thesis are shown to be valuable and sometimes necessary for successful applications of MCMB to linear and nonlinear models.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD

Choice and Interpretation of Statistical Tests Used When Competing Risks Are Present

In clinical cancer research, competing risks are frequently encountered. For example, individuals undergoing treatment for surgically resectable disease may experience recurrence near the removed tumor, metastatic recurrence at other sites, occurrence of second primary cancer, or death resulting from noncancer causes before any of these events. Two quantities, the cause-specific hazard function and the cumulative incidence function, are commonly used to summarize outcomes by event type. Tests for event-specific differences between treatment groups may thus be based on comparison of (a) cause-specific hazards via a log-rank or related test, or (b) the cumulative incidence functions via one of several available tests. Inferential results for tests based on these different metrics can differ considerably for the same cause-specific end point. Depending on the questions of principal interest, one or both metrics may be appropriate to consider. We present simulation study results and discuss examples from cancer clinical trials to illustrate these points and provide guidance for analysis when competing risks are present