Pseudo Observations in Multi-State Models and CUSUM Charts for Monitoring Outcomes of Multi-Center Studies.

This dissertation looks at two different problems essentially. In recent years, pseudo observations have found application in multi-state survival models, models for mean lifetime and competing risks to name a few. We have investigated the performance of estimates and confidence intervals based on pseudo observations in the context of a multi-state model with independent right censoring. This has been compared to estimates from a Cox proportional hazards model with confidence intervals obtained from the bootstrap. While simulations show that the bootstrap is doing well, it becomes evident from simulations and some theory that the pseudo observations method presents difficulty with implementation and may lead to inconsistent estimates, particularly with covariate-dependent censoring. The cumulative sum (CUSUM) procedure has been used for quite some time as a graphical sequential monitoring scheme for detecting small persistent shifts in the mean of observations generated from a manufacturing process. In recent years, it has also found application in the medical literature in the context of monitoring performances of participating centers for quality improvement in a multi-center study involving an ongoing intervention. In this dissertation, we develop and implement risk-adjusted CUSUM charts defined as a process in continuous time when the reports of outcomes are immediate as well as when there is a random delay or lag involved. Approximate theoretical results on the Average Run Length (ARL) of the CUSUM are also provided. A discussion on how to choose a control limit for the CUSUM and some relevant issues that come into play in doing so are also discussed in some detail. Simulation studies show that the new proposal is able to detect changes quicker than other methods in practice. The method is also illustrated on kidney transplant data from the Scientific Registry of Transplant Recipients (SRTR).Ph.D.BiostatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/57629/2/pbiswas_1.pd

Binary isotonic regression procedures, with application to cancer biomarkers

There is a lot of interest in the development and characterization of new biomarkers for screening large populations for disease. In much of the literature on diagnostic testing, increased levels of a biomarker correlate with increased disease risk. However, parametric forms are typically used to associate these quantities. In this article, we specify a monotonic relationship between biomarker levels with disease risk. This leads to consideration of a nonparametric regression model for a single biomarker. Estimation results using isotonic regression-type estimators and asymptotic results are given. We also discuss confidence set estimation in this setting and propose three procedures for computing confidence intervals. Methods for estimating the receiver operating characteristic (ROC) curve are also described. The finite-sample properties of the proposed methods are assessed using simulation studies and applied to data from a pancreatic cancer biomarker study

Semiparametric binary regression under monotonicity constraints

Summary: We study a binary regression model where the response variable $\Delta$ is the indicator of an event of interest (for example, the incidence of cancer) and the set of covariates can be partitioned as $(X,Z)$ where $Z$ (real valued) is the covariate of primary interest and $X$ (vector valued) denotes a set of control variables. For any fixed $X$, the conditional probability of the event of interest is assumed to be a monotonic function of $Z$. The effect of the control variables is captured by a regression parameter $\beta$. We show that the baseline conditional probability function (corresponding to $X=0$) can be estimated by isotonic regression procedures and develop a likelihood ratio based method for constructing confidence intervals for this function that obviates the need to estimate nuisance parameters from the data. We also show how confidence intervals for the regression parameter can be constructed using asymptotically $\chi^2$ likelihood ratio statistics. The confidence sets for the regression parameter and those for the conditional probability function are combined using Bonferroni\u27s inequality to construct conservative confidence intervals for the conditional probability of the event of interest at different fixed values of $X$ and $Z$. We present simulation results to illustrate the theory and apply our results to a prostate cancer data set

Squeezed coherent states for gravitational well in noncommutative space

Gravitational well is a widely used system for the verification of the quantum weak equivalence principle (WEP). We have studied the quantum gravitational well (GW) under the shed of noncommutative (NC) space so that the results can be utilized for testing the validity of WEP in NC-space. To keep our study widely usable, we have considered both position-position and momentum-momentum noncommutativity. Since coherent state (CS) structure provides a natural bridging between the classical and quantum domain descriptions, the quantum domain validity of purely classical phenomena like free-fall under gravity might be verified with the help of CS. We have constructed CS with the aid of a Lewis-Riesenfeld phase space invariant operator. From the uncertainty relations deduced from the expectation values of the observables, we have shown that the solutions of the time-dependent Schr\"{o}dinger equation are squeezed-coherent states.Comment: arXiv admin note: substantial text overlap with arXiv:2006.1125