http://hdl.handle.net/1974/758 2013-05-22T23:01:16Z 2013-05-22T23:01:16Z NIU, YI http://hdl.handle.net/1974/7796 2013-02-02T06:05:06Z 2013-02-01T05:00:00Z

Title: Marginal Models for Modeling Clustered Failure Time Data Authors: NIU, YI Abstract: Clustered failure time data often arise in biomedical and clinical studies where potential correlation among survival times is induced in a cluster. In this thesis, we develop a class of marginal models for right censored clustered failure time data and propose a novel generalized estimating equation approach in a likelihood-based context. We first investigate a semiparametric proportional hazards model for clustered survival data and derive the large sample properties of the regression estimators. The finite sample studies demonstrate that the good applicability of the proposed method as well as the substantial efficiency improvement in comparison with the existing marginal model for clustered survival data. Another important feature of failure time data we will consider in this thesis is a possible fraction of cured subjects. To accommodate the potential cure fraction, we consider a proportional hazards mixture cure model for clustered survival data with long-term survivors and develop a set of estimating equations by incorporating working correlation matrices in an EM algorithm. The dependence among the cure statuses and among the survival times of uncured patients within clusters are modeled by working correlation matrices in the estimating equations. For the parametric proportional hazards mixture cure model, we show that the estimators of the regression parameters and the parameter in the baseline hazard function are consistent and asymptotically normal with a sandwich covariance matrix that can be consistently estimated. A numerical study presents that the proposed estimation method is comparable with the existing parametric marginal method. We also extend the proposed generalized estimating equation approach to a semiparametric proportional hazards mixture cure model where the baseline survival function is nonparametrically specified. A bootstrap method is used to obtain the variances of the estimates. The proposed method is evaluated by a simulation study from which we observe a noticeable efficiency gain of the proposed method over the existing semiparametric marginal method for clustered failure time data with a cure fraction. Description: Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2013-01-30 21:23:48.968

2013-02-01T05:00:00Z Song, Hui http://hdl.handle.net/1974/7759 2013-01-24T06:10:20Z 2013-01-23T05:00:00Z

Title: Joint Modelling of Longitudinal Quality of Life Measurements and Survival Data in Cancer Clinical Trials Authors: Song, Hui Abstract: In cancer clinical trials, longitudinal Quality of Life (QoL) measurements on a patient may be analyzed by classical linear mixed models but some patients may drop out of study due to recurrence or death, which causes problems in the application of classical methods. Joint modelling of longitudinal QoL measurements and survival times may be employed to explain the dropout information of longitudinal QoL measurements, and provide more efficient estimation, especially when there is strong association between longitudinal measurements and survival times. Most joint models in the literature assumed classical linear mixed model for longitudinal measurements, and Cox's proportional hazards model for survival times. The linear mixed model with normal-distribution random effects may not be sufficient to model longitudinal QoL measurements. Moreover, with advances in medical research, long-term survivors may exist, which makes the proportional hazards assumption not suitable for survival times when some censoring times are due to potential cured patients. In this thesis, we propose new models to analyze longitudinal QoL measurements and survival times jointly. In the first part of this thesis, we develop a joint model which assumes a linear mixed tt model for longitudinal measurements and a promotion time cure model for survival data. We link these two models through a latent variable and develop a semiparametric inference procedure. The second part of this thesis considers a special feature of the QoL measurements. That is, they are constrained in an interval (0,1). We propose to take into account this feature by a simplex-distribution model for these QoL measurements. Classical proportional hazards and promotion time cure models are used separately to the situations, depending on whether a cure fraction is assumed in the data or not. In both cases, we characterize the correlation between the longitudinal measurements and survival times by a shared random effect, and derive a semiparametric penalized joint partial likelihood to estimate the parameters. The above proposed new joint models and estimation procedures are evaluated in simulation studies and applied to the QoL measurements and recurrence times from a clinical trial on women with early breast cancer. Description: Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2013-01-23 14:04:14.297

2013-01-23T05:00:00Z Johnston, Andrew http://hdl.handle.net/1974/7684 2012-12-07T06:06:26Z 2012-12-06T05:00:00Z

Title: Networked Control Systems with Unbounded Noise under Information Constraints Authors: Johnston, Andrew Abstract: We investigate the stabilization of unstable multidimensional partially observed single-station, multi-sensor (single-controller) and multi-controller (single-sensor) linear systems controlled over discrete noiseless channels under fixed-rate information constraints. Stability is achieved under communication requirements that are asymptotically tight in the limit of large sampling periods. Through the use of similarity transforms, sampling and random-time drift conditions we obtain a coding and control policy leading to the existence of a unique invariant distribution and finite second moment for the sampled state. We use a vector stabilization scheme in which all modes of the linear system visit a compact set together infinitely often. Description: Thesis (Master, Mathematics & Statistics) -- Queen's University, 2012-12-06 15:06:37.449

2012-12-06T05:00:00Z Mansur, ABDALLA http://hdl.handle.net/1974/7650 2012-11-29T06:13:04Z 2012-11-27T05:00:00Z

Title: Instability of Periodic Orbits of Some Rhombus and Parallelogram Four Body Problems Authors: Mansur, ABDALLA Abstract: The rhombus and parallelogram orbits are interesting families of periodic solutions, which come from celestial mechanics and the N-body problem. Variational methods with finite order symmetry group are used to construct minimizing non-collision periodic orbits. We study the question of stability or instability of periodic and symmetric periodic solutions of the rhombus and the equal mass parallelogram four body problems. We first study the stability of periodic solutions for the rhombus four body problem. An analytical description of the variational principle is used to show that the homographic solutions are the minimizers of the action functional restricted to rhombus loop space [23]. We employ techniques from symplectic geometry and specifically a variant of the Maslov index for curves of Lagrangian subspaces along the minimizing rhombus orbit to prove the main result, Theorem 4.2.2, which states that the reduced rhombus orbit is hyperbolic in the reduced energy manifold when it is not degenerate. We second study the stability for symmetric periodic solutions of the equal mass parallelogram four body problem. The parallelogram family is a family of Z_2× Z_4 symmetric action minimizing solutions, investigated by [7]. In this example, the minimizing solution [7] can be extended to a 4T-periodic solution using symmetries through square and collinear configurations. The Maslov index of the orbits is used to prove the main result, Theorem 5.3.1, which states that the minimizing equal mass parallelogram solution is unstable when it is non-degenerate. Description: Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2012-11-26 11:30:29.688

2012-11-27T05:00:00Z