Hierarchical models for 2D presence/absence data having ambiguous zeroes: With a biogeographical case study on dingo behaviour

This dissertation is primarily an applied statistical modelling investigation, motivated by a case study comprising real data and real questions. Theoretical questions on modelling and computation of normalization constants arose from pursuit of these data analytic questions. The essence of the thesis can be described as follows. Consider binary data observed on a two-dimensional lattice. A common problem with such data is the ambiguity of zeroes recorded. These may represent zero response given some threshold (presence) or that the threshold has not been triggered (absence). Suppose that the researcher wishes to estimate the effects of covariates on the binary responses, whilst taking into account underlying spatial variation, which is itself of some interest. This situation arises in many contexts and the dingo, cypress and toad case studies described in the motivation chapter are examples of this. Two main approaches to modelling and inference are investigated in this thesis. The first is frequentist and based on generalized linear models, with spatial variation modelled by using a block structure or by smoothing the residuals spatially. The EM algorithm can be used to obtain point estimates, coupled with bootstrapping or asymptotic MLE estimates for standard errors. The second approach is Bayesian and based on a three- or four-tier hierarchical model, comprising a logistic regression with covariates for the data layer, a binary Markov Random field (MRF) for the underlying spatial process, and suitable priors for parameters in these main models. The three-parameter autologistic model is a particular MRF of interest. Markov chain Monte Carlo (MCMC) methods comprising hybrid Metropolis/Gibbs samplers is suitable for computation in this situation. Model performance can be gauged by MCMC diagnostics. Model choice can be assessed by incorporating another tier in the modelling hierarchy. This requires evaluation of a normalization constant, a notoriously difficult problem. Difficulty with estimating the normalization constant for the MRF can be overcome by using a path integral approach, although this is a highly computationally intensive method. Different methods of estimating ratios of normalization constants (N Cs) are investigated, including importance sampling Monte Carlo (ISMC), dependent Monte Carlo based on MCMC simulations (MCMC), and reverse logistic regression (RLR). I develop an idea present though not fully developed in the literature, and propose the Integrated mean canonical statistic (IMCS) method for estimating log NC ratios for binary MRFs. The IMCS method falls within the framework of the newly identified path sampling methods of Gelman & Meng (1998) and outperforms ISMC, MCMC and RLR. It also does not rely on simplifying assumptions, such as ignoring spatio-temporal dependence in the process. A thorough investigation is made of the application of IMCS to the three-parameter Autologistic model. This work introduces background computations required for the full implementation of the four-tier model in Chapter 7. Two different extensions of the three-tier model to a four-tier version are investigated. The first extension incorporates temporal dependence in the underlying spatio-temporal process. The second extensions allows the successes and failures in the data layer to depend on time. The MCMC computational method is extended to incorporate the extra layer. A major contribution of the thesis is the development of a fully Bayesian approach to inference for these hierarchical models for the first time. Note: The author of this thesis has agreed to make it open access but invites people downloading the thesis to send her an email via the 'Contact Author' function.

Design and analysis of group key exchange protocols

A group key exchange (GKE) protocol allows a set of parties to agree upon a common secret session key over a public network. In this thesis, we focus on designing efficient GKE protocols using public key techniques and appropriately revising security models for GKE protocols. For the purpose of modelling and analysing the security of GKE protocols we apply the widely accepted computational complexity approach. The contributions of the thesis to the area of GKE protocols are manifold. We propose the first GKE protocol that requires only one round of communication and is proven secure in the standard model. Our protocol is generically constructed from a key encapsulation mechanism (KEM). We also suggest an efficient KEM from the literature, which satisfies the underlying security notion, to instantiate the generic protocol. We then concentrate on enhancing the security of one-round GKE protocols. A new model of security for forward secure GKE protocols is introduced and a generic one-round GKE protocol with forward security is then presented. The security of this protocol is also proven in the standard model. We also propose an efficient forward secure encryption scheme that can be used to instantiate the generic GKE protocol. Our next contributions are to the security models of GKE protocols. We observe that the analysis of GKE protocols has not been as extensive as that of two-party key exchange protocols. Particularly, the security attribute of key compromise impersonation (KCI) resilience has so far been ignored for GKE protocols. We model the security of GKE protocols addressing KCI attacks by both outsider and insider adversaries. We then show that a few existing protocols are not secure against KCI attacks. A new proof of security for an existing GKE protocol is given under the revised model assuming random oracles. Subsequently, we treat the security of GKE protocols in the universal composability (UC) framework. We present a new UC ideal functionality for GKE protocols capturing the security attribute of contributiveness. An existing protocol with minor revisions is then shown to realize our functionality in the random oracle model. Finally, we explore the possibility of constructing GKE protocols in the attribute-based setting. We introduce the concept of attribute-based group key exchange (AB-GKE). A security model for AB-GKE and a one-round AB-GKE protocol satisfying our security notion are presented. The protocol is generically constructed from a new cryptographic primitive called encapsulation policy attribute-based KEM (EP-AB-KEM), which we introduce in this thesis. We also present a new EP-AB-KEM with a proof of security assuming generic groups and random oracles. The EP-AB-KEM can be used to instantiate our generic AB-GKE protocol.

Quality of life after total laparoscopic hysterectomy versus total abdominal hysterectomy for stage I endometrial cancer (LACE) : a randomised trial

Background: The two-stage Total Laparoscopic Hysterectomy (TLH) versus Total Abdominal Hysterectomy (TAH) for stage I endometrial cancer (LACE) randomised controlled trial was initiated in 2005. The primary objective of stage 1 was to assess whether TLH results in equivalent or improved QoL up to 6 months after surgery compared to TAH. The primary objective of stage 2 was to test the hypothesis that disease-free survival at 4.5 years is equivalent for TLH and TAH. Results addressing the primary objective of stage 1 of the LACE trial are presented here. Methods: The first 361 LACE participants (TAH n= 142, TLH n=190) were enrolled in the QoL substudy at 19 centres across Australia, New Zealand and Hong Kong, and 332 completed the QoL analysis. Randomisation was performed centrally and independently from other study procedures via a computer generated, web-based system (providing concealment of the next assigned treatment) using stratified permuted blocks of 3 and 6, and assigned patients with histologically confirmed stage 1 endometrioid endometrial adenocarcinoma and ECOG performance status <2 to TLH or TAH stratified by histological grade and study centre. No blinding of patients or study personnel was attempted. QoL was measured at baseline, 1 and 4 weeks (early), and 3 and 6 months (late) after surgery using the Functional Assessment of Cancer Therapy-General (FACT-G) questionnaire. The primary endpoint was the difference between the groups in QoL change from baseline at early and late time points (a 5% difference was considered clinically significant). Analysis was performed according to the intention-to-treat principle using generalized estimating equations on differences from baseline for the early and late QoL recovery. The LACE trial is registered with clinicaltrials.gov (NCT00096408) and the Australian New Zealand Clinical Trials Registry (CTRN12606000261516). Patients for both stages of the trial have now been recruited and are being followed up for disease-specific outcomes. Findings: The proportion of missing values at the 5%, 10% 15% and 20% differences in the FACT-G scale was 6% (12/190) in the TLH and 14% (20/142) in the TAH group. There were 8/332 conversions (2.4%, 7 of which were from TLH to TAH). In the early phase of recovery, patients undergoing TLH reported significantly greater improvement of QoL from baseline compared to TAH in all subscales except the emotional and social well-being subscales. Improvements in QoL up to 6 months post-surgery continued to favour TLH except for the emotional and social well-being of the FACT and the visual analogue scale of the EuroQoL five dimensions (EuroQoL-VAS). Length of operating time was significantly longer in the TLH group (138±43 mins), than in the TAH group at (109±34 mins; p=0.001). While the proportion of intraoperative adverse events was similar between the treatment groups (TAH 8/142, 5.6%; TLH 14/190, 7.4%; p=0.55), postoperatively, twice as many patients in the TAH group experienced adverse events of CTC grade 3+ than in the TLH group (33/142, 23.2% and 22/190, 11.6%, respectively; p=0.004). Postoperative serious adverse events occurred more frequently in patients who had a TAH (27/142, 19.0%) than a TLH (15/190, 7.9%) (p=0.002). Interpretation: QoL improvements from baseline during early and later phases of recovery, and the adverse event profile significantly favour TLH compared to TAH for patients treated for Stage I endometrial cancer.