Bayesian models for longitudinal data

Longitudinal data, where data are repeatedly observed or measured on a temporal basis of time or age provides the foundation of the analysis of processes which evolve over time, and these can be referred to as growth or trajectory models. One of the traditional ways of looking at growth models is to employ either linear or polynomial functional forms to model trajectory shape, and account for variation around an overall mean trend with the inclusion of random eects or individual variation on the functional shape parameters. The identification of distinct subgroups or sub-classes (latent classes) within these trajectory models which are not based on some pre-existing individual classification provides an important methodology with substantive implications. The identification of subgroups or classes has a wide application in the medical arena where responder/non-responder identification based on distinctly diering trajectories delivers further information for clinical processes. This thesis develops Bayesian statistical models and techniques for the identification of subgroups in the analysis of longitudinal data where the number of time intervals is limited. These models are then applied to a single case study which investigates the neuropsychological cognition for early stage breast cancer patients undergoing adjuvant chemotherapy treatment from the Cognition in Breast Cancer Study undertaken by the Wesley Research Institute of Brisbane, Queensland. Alternative formulations to the linear or polynomial approach are taken which use piecewise linear models with a single turning point, change-point or knot at a known time point and latent basis models for the non-linear trajectories found for the verbal memory domain of cognitive function before and after chemotherapy treatment. Hierarchical Bayesian random eects models are used as a starting point for the latent class modelling process and are extended with the incorporation of covariates in the trajectory profiles and as predictors of class membership. The Bayesian latent basis models enable the degree of recovery post-chemotherapy to be estimated for short and long-term followup occasions, and the distinct class trajectories assist in the identification of breast cancer patients who maybe at risk of long-term verbal memory impairment.

A prototype system for the digital lodgement of spatial data

This dissertation develops the model of a prototype system for the digital lodgement of spatial data sets with statutory bodies responsible for the registration and approval of land related actions under the Torrens Title system. Spatial data pertain to the location of geographical entities together with their spatial dimensions and are classified as point, line, area or surface. This dissertation deals with a sub-set of spatial data, land boundary data that result from the activities performed by surveying and mapping organisations for the development of land parcels. The prototype system has been developed, utilising an event-driven paradigm for the user-interface, to exploit the potential of digital spatial data being generated from the utilisation of electronic techniques. The system provides for the creation of a digital model of the cadastral network and dependent data sets for an area of interest from hard copy records. This initial model is calibrated on registered control and updated by field survey to produce an amended model. The field-calibrated model then is electronically validated to ensure it complies with standards of format and content. The prototype system was designed specifically to create a database of land boundary data for subsequent retrieval by land professionals for surveying, mapping and related activities. Data extracted from this database are utilised for subsequent field survey operations without the need to create an initial digital model of an area of interest. Statistical reporting of differences resulting when subsequent initial and calibrated models are compared, replaces the traditional checking operations of spatial data performed by a land registry office. Digital lodgement of survey data is fundamental to the creation of the database of accurate land boundary data. This creation of the database is fundamental also to the efficient integration of accurate spatial data about land being generated by modem technology such as global positioning systems, and remote sensing and imaging, with land boundary information and other information held in Government databases. The prototype system developed provides for the delivery of accurate, digital land boundary data for the land registration process to ensure the continued maintenance of the integrity of the cadastre. Such data should meet also the more general and encompassing requirements of, and prove to be of tangible, longer term benefit to the developing, electronic land information industry.