A short presentation prising apart two types of non-uniqueness and proposing a method to identify the so-called "polytope of mixture non-uniqueness" using computational geometry software (here, cdd).
Joint work with Robert Gentleman, Department of Statistics, University of Auckland.
Presented at various locations in 1999.
Streamlined version of next presentation.
Presented at various locations in 1998.
Odds and ends relating interval censored data with interval orders, including some thoughts on uniform generation of linear extensions of interval orders (applicable to linear rank tests), on NPMLE, and some possible applications of the incidence probability matrix.
Joint work with Robert Gentleman, Department of Statistics, University of Auckland.
Presented in the Graduate Students Talks Series, Department of Statistics, University of Auckland, October 1996.
In order to efficiently generate linear extensions of interval orders uniformly using a staged sampling generator, it may be desirable to determine the minimal covers of maximal antichains for an interval order. This presentation illustrates two approaches for doing so, & discusses how many such minimal covers there may be, as well as examines an interesting subproblem involving semi-orders of maximal length elements for a fixed number of maximal antichains. Links to Excel files (included in the zipped file) may have to be updated in order for the presentation to work.
Joint work with Marston D. E. Conder, Department of Mathematics, and Robert Gentleman, Department of Statistics, University of Auckland.
Presented in the Algebra, Geometry and Combinatorics Seminar Series, Department of Mathematics, University of Auckland, May 1997.
Where HIV surveillance cannot be implemented because of privacy concerns, only seroincidence studies, seroprevalence studies and AIDS surveillance can be used to assess HIV incidence. The simultaneous consideration of all three types of estimates is often the only way to informally compensate for the biases and other limitations inherent to each method. In the case of AIDS surveillance, backcalculation techniques are necessary to assess historical HIV incidence. Backcalculation rely heavily on a well-described progression from HIV infection to AIDS; recent therapies, most specifically tritherapy involving ZDV, 3TC and protease inhibitors, have had a strong influence on this progression, and thus on AIDS incidence and AIDS-related mortality in North America. This influence has been operating for much longer than the recent homologation date of these therapies would lead to suppose, due to large-scale clinical trials and compassionate drug programs. We consider the extent of this effect in the province of Québec, Canada, and how it can be incorporated within backcalculation models and survival models to provide a realistic picture of HIV incidence and HIV prevalence.
Joint work with Robert S. Remis (Department of Preventive Medicine and Biostatistics, University of Toronto)
Presented at the New Zealand Statistical Association 48th Conference, Student Prize Session, July 1997.
Nonparametric rank-based approaches for interval censored data similar to those used for right censored data have been hard to develop because of the difficulty of generating rank vectors compatible with the data uniformly. Random generators of this type have been proposed in the past which were wrongly assumed to produced such rank vectors uniformly. We develop a pseudo-random generator based on a weak order partition of interval orders which allows a two-staged sampling approach to uniform rank vector generation. The generator is based on the fundamental result that the maximal antichains of an interval order are linearly ordered.
Joint work with Robert Gentleman, Department of Statistics, University of Auckland.
Presented at the New Zealand Statistical Association 48th Conference jointly with Robert Gentleman under the title "A Combinatorial Approach to the Analysis of Interval Censored Data", Medicals Statistics Session, July 1997.