Optimal static and sequential design : a critical review

The aim of this thesis is to review and augment the theory and methods of optimal experimental design. In Chapter I the scene is set by considering the possible aims of an experimenter prior to an experiment, the statistical methods one might use to achieve those aims and how experimental design might aid this procedure. It is indicated that, given a criterion for design, a priori optimal design will only be possible in certain instances and, otherwise, some form of sequential procedure would seem to be indicated. In Chapter 2 an exact experimental design problem is formulated mathematically and is compared with its continuous analogue. Motivation is provided for the solution of this continuous problem, and the remainder of the chapter concerns this problem. A necessary and sufficient condition for optimality of a design measure is given. Problems which might arise in testing this condition are discussed, in particular with respect to possible non-differentiability of the criterion function at the design being tested. Several examples are given of optimal designs which may be found analytically and which illustrate the points discussed earlier in the chapter. In Chapter 3 numerical methods of solution of the continuous optimal design problem are reviewed. A new algorithm is presented with illustrations of how it should be used in practice. It is shown that, for reasonably large sample size, continuously optimal designs may be approximated to well by an exact design. In situations where this is not satisfactory algorithms for improvement of this design are reviewed. Chapter 4 consists of a discussion of sequentially designed experiments, with regard to both the philosophies underlying, and the application of the methods of, statistical inference. In Chapter 5 we criticise constructively previous suggestions for fully sequential design procedures. Alternative suggestions are made along with conjectures as to how these might improve performance. Chapter 6 presents a simulation study, the aim of which is to investigate the conjectures of Chapter 5. The results of this study provide empirical support for these conjectures. In Chapter 7 examples are analysed. These suggest aids to sequential experimentation by means of reduction of the dimension of the design space and the possibility of experimenting semi-sequentially. Further examples are considered which stress the importance of the use of prior information in situations of this type. Finally we consider the design of experiments when semi-sequential experimentation is mandatory because of the necessity of taking batches of observations at the same time. In Chapter 8 we look at some of the assumptions which have been made and indicate what may go wrong where these assumptions no longer hold.

Leptospirosis in northern Tanzania: exploring the role of rodents and ruminant livestock in a neglected public health problem

Leptospirosis is an important but neglected zoonotic disease that is often overlooked in Africa. Although comprehensive data on the incidence of human disease are lacking, robust evidence of infection has been demonstrated in people and animals from all regions of the continent. However, to date, there are few examples of direct epidemiological linkages between human disease and animal infection. In East Africa, awareness of the importance of human leptospirosis as a cause of non-malarial febrile illness is growing. In northern Tanzania, acute leptospirosis has been diagnosed in 9% of patients with severe febrile illness compared to only 2% with malaria. However, little is known about the relative importance of different potential animal hosts as sources of human infection in this area. This project was established to investigate the roles of rodents and ruminant livestock, important hosts of Leptospira in other settings, in the epidemiology of leptospirosis in northern Tanzania. A cross-sectional survey of rodents living in and around human settlements was performed alongside an abattoir survey of ruminant livestock. Unusual patterns of animal infection were detected by real-time PCR detection. Renal Leptospira infection was absent from rodents but was detected in cattle from several geographic areas. Infection was demonstrated for the first time in small ruminants sub-Saharan Africa. Two major Leptospira species and a novel Leptospira genotype were detected in livestock. L. borgpetersenii was seen only in cattle but L. kirschneri infection was detected in multiple livestock species (cattle, sheep and goats), suggesting that at least two distinct patterns of Leptospira infection occur in livestock in northern Tanzania. Analysis of samples from acute leptospirosis in febrile human patients could not detect Leptospira DNA by real-time PCR but identified social and behavioural factors that may limit the utility of acute-phase diagnostic tests in this community. Analysis of serological data revealed considerable overlap between serogroups detected in cattle and human leptospirosis cases. Human disease was most commonly attributed to the serogroups Mini and Australis, which were also predominant reactive serogroups in cattle. Collectively, the results of this study led to the hypothesis that livestock are an important reservoir of Leptospira infection for people in northern Tanzania. These results also challenge our understanding of the relationship between Leptospira and common invasive rodent species, which do not appear to maintain infection in this setting. Livestock Leptospira infection has substantial potential to affect the well-being of people in East Africa, through direct transmission of infection or through indirect effects on food production and economic security. Further research is needed to quantify the impact of livestock leptospirosis in Africa and to develop effective interventions for the control of human and animal disease.