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.

“Enjoy your baby” Internet-based CBT for mothers with babies: a feasibility randomised control trial

Background: Postnatal depression is a global health problem with lasting effects on the family. Government policy is focussed on early intervention and increasing access to psychological therapies. There is a growing evidence base for the use of computerised CBT packages and this study investigated the feasibility of a CBT-based self-help internet intervention for new mothers. Objective: To assess the ability to recruit mothers, deliver an internet course, obtain follow-up data and evaluate what mothers think of the course. Design: A feasibility randomised control design was used to compare a waiting list control group (delayed access= DA) to the Enjoy Your Baby course (immediate access= IA). Measures were administered at baseline and 8 week follow-up. Methods: Adverts were placed in the Metro freesheet, on charity web pages, on social media, posters were put up in the community, and leaflets were handed out at mother and baby groups. Participants had to be 18 years old or over with a child less than 18 months old. The IA arm was given access to the course straight away. After 8 weeks all participants were asked to recomplete the original measures and those in the IA arm also gave feedback on the course. Participants in the DA arm were given access after recompleting the questionnaires. Due to a lack of follow-up data a small discussion group was conducted. Intervention: The course contains 4 core modules including helping mothers understand why they feel the way they do and helping them build closeness to their babies. Additional modules, worksheets and homework tasks were available. The DA group were given a list of additional support resources and services, and encouraged to seek additional help if required. All participants received weekly automated emails for 12 weeks as they worked through the course. It was not possible to deliver individualised support. 34 Results: Despite using a number of recruitment strategies, recruitment was lower and slower than anticipated, and attrition was high. 41 women, primarily recruited via the internet, were randomised (IA n=21, DA n=20). No significant differences were observed between participants in either arm at baseline and no statistically significant differences were identified when the demographics and baseline measures of participants who logged-on to the course were compared to those who did not, or when participants who completed follow-up measures were compared to those who did not. Pre and post intervention scores on the EPDS approached statistical significance (P=.059, r=.444) favouring the intervention arm. The discussion group suggested strengths of the course and recommended areas for improvement, including making the course more mobile friendly. Conclusion: Internet interventions show promise; however it is difficult to recruit mothers, engagement is low and attrition high. A number of recommendations are made and a further pilot or an internal pilot of a larger substantive study should be conducted to confirm recruitment and retention. Trial ID: ISRCTN90927910.