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The development of new treatments to aid patients who suffer from rare diseases is a challenging area of medicine, particularly since the patient populations are limited. Therefore, traditional clinical trial designs and their sample size calculations often require a large proportion of the total patient population to be recruited into the clinical trial. Due to this, many novel designs of clinical trials seek to increase the benefit to the patients recruited into the trials. This is a motivation for response adaptive randomisation designs and their extension, covariate adjusted response adaptive (CARA) randomisation designs. These designs use previous patients' outcomes (and the CARA design also uses the previous patients' covariates) from within the trial to predict which treatment will be superior for future patients, and prioritise the allocation of said predicted superior treatment. In this thesis, two methods to maximise the benefit to patients are explored. The first method focuses on increasing the benefit to patients within the trial. A CARA trial design, which can be used for several different types of covariates and patient outcomes, is explored using two simulation studies; one includes a continuous covariate and outcome, the other includes two binary covariates and a survival outcome. The design is then extended to incorporate historical trial data. This extension is evaluated using two simulations studies that incorporate a continuous covariate and outcome. Different versions of both trial designs are evaluated in simulations across a wide range of scenarios. The second method is an alternative sample size calculation for a randomised controlled trial, which optimises the trial sample size such that the benefit to the whole patient population is maximised. Two different versions of the approach are investigated and compared using a continuous patient outcome trial, for a range of scenarios.

Introduction: To test drugs with the potential to prevent the onset of Parkinson’s disease (PD), it is key to identify individuals in the general population at high risk of developing PD. This is often difficult because most of the clinical markers are non-specific, common in PD but also common in older adults (e.g., sleep problems). Objective: We aimed to identify the clinical markers at high specificity for developing PD by comparing individuals with PD or prodromal PD to healthy controls. Methods: We investigated motor and non-motor symptoms (Movement Disorder Society Unified Parkinson’s Disease Rating Scale Part 1 and 2 items) in 64 prodromal PD and 422 PD individuals calculating the odds ratios, adjusting for age and gender, for PD and prodromal PD versus 195 healthy controls. Symptoms at high specificity were defined as having an adjusted odds ratio ≥ 6. Results: Constipation had an adjusted odds ratio, 6.14 [95% CI: 2.94–12.80] showing high specificity for prodromal PD, and speech difficulties had an adjusted odds ratio, 9.61 [95% CI: 7.88–48.81] showing high specificity for PD. The proportion of participants showing these specific markers was moderate (e.g., prevalence of constipation was 43.75% in prodromal PD, and speech difficulties was 33.89% in PD), suggesting these symptoms may make robust predictors of prodromal PD and PD, respectively. Discussion: Clinical markers at high specificity for developing PD could be used as tools in the screening of general populations to identify individuals at higher risk of developing PD.

The majority of phase III clinical trials use a 2-arm randomized controlled trial with 50% allocation between the control treatment and experimental treatment. The sample size calculated for these clinical trials normally guarantee a power of at least 80% for a certain Type I error, usually 5%. However, these sample size calculations, do not typically take into account the total patient population that may benefit from the treatment investigated. In this article, we discuss two methods, which optimize the sample size of phase III clinical trial designs, to maximize the benefit to patients for the total patient population. We do this for trials that use a continuous endpoint, when the total patient population is small (i.e., for rare diseases). One approach uses a point estimate for the treatment effect to optimize the sample size and the second uses a distribution on the treatment effect in order to account for the uncertainty in the estimated treatment effect. Both one-stage and two-stage clinical trials, using three different stopping boundaries are investigated and compared, using efficacy and ethical measures. A completed clinical trial in patients with anti-neutrophil cytoplasmic antibody (ANCA)-associated vasculitis is used to demonstrate the use of the method. Supplementary materials for this article are available online.

The majority of phase III clinical trials use a 2-arm randomized controlled trial with 50% allocation between the control treatment and experimental treatment. The sample size calculated for these clinical trials normally guarantee a power of at least 80% for a certain type I error, usually 5%. However, these sample size calculations, do not typically take into account the total patient population that may benefit from the treatment investigated. In this paper, we discuss two methods, which optimize the sample size of phase III clinical trial designs, to maximize the benefit to patients for the total patient population. We do this for trials that use a continuous endpoint, when the total patient population is small (i.e. for rare diseases). One approach uses a point estimate for the treatment effect to optimize the sample size and the second uses a distribution on the treatment effect in order to account for the uncertainty in the estimated treatment effect. Both one-stage and two-stage clinical trials, using three different stopping boundaries are investigated and compared, using efficacy and ethical measures. A completed clinical trial in patients with anti-neutrophil cytoplasmic antibody (ANCA)-associated vasculitis is used to demonstrate the use of the method.

Computational flattening algorithms have been successfully applied to X-ray microtomography scans of damaged historical documents, but have so far been limited to scrolls, books, and documents with one or two folds. The challenge tackled here is to reconstruct the intricate folds, tucks, and slits of unopened letters secured shut with “letterlocking,” a practice—systematized in this paper—which underpinned global communications security for centuries before modern envelopes. We present a fully automatic computational approach for reconstructing and virtually unfolding volumetric scans of a locked letter with complex internal folding, producing legible images of the letter’s contents and crease pattern while preserving letterlocking evidence. We demonstrate our method on four letterpackets from Renaissance Europe, reading the contents of one unopened letter for the first time. Using the results of virtual unfolding, we situate our findings within a novel letterlocking categorization chart based on our study of 250,000 historical letters.