Feasibility study to inform the design of a UK multi-centre randomised controlled trial of prophylactic antibiotics for the prevention of recurrent cellulitis of the leg

Background: This paper describes the results of a feasibility study for a randomised controlled trial (RCT). Methods: Twenty-nine members of the UK Dermatology Clinical Trials Network (UK DCTN) expressed an interest in recruiting for this study. Of these, 17 obtained full ethics and Research & Development (R&D) approval, and 15 successfully recruited patients into the study. A total of 70 participants with a diagnosis of cellulitis of the leg were enrolled over a 5-month period. These participants were largely recruited from medical admissions wards, although some were identified from dermatology, orthopaedic, geriatric and general surgery wards. Data were collected on patient demographics, clinical features and willingness to take part in a future RCT. Results: Despite being a relatively common condition, cellulitis patients were difficult to locate through our network of UK DCTN clinicians. This was largely because patients were rarely seen by dermatologists, and admissions were not co-ordinated centrally. In addition, the impact of the proposed exclusion criteria was high; only 26 (37%) of those enrolled in the study fulfilled all of the inclusion criteria for the subsequent RCT, and were willing to be randomised to treatment. Of the 70 participants identified during the study as having cellulitis of the leg (as confirmed by a dermatologist), only 59 (84%) had all 3 of the defining features of: i) erythema, ii) oedema, and iii) warmth with acute pain/tenderness upon examination. Twenty-two (32%) patients experienced a previous episode of cellulitis within the last 3 years. The median time to recurrence (estimated as the time since the most recent previous attack) was 205 days (95% CI 102 to 308). Service users were generally supportive of the trial, although several expressed concerns about taking antibiotics for lengthy periods, and felt that multiple morbidity/old age would limit entry into a 3-year study. Conclusion: This pilot study has been crucial in highlighting some key issues for the conduct of a future RCT. As a result of these findings, changes have been made to i) the planned recruitment strategy, ii) the proposed inclusion criteria and ii) the definition of cellulitis for use in the future trial.

Adaptivity and a posteriori error control for bifurcation problems I: the Bratu problem

This article is concerned with the numerical detection of bifurcation points of nonlinear partial differential equations as some parameter of interest is varied. In particular, we study in detail the numerical approximation of the Bratu problem, based on exploiting the symmetric version of the interior penalty discontinuous Galerkin finite element method. A framework for a posteriori control of the discretization error in the computed critical parameter value is developed based upon the application of the dual weighted residual (DWR) approach. Numerical experiments are presented to highlight the practical performance of the proposed a posteriori error estimator.