The aim of this document is to provide practical guidance on the choice of target difference used in the sample size calculation of a randomised controlled trial (RCT). Guidance is provided with a definitive trial, one that seeks to provide a useful answer, in mind and not those of a more exploratory nature. The term “target difference” is taken throughout to refer to the difference that is used in the sample size calculation (the one that the study formally “targets”). Please see the glossary for definitions and clarification with regards other relevant concepts. In order to address the specification of the target difference, it is appropriate, and to some degree necessary, to touch on related statistical aspects of conducting a sample size calculation. Generally the discussion of other aspects and more technical details is kept to a minimum, with more technical aspects covered in the appendices and referencing of relevant sources provided for further reading.The main body of this guidance assumes a standard RCT design is used; formally, this can be described as a two-arm parallel-group superiority trial. Most RCTs test for superiority of the interventions, that is, whether or not one of the interventions is superior to the other (See Box 1 for a formal definition of superiority, and of the two most common alternative approaches). Some common alternative trial designs are considered in Appendix 3. Additionally, it is assumed in the main body of the text that the conventional (Neyman-Pearson) approach to the sample size calculation of an RCT is being used. Other approaches (Bayesian, precision and value of information) are briefly considered in Appendix 2 with reference to the specification of the target difference.

Background: MOST-plus is a multicenter, randomized, open-label, adaptive Phase II trial evaluating the clinical benefit of targeted treatments matched to molecular alteration in advanced/metastatic solid tumors. Sorafenib was tested on patients with tumors harboring sorafenib-targeted genes Methods: The MOST-plus trial used a randomized discontinuation design. After 12 weeks of sorafenib (400 mg, po BID), patients with progressive disease dis-continued study, patients with objective response were proposed to continue sorafenib, whereas patients with stable disease (SD) were randomly assigned (1:1) to maintenance or interruption of treatment. Primary endpoint was RE-CIST version 1.1 progression-free rate at 16 weeks after randomization (PFR-16w). Secondary endpoints included progression-free survival (PFS), overall survival (OS), and toxicity. Statistical analyses used a sequential Bayes-ian approach with interim efficacy analyses. The enrolment could be stopped in the case of a 95% probability for the estimated PFR-16w to be higher in the maintenance than in the interruption arm (NCT02029001). Results: 151 patients were included, of whom 35 had SD at 12 weeks of Soraf-enib. For the 35 patients with SD on sorafenib, the PFR-16w was 65% [95% credibility interval 43.4–83.7] in the continuation arm and 25% [7.8–48.1] in the interruption arm. Median PFS and OS were improved in maintenance versus interruption arm (mPFS: 5.6 [95%CI 1.97–6.77] months versus 2.0 [95%CI 1.61–3.91] months (p =0.0231) and mOS : 14.3 [95%CI 8.9–23.8] versus 8.0 months [95%CI 3.5–15.2] (p =0.0857)). Conclusion: Sorafenib showed activity in progressive patients with solid tu-mors harboring somatic genomic alterations in sorafenib-targeted genes. Con-tinuing sorafenib when SD is achieved improves PFR compared to interruption

Background: Feasibility trials are preliminary trials that assess the viability and acceptability of intervention studies and the effects of the intervention on intermediate endpoints. Due to their short duration, they are unable to establish the effects of the intervention on long-term clinical outcomes. We propose a novel method that could transform the interpretation of feasibility trials using modified two-stage randomisation analyses. Methods In this two-stage process, we explored the effects of a 6-month feasibility factorial randomised controlled trial (RCT) of lycopene and green tea dietary interventions (ProDiet) on 159 serum metabolic traits in 133 men with raised PSA levels but prostate cancer (PCA) free. In the first stage, we conducted an intention-to-treat analysis, using linear regression to examine the effects of the interventions on metabolic traits, compared to the placebo group and instrumental variable analysis to assess the causal effect of the intervention on the outcomes. In the second stage, we used a two-sample Mendelian Randomization (MR) approach to assess the causal effect of metabolic traits altered by the interventions, on PCA risk, using summary statistics data from an international PCA consortium of 44,825 cancer cases and 27,904 controls. ResultsThe systemic effects of lycopene and green tea supplementation on serum metabolic profile were comparable to the effects of the respective dietary advice interventions (R2= 0.65 and 0.76 for lycopene and green tea respectively). Metabolites which were altered in response to lycopene supplementation were acetate (standard deviation difference versus placebo (β)): 0.69; 95% CI= 0.24, 1.15; p=0.003), valine (β: -0.62; -1.03, -0.02; p=0.004), pyruvate (β: -0.56; -0.95, -0.16; p=0.006), and docosahexaenoic acid (β: -0.50; -085, -0.14; p=0.006). The instrumental variable analysis showed there was no evidence that green tea altered the metabolome, but lycopene was associated with an increase in acetate (β=2.13; p=0.006) and decreases in pyruvate (β=-1.90; p=0.009), valine (β=-1.79; p=0.023), diacylglycerol (β=-1.81; p=0.026), alanine (β=-1.55; p=0.015) and DHA (p=0.097), where the regression coefficient represents the standard deviation (SD) difference in metabolite measures per unit change in lycopene (µmol/L) or EGCG (nM).Using MR, a genetically instrumented SD increase in pyruvate increased the odds of PCA by 1.29 (1.03, 1.62; p=0.027). Conclusion Using a two-stage randomization analysis in a feasibility RCT, we found that lycopene lowered levels of pyruvate, which our Mendelian randomization analysis suggests may be causally related to reduced PCA risk.

The Cochran–Mantel–Haenszel (CMH) methodology is a suite of tests applicable to particular tables of count data. Inference is conditional on the treatment and outcome totals on each stratum being known before sighting the data. The CMH tests are important for analyzing randomised blocks data when the responses are categorical rather than continuous. This overview will first review the traditional CMH tests and then explore new alternative presentations of the ordinal CMH tests. Next the ordinal CMH tests will be extended so they can be used to test for higher moment effects. Finally unconditional analogues of the extended CMH tests will be developed.

Since autism was first recognised, prevalence has increased rapidly. The growing economic as well as social cost to society can only be mitigated by effective interventions and supports. It is therefore not surprising that most governments have developed public policy documents to address the management of autism. Over the past 40-50 years, meaningful evidence has accrued showing that interventions based on the scientific discipline of Applied Behaviour Analysis (ABA) can help people with autism reach their potential. In view of this, nearly all of North America has laws to mandate that ABA-based interventions are available through the health care systems. In contrast, across Europe there are no such laws. In fact, the National Institute for Health and Care Excellence (NICE), the body guiding health and social policy in the UK, concluded that it could not find any evidence to support ABA, and therefore could not recommend it. This paper addresses the reasons for these diametrically opposed perspectives. In particular, it examines what happens when health and social care policy is misinformed about effective autism intervention.

Risk-averse areas such as the medical, aerospace and energy sectors have been somewhat slow towards accepting and applying Additive Manufacturing (AM) in many of their value chains. This is partly because there are still signicant uncertainties concerning the quality of AM builds. This paper introduces a machine learning algorithm for the automatic detection of faults in AM products. The approach is semi-supervised in that, during training, it is able to use data from both builds where the resulting components were certied and builds where the quality of the resulting components is unknown. This makes the approach cost ecient, particularly in scenarios where part certication is costly and time consuming. The study specically analyses Selective Laser Melting (SLM) builds. Key features are extracted from large sets of photodiode data, obtained during the building of 49 tensile test bars. Ultimate tensile strength (UTS) tests were then used to categorise each bar as `faulty' or `acceptable'. A fully supervised approach identied faulty specimens with a 77% success rate while the semi-supervised approach was able to consistently achieve similar results, despite being trained on a fraction of the available certication data. The results show that semi-supervised learning is a promising approach for the automatic certication of AM builds that can be implemented at a fraction of the cost currently required.

The solution of structural problems with nonlinear material behaviour in a model order reduction framework is investigated in this paper. In such a framework, greedy algorithms or adaptive strategies are interesting as they adjust the reduced order basis (ROB) to the problem of interest. However, these greedy strategies may lead to an excessive increase in the size of the reduced basis, i.e. the solution is no more represented in its optimal low-dimensional expansion. Here, an optimised strategy is proposed to maintain, at each step of the greedy algorithm, the lowest dimension of the PGD basis using a randomised SVD algorithm. Comparing to conventional approaches such as Gram-Schmidt orthonormalisation or deterministic SVD, it is shown to be very efficient both in terms of numerical cost and optimality of the reduced basis. Examples with different mesh densities are investigated to demonstrate the numerical efficiency of the presented method.

Education for Sustainable Development (ESD) is considered vital to the success of the United Nations’ Sustainable Development Goals. Systems Thinking has been identified as a core competency necessary to incorporate into ESD. Systems Thinking orientated ESD learning tools, established methods of assessment of sustainability skills, and studies to demonstrate effectiveness of such learning tools, are all lacking. There is a wealth of experience in the System Dynamics field regarding the application of Systems Thinking and simulation to environmental problems, sustainability and systems education. Many System Dynamicists regard simulation as essential for teaching Systems Thinking. The substantial body of research into the design of effective simulation-based learning environments (SBLEs) can also inform ESD initiatives. This research describes a randomised controlled trial (n=106) to investigate whether an online sustainability learning tool that incorporates Systems Thinking and System Dynamics simulation increases understanding of a specific problem and supports transfer of knowledge to a second problem with a similar systemic structure. The effects of Systems Thinking and simulation were tested separately and in combination. The learning tool was designed for a single online learning session. Simulation was found to increase ESD learning outcomes significantly, and also to support transfer of skills, although less significantly.

Background: Globally, women’s responsibility for unpaid care work (UCW) remains a barrier to gender equality and women’s empowerment. Rwanda, a low-income country, has a legal and policy framework for promoting gender equality but remains a patriarchal society with women responsible for UCW. Reseaux des Femmes, a local NGO, has been delivering a programme targeted at reducing and redistributing the UCW of women with the objective of gender transformational change. However, there has been no impact evaluation of their intervention to date. Methods/Design: The impact evaluation will be a proof-of-concept critical realist cluster control trial (CRcCT) to evaluate for which women, how and under what circumstances the intervention reduces and redistributes women’s UCW, promote gender equality and women’s empowerment, and improves women’s quality of life. Four clusters of villages in each of five districts in Rwanda will be randomly allocated to the intervention or control arms, and all eligible households, those headed by a couple with at least one child under 12 years, will be recruited. This will yield a sample of around 550 intervention households and 550 control. Discussion: This protocol describes the design of mixed-methods research to evaluate an intervention in Rwanda aimed at reducing and redistributing the time women spend on UCW, thereby promoting gender equality and women’s empowerment. This paper will contribute to our understanding of interventions for transforming gender relations from a scholarly perspective. From a policy perspective, it will act as a proof of concept of Reseaux des Femmes’ Programme.