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Funder: National Institute of Health Research (NIHR) Cambridge Biomedical Research Centre, A standard two-arm randomised controlled trial usually compares an intervention to a control treatment with equal numbers of patients randomised to each treatment arm and only data from within the current trial are used to assess the treatment effect. Historical data are used when designing new trials and have recently been considered for use in the analysis when the required number of patients under a standard trial design cannot be achieved. Incorporating historical control data could lead to more efficient trials, reducing the number of controls required in the current study when the historical and current control data agree. However, when the data are inconsistent, there is potential for biased treatment effect estimates, inflated type I error and reduced power. We introduce two novel approaches for binary data which discount historical data based on the agreement with the current trial controls, an equivalence approach and an approach based on tail area probabilities. An adaptive design is used where the allocation ratio is adapted at the interim analysis, randomising fewer patients to control when there is agreement. The historical data are down-weighted in the analysis using the power prior approach with a fixed power. We compare operating characteristics of the proposed design to historical data methods in the literature: the modified power prior; commensurate prior; and robust mixture prior. The equivalence probability weight approach is intuitive and the operating characteristics can be calculated exactly. Furthermore, the equivalence bounds can be chosen to control the maximum possible inflation in type I error.

Summary The statistical concept of sampling is often given little direct attention, typically reduced to the mantra “take a random sample”. This low resource and adaptable activity demonstrates sampling and explores issues that arise due to biased sampling.

Probability and chance are essential concepts, not just in statistics but in real life. We present an adaptable activity which investigates what we mean by bias, how we can identify bias, and how we can use it to our advantage!

$\textbf{Background}$ Among adults with intellectual disabilities (ID), problems with eating, drinking and swallowing (EDS), and an associated need for mealtime support, are common, with an estimated 15% of adults known to specialist ID services requiring mealtime support. We set out to identify which adults with ID who receive mealtime support are at an increased risk of $\textit{respiratory infections}$ and $\textit{emergency hospitalisation related to EDS problems}$. $\textbf{Method}$ An exploratory, prospective cohort study was undertaken in the East of England. At baseline, structured interviews with the caregivers of 142 adults with ID and any type of mealtime support needs were used to gather information on health and support needs over the previous 12 months. These interviews were repeated at follow-up, 12 months later. The resulting dataset, covering a 24-month period, was analysed with logistic regression, using model averaging to perform sensitivity analysis, and backwards step-wise variable selection to identify the most important predictors. $\textbf{Results}$ Individuals with $\textit{a history of respiratory infections}$ (in the first year of study), those who had $\textit{epilepsy}$ and those with $\textit{caregiver-reported difficulty swallowing}$ were most likely to have $\textit{respiratory infections}$ in the second year. Adults with $\textit{increasing mealtime support needs, epilepsy}$ and/or $\textit{full mealtime support needs}$ (fed mainly or entirely by a caregiver or enterally) were at increased risk of $\textit{emergency hospitalisation}$ for EDS-related problems. $\textbf{Conclusions}$ Our findings highlight the importance of carefully monitoring health issues experienced by adults with ID and EDS problems, as well as their eating, drinking and swallowing skills. However, the models developed in this exploratory research require validation through future studies addressing the EDS problems commonly experienced by adults with ID and their implications for health outcomes and quality of life. Further research into the relationship between epilepsy and EDS problems would provide much-needed insight into the complex relationship between the two areas.