**The Centre for Mathematical Sciences**** research seminars and events are listed below.**

The four main seminar series are in applied mathematics, pure mathematics, statistics and theoretical physics. Visit the centre's webpages for the latest seminar updates and information.

**Wednesday 13 February (14:00-15:00, Room 211, Rolle Building)**

**Pupil Advantage Index as an Alternative to Subgroup Analysis in RCTs for Education**

- Speaker: ZhiMin Xiao (University of Exeter)

**Abstract:** Analyses of social interventions need to produce evidence that is relevant to different groups of people in a society. When such a group is not the target group of an intervention, this is called subgroup analysis, even when the group of interest is pre-specified prior to data collection. Amongst statisticians, subgroup analysis is often regarded as a statistical malpractice, as its findings are often underpowered, unreliable, and can be prone to overinterpretation at best, or misleading at worst. Meanwhile, researchers would be criticised for generating irrelevant evidence and accused of wasting research money if they do not conduct relevant subgroup analysis. As a result, “they are damned if they do, and damned if they don’t” (Petticrew et al., 2012).

In this study, we estimated intervention effects for Free School Meal (FSM) pupils in English schools, which is a pre-specified subgroup in most educational interventions funded by the Education Endowment Foundation (EEF) in England. Specifically, we first ran a treatment-FSM interaction test in each and every outcome to see if the difference-in-effects is statistically significant between FSM and Non-FSM pupils. We then calculated separate effect sizes within the two subgroups. Finally, we examined the p-values from the interaction tests and compared the overall effect sizes for both FSM and Non-FSM pupils with the two separate subgroup estimates. We found that conventional interaction tests can produce self-contradictory results. To help solve the problem, we propose a new approach, Pupil Advantage Index (PAI), as an alternative to subgroup analysis and apply it to real RCT data extracted from the EEF data archive. We demonstrate that PAI does not just indicate where an intervention worked and by how much in existing trials, but it can also be utilised to optimise treatment recommendation for future interventions.

Contact yinghu.wei@plymouth.ac.uk for queries.

**Wednesday 20 February (14:00-15:00, Room, 115, Rolle Building)**

**Modelling numbers of births by day of the week in relation to onset of labour and mode of giving birth in England 2005–2014
**

(Mario Cortina Borja, in collaboration with Professor Alison Macfarlane, Ms Nirupa Dattani, Dr Miranda Dodwell, Mr Rod Gibson, Dr Gill Harper, Dr Peter Martin and Dr Mary Newburn)

- Speaker: Mario Cortina Borja (UCL)

**Abstract:** Maternity care has to be available 24 hours a day, seven days a week. It is known that obstetric intervention can influence the time of birth, but no previous analysis at a national level in England has yet investigated in detail the ways in which the day and time of birth varies by onset of labour and mode of giving birth. We linked data from birth registration, birth notification, and Maternity Hospital Episode Statistics and analysed 5,093,615 singleton births in NHS maternity units in England from 2005 to 2014. We built statistical models to establish how patterns of timing of birth vary by onset of labour, mode of giving birth and gestational age. We found that the timing of birth by time of day and day of the week varies considerably by onset of labour and mode of birth. These patterns have implications for midwifery and medical staffing.