With [Rumana Omar](https://www.ucl.ac.uk/statistics/people/rumanaomar), [Gareth Ambler](http://www.ucl.ac.uk/statistics/people/garethambler), [Andrew Copas](https://iris.ucl.ac.uk/iris/browse/profile?upi=AJCOP98) and [Emma Beard](http://www.ucl.ac.uk/hbrc/tobacco/bearde.html)
Introduction SWSamp is an R package designed to allow a wide range of simulation-based sample size calculations, specifically (but not exclusively!) for a Stepped Wedge Trial (SWT) and is based on the general framework described in Baio et al (2015). In its current version, SWSamp consists of 5 main functions: the first one (which is currently in fact specified by three different commands) performs the analytic sample size calculations using the method of Hussey and Hughes (2007).
Introduction Sample size calculations are one of the fundamental components in the design of experimental studies and are mandatory in virtually all settings involving randomised trials, eg in medical research. Sample size calculations aim at determining the smallest sample that is necessary to observe, under a given design (eg distributional assumptions and expected characteristics of the intervention(s) being assessed), in order to correctly determine the “signal” (eg the “treatment effect”) as statistically significant and thus not due to chance.
Final time — the model (and bookies) predictions have indeed materialised and Italy face England in the final. I’ve done the final update after the semi-finals and here’s the model prediction.
Italy are favourite — I think this is probably right, though I also believe it’ll probably be a slightly closer game. The bookies go the other way and, I think a bit overly-enthusiastically, tip England to be just above Italy (the odds map to probabilities of about 31% for Italy to win, 37% for England to win and 32% for a draw).
I haven’t posted the results for the quarter-finals ahead of the games, but I did run the model and here were the predictions.
Not too bad, in the end: the model did get that Spain-Switzerland would be a tough one and the resulting 1-1 was one of the most likely outcomes. Similarly, while giving Belgium a bit of an edge, the model had predicted that their clash with Italy would be very close and the eventual 2-1 win for the Azzurri (yay!
OK: I’ve now re-run the model using the updated data including all the games after the group stage. Firstly, a few comments/caveates:
I think the model predictions for the round of 16 make kind of sense and I’m reasonably happy with them.
BUT: there’s lots that the model doesn’t really know… For example, I’ve made no real adjustment for the fact that this batch of games is at the knockout stage, which means that, probably, we may see fewer goals as some teams may have a different attitude and would rather not lose the game at the 90th minute, in search of penalty glory.
This is a follow up on my previous post. The group stage is now finished and I have updated the model as more games were being played. In particular, I have slightly changed the set up by adding a smooth time trend, modelled as a RW(2), based on the date in which each game in my dataset was played (considered as a unique identifier). This basically accounts for the “historical performance” by each team and has slightly improved the model performance, I think.
I wasn’t going to do much about this (and probably, I shouldn’t have done anything and used my time more wisely…), but a couple of friends/colleagues have actually asked me if I had done it and Italy did so well in their first outing, that I was up last night to whip something up… 😉 (in case it’s not clear yet, yes: this is a post on using Bayesian modelling to predict the outcome of football games, specifically for the ongoing Euro championships).
This is, in many ways, very old news — but last summer (sic!) I applied for and was made the new Head of Department of UCL Statistical Science (and I think — checks in place — for the first time since the department was founded in 1911, the post has gone to somebody who isn’t British or from a Commonwealth country, of which I’m very proud — again, pending checks…).