Our short course

We've opened officially registration for our short course on Bayesian methods in health economics (this is a link to last year's edition, with a little more information than the official webpage for this year's course). When we decided to do this, we agreed we'd have it rotating between UCL and the MRC Biostats Unit in Cambridge. This is where you can actually register.

The dates for this year are: Tuesday 24th - Thursday 26th November 2015 $-$ put that in your calendar!

The good, the bad and the ugly

This is me kind of whining $-$ although I do have some positive (and I think I'm right in whining).

First off: chapeau to the iHEA local organisers at Bocconi University in Milan! I think they've done an incredible job $-$ I think iHEA staff do help and get involved quite a lot in the organisation. But as far as I can tell, the whole thing went perfectly. In typical Italian style, the coffee and lunch breaks were really good, too (a nice change from previous iHEAs I went to).

Then the bad (here comes the whining)... As I mentioned here, this has been sort of a mixed conference experience, since I've not stayed in Milan for the whole time and have sort of commuted from Marta's parents' (they live on the lake). Anyway: yesterday I took the train to come back home after the afternoon sessions and I needed a ticket to the tram/metro to get to the train station. The first place I found on my way to the tram stop, told me that they had run out of tickets $-$ the man wasn't very friendly. "Go to the newsagent around the corner". So I went but as it turned out, they had run out too $-$ the man was even less friendly than the previous one. Third time lucky, I found another place who could sell me the €1.5 ticket, a bit further down the road $-$ by then I'd already walked a good 1/3 of the way.

Thanks to this, I just about manage to catch my train $-$ and here comes the ugly: firstly, the air conditioning wasn't working. Sitting next to me was an English family on holiday $-$ the little boy was wearing a Liverpool FC shirt which got so drenched with sweat I doubt he was able to take it off, last night... Then, when I got to my station and tried to get off the train, I simply couldn't because the door wasn't working. I did rush to the next carriage $-$ but that door didn't work either! Mid way my rush to the next-next carriage, the train left the station and I had to get off the next one $-$ luckily not very far from my stop.

Going to iHEA

iHEA's conference is kind of big deal in health economics: it's usually very big, with lots of sessions and lots of people participating. I have been to a few, both sides of the Atlantic and they are usually very good. This year it's in Milan (I think building on the Expo) and tomorrow I'm off to go. I'll be talking about the Structural Zero Costs model (not super-new $-$ I've mentioned this already here, here, here and here) in an interesting session on Tuesday.

It's always a bit weird, I think, going to conferences in Italy (or in London, for that matter) $-$ I think the spirit of being "away" at the conference kind of goes away. Still... I'm looking forward to some of the sessions!

Back to the future (or the day of the crises)

Yesterday was a very interesting day $-$ not sure if "interesting" is the best word to describe it, but for now I'll just use it...

We had our workshop on survival analysis in health economic evaluations, which instigated the first crisis of the day: Patricia Guyot, who was supposed to talk about digitising data from published studies, had to bail out $-$ this is somewhat similar to the Passport incident (except that that was entirely my fault, while this time, Patricia's train was delayed, which meant she missed her flight from Amsterdam). So, we had to reshuffle the order of the talks and make do with one less $-$ fortunately, both Nick and Chris had plenty of interesting things to say. In the end, the workshop was very good, I thought and I enjoyed it very much. The slides are available here.

On to the next crisis: when I got back to the office, there was a bunch of emails waiting for me to inform me that we may have a series of potential clashes with speakers not being able to give the talks they are supposed to, at the next ISBA World Meeting, at which our Section is organising a session (I will be talking about the RDD project). I think we managed to solve that crisis too $-$ luckily we had organised a session with 4 (instead of 3) speakers, so we could just lose one without impacting too much.

On to the next crisis: as I was finally riding my Vespa back home, I moved my phone from my jeans pocket to my jacket pocket. Or so I thought $-$ evidently it never made it to the jacket pocket and fell on the floor, without me noticing until I got home. So I've now been catapulted back to the 1980s with no phone or internet always with me... 

For example, I had to go to a meeting in a part of UCL where I'd never been, earlier today. But because I couldn't rely on a map on my phone, I had to print out a paper copy of all the references (name and phone number of the person I was supposed to meet, address, etc). Even though, spectacularly, I managed to lose the piece of paper with all this info in a matter of minutes (and I can't figure out how this may have happened!), I did get to the meeting on time.

Stress testing

Lately, we've been spending a lot of time "stress-testing" our method for the computation of the Expected Value of Partial Perfect Information (EVPPI $-$ I know: the terminology is a bit strange and possibly not-very helpful, as "perfect" information doesn't really exist, in statistical terms...).

I have mentioned this already here, here and here and the idea is to combine results from spatial statistics (and INLA) and Gaussian Process regression into the health economic problem. 

In a nutshell (I'll avoid all the technical details here), the "data" for our model consist on a vector of values $\mbox{NB}(\theta)$ (the "monetary net benefit", which determines the utility of a given health intervention) and a matrix of simulations from the (joint posterior) distributions of a set of relevant model parameters. The idea is that the multivariate parameter set can be split in a subset of "parameters of interest" ($\phi$), while the rest ($\psi$) are sort of "nuisance" or "unimportant" parameters. 

Following up on the work by Mark Strong et al, the relevant model can be written as
$$ \mbox{NB}(\theta) = g(\phi) + \varepsilon $$and the objective is to estimate the function $g(\phi)$, which is then used to compute the EVPPI. This saves up a huge computation time, in comparison to other methods.

In our model, we extended this framework and modelled
$$ \mbox{NB}(\theta) = H\beta + \omega + \varepsilon$$where $H\beta$ is a linear component depending on the simulations for all the "important" parameters, while $\omega$ is a spatially structured component, which accounts for the correlation among the important parameters. The big advantage is that using this formulation we are able to make inference based on INLA/SPDE, which is super-fast and can save up a lot of time even in comparison with the already fast "standard" Gaussian Process regression model.

Our first tests were giving very good results (as reported here). Then we've used a more complex model and found that while still being faster, our method was losing in accuracy for some specific parameters. This was a bummer, but it also meant that we had to go back and try and understand a bit better what was going on.

I'll make this sound very easy (when in fact Anna has spent a lot of time on this $-$ and wishing she never met me and started her PhD on this, I'm sure!), but eventually we figured out what the problem was. Firstly, in very complex situations (which are not that uncommon in real health economic evaluation problems), there may be quite a large correlation and non-linearity in the relationships among the parameters in $\phi$. This means that the combination of the standard linear predictor and the spatially structured effect cannot model properly the observed data, resulting in lower accuracy in the estimations. But, interestingly, extending $H\beta$ to include interactions among the relevant parameters can fix this problem, with only a small increase in computational cost.

Secondly (this is a bit more technical, but also quite interesting), the spatially structured component is based on constructing a mesh which describes the relationship between the parameters in a Euclidean space. If the "boundaries" of the resulting mesh are too close to the range of the observed points, then the estimation procedure will return several predictions at 0 $-$ in a rather vague sense, something like: the boundaries are areas where the estimated smooth curve is 0. But this means that in the computation of the EVPPI there is an artificially large number of 0 values, which produces an under-estimation of the "true" value.

We have fixed this by modifying the evppi function in the development version of BCEA and now the user can specify a non-linear part as well as fiddle with the INLA-specific parameters defining the mesh for the spatially structured component. The results seem to be much more accurate, still with some substantial computational savings. I'll try to put some R script to help people test the function (although I've also modified the help for evppi) to guide through the example involving the (simpler) Vaccine model

Job advert

This is an interesting post just advertised at Imperial College London by Marta.

Department of Epidemiology and Biostatistics

School of Public Health

Research Associate in Biostatistics

Salary: £33,410 to £42,380 per annum

Duration: 3 years fixed term

This is an exciting opportunity for a researcher with a PhD in statistics, biostatistics or a related quantitative subject to join the research team at the national MRC-PHE Centre for Environment and Health (http://www.environment-health.ac.uk/). The post is based within the Department of Epidemiology and Biostatistics and will be line managed by Dr Marta Blangiardo.

The post holder will work on the MRC methodology funded grant: “A general framework to adjust for missing confounders in observational studies” to develop a Bayesian statistical approach to integrate different sources of data and to use the propensity score for missing data imputation in the context of epidemiological observational studies. This is a collaborative project between Imperial College, LSHTM and Cambridge MRC-BSU.

You should have a thorough working knowledge of Bayesian modelling and some experience of working with spatial statistics and of analysing epidemiological/biomedical data. Familiarity with R/BUGS is essential. You should be motivated and extremely organised with experience of working in multi-disciplinary teams.

This full-time post is based at the St Mary’s Campus, Paddington and will be fixed term for three years. For informal enquiries please contact Dr Marta Blangiardo: m.blangiardo@imperial.ac.uk. Our preferred method of application is online via our website at http://www3.imperial.ac.uk/employment (please select “Job Search” then enter the job title or vacancy reference number into “Keywords”). Please complete and upload an application form as directed quoting reference number SM137-15AL.

Alternatively, if you are unable to apply online, please email smrecr@imperial.ac.uk to request an application form. Closing date: 22nd July 2015 (midnight BST)

Back log

Last week I went to Madrid to examine a PhD (I've mentioned this in another post). The thesis was focussed on a mixture of computer science and health economics $-$ in particular, much of the work was about developing suitable algorithms for running efficiently Markov models using extensions of tools such as Influence Diagrams. 

I have done some work on related issues when I was doing my own PhD, back in the 1900's, so I was interested in this work and it was good to being "forced" to read about it, now.

The main innovation is the development of algorithms and a specific software, called OpenMarkov. From my perspective, this can be a very good tool, especially when compared with Excel, which is still used by many practitioners to develop their Markov models for economic evaluation.

The main advantage over Excel is that OpenMarkov allows the user to specify a graphical structure for the model and then define a set of conditional probability tables to determine the transition probabilities from one state to another. Interestingly, it is also possible to use (some) probability distributions to represent these, which is good to then perform probabilistic sensitivity analysis (PSA).
What is currently missing is the possibility of propagating evidence to estimate the value of the main parameters (ie the transition probabilities, or functions thereof). So, you have to "know" what the values or distributions are for the transition probabilities when running the model. In this sense, I see OpenMarkov (at least in its current version!) as an "advanced version" of Excel-based models.

This of course has implications in terms of PSA, since while you can allow for multiple parameters to be modelled using a probability distribution, you're likely to miss on the potential underlying correlation. A full Bayesian model (for example like those described in BMHE) would overcome this problem $-$ perhaps at the expense of increasing the model complexity. But, as I said in my talk, if you have complex problems and you want to model them efficiently, then you probably shouldn't be too surprised that the models are complex and suitable tools are needed...

All in all, I did like the idea of OpenMarkov quite a lot, though $-$ particularly, I thought that there may be quite some scope for integrating it with R/BCEA (or similar tools), which would be very useful in many applied cases (as Markov models are extremely popular in health economics!). I may even try and play around with it, if I find a good student willing to do so...

Survival of the fittest (health economic model)

To make up for the fact that we've missed a couple of slots over the past months in our seminar series, we thought we organised a more structured event. 

So, our next seminar will in fact be a workshop and will be held at UCL on 7 July from 1.30pm to 4.30pm, room 102 on the first floor of 1-19 Torrington Place. 

The title is "Statistical issues in modelling survival data for health economic evaluation" and we have an exciting line-up of speakers. 

Nick Latimer will first introduce the general issue of statistical modelling of survival data and extrapolation in health economics and then discuss the interesting issue of treatment switching. Chris Jackson will present and discuss flexible methods to perform extrapolation of survival data and the combination of evidence. Finally, Patricia Guyot will then discuss methods to reconstruct individual survival data from published survival curves.

The tentative timetable of the event is the following:

• 1.30-1.50: Nick Latimer (HEDS, ScHARR. University of Sheffield): Standard survival analysis techniques - methods typically used in HTA
• 1.50-2.35: Chris Jackson (MRC Biostatistics Unit, Cambridge): Improving long-term survival estimation through flexible models, combining evidence and accessible software
• 2.35-2.50: Coffee break
• 2.50-3.15: Nick Latimer (HEDS, ScHARR. University of Sheffield): Methods for adjusting survival estimates in the presence of treatment switching
• 3.15-4.00: Patricia Guyot (Mapi, Utrecht, Netherlands): Reconstructing Kaplan Meier data from published survival curves
• 4.00-4.30: Discussion

If you didn't know about this from our mailing list and still would like to attend, please drop me an email, so we can arrange and avoid space issues!