1. Structural uncertainty from an economists’ perspective
Laura Bojke
Centre for Health Economics, University of York
Looked at the issue of structural uncertainty – specifically relating to decision analytic models – during my phd. Here is just a very brief overview of some thoughts that emerged from it.

2. Structure of the presentation
Why structural uncertainty is a problem in decision modelling
What is structural uncertainty
Some examples
Methods available to characterise structural uncertainty
Outstanding issues/discussion points
I will go through the following points

3. Uncertainty in decision analytic models
Uncertainty is pervasive in any assessment of cost-effectiveness.
Need to produce accurate estimates of cost-effectiveness and assess if current evidence is a sufficient basis for an adoption decision.
Much of the focus on uncertainty in decision analysis has been on parameter uncertainty
Other forms of model uncertainty exist and these have received much less attention in the HTA literature .
The issue of structural uncertainty in particular is under researched.
I guess we all know why uncertainty is important in DAMs.
Parameter uncertainty in particular is well researched and the methods to characterise it are used widely. SU is under researched so I wanted to look at the issue in more detail for my phd.

4. What is structural uncertainty?
Aside from parameter and methodological uncertainties, other sources of uncertainty include the different types of simplifications and scientific judgements that have to be made when constructing and interpreting a model of any sort.
These have been classified in a number of different ways but can be referred to collectively as structural uncertainties.
Used to describe uncertainty that does not fit into other 2 categories.
Although definitions are of limited use it is important to know what we mean when we use the term SU. It is often used to describe uncertainties that are not parameter or methodological. A catch all group.

5. Examples from a review of the HTA literature
Inclusion/exclusion of potentially relevant comparators.
The selection of comparators should be informed by current evidence or opinion.
Choice of comparators is often governed by the scope of the model, and rarely are all possible comparisons made.
This is often the case where unlicensed comparators exist. Even if the excluded comparators are not cost-effective, excluding them may change EVPI estimates.
Inclusion/exclusion of potentially relevant events.
The process of simplification will inevitably require certain assumptions to be made.
These assumptions should be supported by evidence and choices between alternative assumptions should be justified and made transparent.
Events thought to be unrelated to treatment can have a noticeable impact on estimates of cost-effectiveness and EVPI.
Conduced a review of HTA models up to 2005 to look at examples of uncertainties that had been called structural or model uncertainties. There were around 12 examples and they allowed me to classify the structural uncertainties seen in DAM as 4 types.

6. Examples from a review of the HTA literature (2)
Statistical models to estimate specific parameters.
Decision models are using increasingly sophisticated statistical techniques to derive estimates of parameters.
This increased complexity can introduce statistical uncertainties.
May be alternative survival models – each plausible given data. Which model is best for survival beyond the observed period?
Clinical uncertainty or lack of clinical evidence.
A decision model may be commissioned on the basis of a lack of clinical evidence to inform a decision.
Even when RCT evidence is available there may be an absence of evidence about key parameters such as treatment effect, baseline event rates, clinical pathways, interaction between model parameters and clinical practice norms.
Often scenarios are presented based on alternative but extreme assumptions that could be made.

7. Identifying current approaches to characterise structural uncertainty
Undertook a review to find methods which explore the types of structural uncertainties apparent in DAM
Focus on analytical methods rather than qualitative methods of synthesis.
Very little published in HTA literature. Methods from statistics, mathematical and operational research are relevant.
3 methods are available:
Now that I had an idea of what types of uncertainties were thought of as structural uncertainties I wanted to look at methods to characterise these uncertainties explicitly. Focus on quantitative methods rather than just a narrative synthesis.

8. Available methods Scenario analysis: Model selection
Alternative assumptions presented as separate scenarios
Multiple models to digest
Model selection
Rank alternative models according to some measure of prediction performance, goodness of fit or probability of error
Choose the model that maximises that particular criterion
In HTA decision modelling it is difficult to define a ‘gold standard’ for outcomes and costs
Where there are many competing objectives, it is often not possible to identify one particular parameter whose performance must be maximised by a fitted model
Absence of data required to assess fit.
Not always advantageous to choose the best model – discards information on other alternative model
3 methods are available.

9. Available methods (2) Model averaging:
Build alternative models and average their results, weighted by some measure of their adequacy or credibility
Models can be assigned equal weights or differential weights can be determined using either ranking measures or derived using expert elicitation methods.
Bayesian methods for model averaging are commonly used in mathematics and statistics.
Issue of determining the posterior distribution of a parameter given the data, when the data may not be available
Non-bayesian methods can be used
Require a a measure of uncertainty that captures both uncertainty between expectations and uncertainty within expectations.
Model averaging must be undertaken for each realisation of the uncertain parameters so as not to underestimate uncertainty.

10. Available methods (3) Parameterising structural uncertainty:
Approach not identified in the review
Assumptions that distinguish different models or scenarios can often be thought of as either missing parameters or parameters assigned a single and often extreme value.
By generalising the model, to include additional ‘uncertain’ parameters the source of structural uncertainty can be represented directly in the analysis.
This approach is analogous to model averaging on individual or sets of model inputs.
Treats structural uncertainty like parameter uncertainty
A extension of model averaging that is possible – called this parameter sing structural uncertainty. In many circumstances model averaging and parameterising will give the same cost-effectiveness results. But allows value of information on uncertain parameters to be determined.

11. Case studies
See: Characterizing Structural Uncertainty in Decision Analytic Models: A Review and Application of Methods. Laura Bojke, Karl Claxton, Mark Sculpher, Stephen Palmer. Value in Health, 2009 forthcoming.
See case studies appling these methods in a forthcoming VIH paper.

12. Discussion points and further work
When is structural uncertainty really parameter uncertainty?
Is uncertainty that can be parameterised directly in the model structural uncertainty?
If not, what is structural uncertainty?
Do we really need a definition?
Do issues of what comparators to include/exclude relate to defining the decision scope?
Do issues of what events to include/exclude relate to specifying the correct model structure – avoiding over simplification?
Clear statement about the definiton of SU (or lack of need for any definition). Are some things not SU?

13. Discussion points and further work (2)
Should the focus be on establishing guidelines on how to structure a model?
Is a lot of structural uncertainty just modeller uncertainty?
Should we average across models?
Does this reflect uncertainty about structure?
How do we determine weights?
Expert opinion – method of elicitation, which experts?
Can we get rid of a lot of SU. Still issues about methods. Ultimately if we average or parameterise we need weights – expert elicitation. Develop methodology in DAM.