Value of information analysis
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Value of information (VOI) is a decision analysis method that estimates the benefits of collecting additional information. Yokota and Thompson (2004a) described VOI method as "…a decision analytic technique that explicitly evaluates the benefits of collecting additional information to reduce or eliminate uncertainty."
[1]
The term value of information covers a number of different analyses with different requirements and objectives.
To be able to perform a value of information analysis, the researcher needs to define possible decision options, consequences of each option, and uncertainty of each input variable. With the VOI method, the researcher can estimate the effect of additional information to decision making and guide the further development of the model. Thus, the VOI analysis can be used as a sensitivity analysis tool.
This review will shortly consider different VOI methods, requirements of the analysis, mathematical background and applications. In the end a short summary of the previously published VOI reviews by Yokota and Thompson (2004a, 2004b) [1] [2] , is provided.
A family of analyses
Term value of information analyses covers a number of different decision analyses. The expected value of perfect information (EVPI) analysis estimates the value of completely eliminating uncertainty from the particular decision. The EVPI analysis does not consider the sources of uncertainty, but how much the decision would benefit if uncertainty was removed. The VOI of a particular input variable X can be analysed with expected value of perfect X information (EVPXI) (or expected value of partial perfect information (EVPPI) analysis. The sum of all individual EVPXIs from all input variables is always less than EVPI.
The situations where uncertainty of the decision could be reduced to zero are exceptional, especially in the field of environmental health. Therefore, the results of EVPI and EVPXI analyses should be treated as maximum gain that could be achieved by reducing uncertainty. For more realistic approach, the expected value of sample information (EVSI) and expected value of sample X information (EVSXI) (or partial imperfect ie. EVII and EVPII, respectively) analyses could be used to estimate the value of reducing uncertainty of the model for a certain level or reducing uncertainty of the certain input variable for a certain level, respectively. The use of these two analyses increase requirements of the model since the targeted uncertainty level must be defined. The expected value of including uncertainty (EVIU) evaluates the effect of uncertainty in the specific decision problems and is out of the scope of this review.
Estimating the value of information
The VOI analyses estimate the difference between expected utility of the optimal decision, given new information, and the expected utility of the optimal decision given current information. Yokota and Thompson (2004b)[2] defined the EVPI (page 636):
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle EVPI = integral_{s belongs S} [max u_{a belongs A}(a,s)]f(s)ds - max[integral_{s belongs S} u_{a belongs A}(a,s)f(s)ds]}
In the equation, s is the uncertain input, and f(s) represents the probability distribution representing prior belief about the likelihood of s.
The complete review of different mathematical solutions is beyond the scope of this review and thus only the EVPI is presented here. Those interested to know more, the book Uncertainty: A guide to Dealing with uncertainty in Quantitative Risk and Policy Analysis (Morgan and Henrion 1992) [3] and recent methodological review by Yokota and Thompson (2004b)[2] describes more detailed the mathematical background of the different VOI analyses and the solutions used in the past analyses.
The set-up of the analyses
To be able to perform a VOI analysis a modeller needs information on (i) the available decision options, (ii) the consequences of each option, and (iii) the uncertainties and reliability of the data. In addition to these, both gains and losses of the options must be quantified with common metrics (monetary or non-monetary). In the following chapter these requirements are discussed in more detail.
The first requirement for the VOI analysis is that the available options have been defined. In the economic literature the decision is usually seen e.g. whether or not to invest. In the field of environmental health the decisions could be e.g. choices between different control technologies or choices between available regulations. In ideal case the possible options have been defined explicitly by the authorities or the customer of the study. More often the available options are defined during the risk assessment process and risk communication has a crucial part when identifying the different options. In pure academic research the possible options can be defined by the modeller or the modelling team.
The second requirement is that the consequences of each possible option must be defined (e.g. effect of some control technology for the emissions and consequently to human health). Number of methods, such as DPSEEA or IEHIA, are been used in the field of environmental health to identify and define the causal connections.
Third requirement is that the uncertainties and reliability of the data have been defined explicitly in the model. Again, in the ideal case the uncertainties of the data have been defined or the data is available so that the modeller can assess the uncertainties. In reality, the data is sparse and the uncertainties must be assessed based on e.g. two different point estimates reported in the different studies. Expert elicitation [4] and similar methods are available to define the uncertainties explicitly. In the absence of data the modeller's choice (author judgement) could be used to estimate the uncertainties.
The outcomes of the actions must be quantified with a monetary or non-monetary metric. Again, in the economic analyses the common metric is by definition monetary. In the environmental field the common metric could also be health effect or some summary metric of health effects (e.g. life expectancy, QALY, DALY). Of course, the use of e.g. QALYs increase the complexity and uncertainty of the model.
Applications for risk assessment
The value of information analyses can be used to guide the information gathering and model building. In the decision making, the decisions can be made based on available information or wait and collect more information. The VOI analysis can estimate the value of additional information for the decision and guide the decision between immediate actions and data collection. In the economic literature this is often seen as the main value of the VOI analysis. However, in the field of environmental health and risk assessment, situations where the decision maker can allocate more funding for additional research and data collection are rare, and this kind of exploitation of VOI analysis is more an exception than rule.
Another way to use VOI analyses is to guide the process of model building. In this case, the decision maker is the modeller or the modeller team who makes the decisions of the modelling work. Thus, the VOI analyses can be used like sensitivity analysis method. This use is also the most prominent use of VOI analyses in the field of environmental health and risk assessment. The decisions that can be addressed are e.g. (i) whether (and which parts of) the model should contain explicit uncertainties, (ii) what are the key input parameters or assumptions in the model, and (iii) which parts of the model should be specified more detailed. All of these start from the question whether or not model uncertainties have an effect on decision making.
VOI analyses in past risk assessments
The use of value of information analyses in the medical and environmental field applications has been extensively reviewed by Yokota and Thompson in two different papers [2]. The first review [1] covers issues such as (i) the use of VOI analyses in different fields, (ii) the use of different VOI analyses, and (iii) motivations behind the analyses, while the second review [2] focused in more detail on environmental health applications and the methodological development and problems. The following summary of the use of VOI analyses is based on these two reviews.
The concept of VOI has been defined in the 1960's. The first identified applications in the medical and environmental field are from the 1970's, but only after 1985 the use of VOI analyses have spread more widely and its use has grown rapidly. In most of the analyses the number of uncertain input variables has been 1-4. EVPI or EVSI analyses have been the most common, while the EVPXI and EVSXI analyses have been more exceptional. The reviewers noticed that the VOI analyses have been applied in a number of different fields from toxicology to water contamination studies.
The reviewers' view of the published analyses was that most of them were performed to show the usefulness of the analyses rather than actually use the results of analyses in the decision making. The review showed "a lack of cross-fertilization across topic areas and the tendency of articles to focus on demonstrating the usefulness of the VOI approach rather than applications to actual management decisions"[1]. This result may illustrates the complexity of the environmental and risk assessment field decisions. Authors also concluded that inside the medical and environmental field the different research groups are doing VOI analyses separately without citing or learning from other groups' work.
In the second review, the authors raised several analytical challenges in the VOI analyses [2]). These included e.g. difficulty to model the decisions, valuing the outcomes and characterizing uncertainties. Although the development of the personal computers has increased the analytical possibilities, number of analytical problems still exists.
Conclusions
The value of information is a decision analysis method that has been used and could be used in number of situations in the field of environmental health. The value of information covers a variety of different analyses with different scopes and requirements. The most difficult analytical challenges relate to the assessment of uncertainties in a model, valuing outcomes, and, especially, modelling different decisions. In the field of environmental health and risk assessment, identifying and modelling different decisions is probably the most challenging part of the analysis.
See also
- Value of information
- Value of information in Wikipedia
- Expected value of perfect information in Wikipedia
- Expected value of sample information in Wikipedia
Keywords
Value of information, decision analysis, optimising, uncertainty, ignorance
References
- ↑ 1.0 1.1 1.2 1.3 Yokota F. and Thompson K.M. (2004a). Value of information literature analysis: A review of applications in health risk management. Medical Decision Making, 24 (3), pp. 287-298.
- ↑ 2.0 2.1 2.2 2.3 2.4 2.5 Yokota F. and Thompson K.M. (2004b) Value of information analysis in environmental health risk management decisions: Past, present, and future. Risk Analysis, 24 (3), pp. 635-650.
- ↑ Morgan M.G. and Henrion M. (1992). Uncertainty: A guide to dealing with uncertainty in quantitative risk and policy analyses. Cambridge University Press. 332 pp.
- ↑ Cooke, R.M. (1991). Experts in uncertainty: Opinion and subjective probability in science. Oxfort university press, New York. 321 pp.
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