Value of information (VOI) analysis is  "…a decision analytic technique that explicitly evaluates the benefits of collecting additional information to reduce or eliminate uncertainty"  (Yokota and Thompson 2004a).   As such, it covers a number of different approaches 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 the uncertainty of each input variable.  With the VOI method, the researcher can then estimate the effect of additional information to decision making and guide the further development of the analytical model(s) that underpin the assessment.

This review outlies different VOI methods, requirements of the analysis, mathematical background and applications. It concludes with a short summary of the previously published VOI reviews by Yokota and Thompson (2004a, 2004b).  A link to further information is also included under See also, below.

A family of analyses

The term value of information analysis covers a number of different decision analyses. 

Expected value of perfect information (EVPI) analysis estimates the value of completely eliminating uncertainty from a specified decision. EVPI analysis does not consider the sources of uncertainty, but only how much the decision would benefit if uncertainty were 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 an indication of the maximum gain that could be achieved by reducing uncertainty.  A more realistic approach is therefore provided by expected value of sample information (EVSI), or partial imperfect (ie. EVII) analysis, which estimates the gain (in terms of the quality of the decision) of reducing uncertainty of the model to a specified level.  Expected value of sample X information (EVSXI) (or EVPII) does the same in relation to a particular input variable.  The use of these two analyses increases requirements of the model since the targeted uncertainty level must be defined.  A further method - the expected value of including uncertainty (EVIU) - evaluates the benefit of allowing for uncertainty in the decision, but is beyond the scope of this review.

Estimating the value of information

VOI analysis estimates the difference between the expected utility of the optimal decision, given new information, and the expected utility of the optimal decision given current information. Yokota and Thompson (2004b) defined the EVPI as:

where: 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.  The detailed  mathematical background of different VOI analyses, and the solutions used in past analyses, are given by Morgan and Henrion (1992) and Yokota and Thompson (2004b).

Setting up the analyses

To be able to perform a VOI analysis a modeller needs information on:

1. the available decision options;
2. the consequences of each option; and
3. the uncertainties and reliability of the data.

In addition to these, both gains and losses of the options must be quantified using common metrics (monetary or non-monetary). 

Available decision options.  The first requirement for the VOI analysis is that the available options have been defined. In the economic literature the decision is usually seen, for example, as a question of whether or not to invest.  In the field of environmental health the decisions might represent choices between different control technologies or available regulations. In an ideal case, the possible options would have been explicitly defined by the authorities or the customer of the study.  More often, however, the available options are defined during the assessment process; effective methods of stakeholder communication are then needed during this stage to help identify the different options. In a research context, the possible options can be defined by the modeller or the modelling team.

Consequences of each option.  The second requirement is that the consequences of each possible option must be defined (e.g. the effect of a specified control technology on the emissions and, consequently, on human health).  These imply the development of a causal model of the system being analysed. 

Uncertainties and reliability of the data.  The third requirement is that the uncertainties and reliability of the data must be made explicit in the model.  Again, in the ideal case the uncertainties in the data will have been pre-defined, or the data are available in a form that enables the modeller to assess the uncertainties. In reality, the data are usually sparse, and the uncertainties must be assessed based on inadequate information - for example, from different point estimates reported in the different studies.  Expert elicitation and similar methods are available to define the uncertainties. In the absence of data, uncertainties may have to be evaluated by the modeller (author judgement).

The outcomes of the actions must be quantified using a monetary or non-monetary metric.  Again, in economic analyses, the common metric is by definition monetary. In the area of environmental health, metrics based on health effect (e.g. life expectancy, QALY, DALY) may be used. Inevitably, using summary measures such as these tends to increase the complexity and uncertainty of the model.

Applications for health impact assessment 

In environmental health impact assessment, the main use of value of information analysis is to help identify and manage uncertainties.  In this context, it provides a form of sensitivity analysis, aimed at determining:

• whether the assessment model contains explicit uncertainties, and if so in which parts;
• what are the key input parameters or assumptions in the model;
• which parts of the model need to be specified in more detailed.

All of these start from the question of whether or not model uncertainties have an effect on decision making.

VOI analysis can also be used, however, at other stages in the assessment.  At the screening stage, for example, it can help to determine whether to proceed with the assessment on the basis of readily available information or to wait and collect more information.   Likewise, during appraisal of the results, it can indicate whether the assessment provides a sufficient basis for action, or whether it would be more effective to delay intervention until more information as been gathered.  In the economic literature, this latter role is often seen as the main contribution of VOI analysis.  In the context of environmental health impact assessment, however, opportunities to seek or allocate more funding for additional research and data collection are rare, so VOI is less useful at the appraisal stage.

VOI analysis in past risk assessments

The use of value of information analysis in the medical and environmental fields has been extensively reviewed in two articles by Yokota and Thompson (2004a, 2004b).

The first review covers issues such as the use of VOI analyses in different fields, the use of different VOI analyses, and motivations behind the analyses.  In this, they trace the concept of VOI back to the 1960s.  The earliest applications in the medical and environmental fields date from the 1970s, but it has only been since 1985 that the use of VOI analysis spread more widely and grown more rapidly.  In most of the analyses the number of uncertain input variables has been between one and four.  EVPI or EVSI analyses have been the most common approaches, while EVPXI and EVSXI analyses have been relatively rare.  Applications extend across a number of different fields from toxicology to water contamination studies.  Yokota and Thompson (2004a) argue, however, that the published analyses show "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".   This may reflect the  complexity of these areas of application, and of the policy decisions that need to be made. 

The second review focuses in more detail on environmental health applications and the methodological development andthe challenges that the methods face.  Although the development of the personal computers has increased the analytical possibilities, a number of analytical problems  still exist. More fundamental, however, are the questions of how to model decisions, how to value the outcomes and how to characterise uncertainties.    In the field of environmental health impact assessment, it might be noted, identifying and modelling different decisions is probably the most challenging of these problems.