RAMAS^® Risk Imaging
Risk Visualization under Uncertainty

Medical imaging technologies such as MRI, ultrasound, and computed tomography have revolutionized medicine.  We believe that risk analysts, regulators, decision makers, and the public would benefit if analogous imaging techniques were available to penetrate the cloud of uncertainty and disagreement surrounding risk data.  RAMAS Risk Imaging software provides visualizations of risk in the face of uncertainty regarding the frequency of adverse events and of uncertainty regarding the severity of adverse events. 

Psychometric and socio-cultural theories of risk perception emphasize the disparity between expert risk assessments, which focus on the frequency of adverse events of measured magnitudes, and lay assessments, which are conditioned by additional qualities of the hazard and of the risk perceiver.  The RAMAS Risk Imaging approach treats this disparity as a form of uncertainty and employs methods to bound variability and incertitude in risk assessments. 

Risk is perceived differently by different individuals and interest groups.  RAMAS Risk Imaging visualizes risk by quantifying attitudes regarding the importance of uncertainty, the meaning of disagreements between measurements or opinions, and the meaning of absence of evidence.  Visualizations of risk are generated for different risk perceivers.  Comparing and contrasting these visualizations facilitates communication and decision making.

Although the development of this software was guided by theory formulated in risk perception and risk communication research, the method is theoretically eclectic and meant to be adaptable to a wide range of applications and levels of analysis.  The commonality expected across applications is the need of risk analysts and decision makers to convert highly uncertain measurements of the frequency and adversity of multiple harms associated with a potential hazard into an image of risk as variably perceived by different individuals and interest groups.  Risk perception, as conceived in this sense, is unlike an MRI image in that there is no “correct” perception to be recorded.  Occupational, environmental, and health risks are experienced and perceived in the context of culturally complex and highly politicized arenas.  An analysis informed and colored by these complexities is required.  RAMAS Risk Imaging is intended as an aid in the production of uncertainty-informed risk assessment.

Approach

RAMAS Risk Imaging requires data regarding the frequency and the adversity of each harm due to a hazard. This data may come from various sources, including controlled trials, surveys, and expert opinions and judgments. Each of these sources results in an uncertain estimate of the true frequency and/or adversity of the harms that comprise a hazard. RAMAS Risk Imaging uses both the uncertain estimates and the uncertainty associated with them to generate an image of risk.

The RAMAS Risk Imaging approach follows four steps in the visualization of risk. The first step is to decompose the risk into it's frequency and adversity components. The next step is to incorporate quantitative uncertainty into these components using methods such as interval arithmetic, info-gap, ordination based upon revealed preferences, and dependency bounding. The third step is to re-compose the risk as a function of uncertain frequency and uncertain adversity. The final step is to focus the risk image on particular risk perceptions by specifying attitudes towards risk and uncertainty.

Example: Risk from hypertension drugs

Uncertain adversity and uncertain frequency of seven adverse reactions to benazepril are shown below. The dashed black lines forming a box show bounds around frequency and adversity combinations for headache that are consistent with the uncertain data. Note that the vertical axis is truncated at 0.1 for the purpose of display.

Next, we combine the risks of each harm, allowing for any and all possible forms of dependence between them, to produce a risk profile of the drug.  The figure below shows the risk profile.

Finally, we can focus this visualization of risk to examine the risk perceptions of individuals with different attitudes towards risk and uncertainty. The attitude control panel is shown below. It contains three attitudes which may be adjusted to focus the risk image on particular perceptions. Burden of proof quantifies the perceiver’s attitude towards the meaning of absence of evidence. Dispute tolerance probes the risk perceiver’s interpretation of differences in opinion and judgment, differences in models, and differences in information regarding the severity of an adverse event. Uncertainty display gauges the risk perceiver’s attitudes towards the importance of uncertainty in a risk assessment.

Adusting the attitude sliders changes the image of perceived risk. The figure below shows some of the ways the risk image changes when the Burden of proof settings are adjusted.

Requirements:  See RAMAS Risk Imaging Technical Requirements.

Cost: See Software Price List and Ordering Information.

RAMAS^® Risk Imaging software was developed with funding from Pfizer Inc., and it is jointly owned by Pfizer Inc. and Applied Biomathematics. The product will be shipped beginning June 1, 2005.

Links and references

Alba, J.W., W. Chromiak, L. Hasher, and M.S. Attig. 1980. Automatic Encoding of Category Size Information. Journal of Experimental Psychology: Human Learning and Memory 6:370-378.

Atman, C.J., A. Bostrom, B. Fischhoff, and M.G. Morgan. 1994. Designing Risk Communications: Completing and Correcting Mental Models of Hazardous Processes, Part I. Risk Analysis 14(5):779-788.

Barkow, J.H., L. Cosmides, and J. Tooby (eds.). 1992. The Adapted Mind: Evolutionary Psychology and the Generation of Culture. New York: Oxford University Press.

Bostrom, A., C. Atman, B. Fischhoff, and M.G. Morgan. 1994. Evaluating Risk Communications: Completing and Correcting Mental Models of Hazardous Processes, Part II. Risk Analysis 14(5):789-798.

Cosmides, L. and J. Tooby. 1996. Are Humans Good Intuitive Statisticians after All? Rethinking some Conclusions from the Literature on Judgment under Uncertainty. Cognition 58:1-73.

Crow, E.L., F.A. Davis, and M.W. Maxfield. 1960. Statistics Manual. New York: Dover Publications, Inc.

Fischhoff, B. 1995. Risk Perception and Communication Unplugged: Twenty Years of Process. Risk Analysis 15(2):137-145.

Fischhoff, B., P. Slovic, S.Lichtenstein, S. Read, and B. Combs. 1978. How Safe is Safe Enough? A Psychometric Study of Attitudes towards Technological Risks and Benefits. Policy Sciences 9:127-152.

Florig, H.K., M.G. Morgan, K.M. Morgan, K.E. Jenni, B. Fischhoff, P.S. Fischbeck, and M.L. DeKay. 2001. A Deliberative Method for Ranking Risks (I): Overview and Test Bed Development. Risk Analysis 21(5):913-922.

Fréchet, M. 1935. Généralisations du théorème des probabilités totales. Fundamenta Mathematica 25: 379–387.

Gigerenzer, G. 2002. Calculated Risks: How to Know when Numbers Deceive You. New York: Simon and Schuster.

Gigerenzer, G. and A. Edwards. 2003. Simple Tools for Understanding Risks: from Innumeracy to Insight. British Medical Journal 327:741-744.

Gigerenzer, G. and P.M. Todd, the ABC Research Group. 1999. Simple Heuristics that Make Us Smart. New York: Oxford University Press.

Glimcher, P.W. 2003. Decisions, Uncertainty, and the Brain: The Science of Neuroeconomics.MIT Press: Cambridge, MA.

Glimcher, P.W. and A. Rustichini. 2004. Neuroeconomics: The Consilience of Brain and Decision. Science 306:447-452.

Hammond, K.R. 1996. Human Judgment and Social Policy: Irreducible Uncertainty, Inevitable Error, Unavoidable Injustice. New York: Oxford.

Hasher, L. and W. Chromiak. 1977. The Processing of Frequency Information: An Automitic Mechanism? Journal of Verbal Learning and Verbal Behavior 16:173-184.

Hasher, L. and R.T. Zacks. 1979. Automatic and Effortful Processes in Memory. Journal of Experimental Psychology: General 108:356-388.

HSE (Health Safety Executive). 2001. Reducing Risks, Protecting People: HSE’s Decision-making Process. Previously available for download at http://www.hse.gov.uk/dst/r2p2.pdf, but now gone after "a large scale review".

Kasperson, R.E. 1992. The Social Amplification of Risk: Progress in Developing an Integrative Framework. Chapter 6 in Social Theories of Risk, S. Krimsky and D. Golding (eds.), Praeger, Westport, Connecticut.

Löfstedt, R.E. 2003. The Precautionary Principle: Risk, Regulation, and Politics. Trans IchemE 81(B):36-43.

Löfstedt, R.E. and O. Renn. 1997. The Brent Spar Controversy: An Example of Risk Communication Gone Wrong. Risk Analysis 17(2):131-136.

Löfstedt, R.E. and D. Vogel. 2001. The Changing Character of Regulation: A Comparison of Europe and the United States. Risk Analysis 21(3):399-416.

MacGregor, D.G., P. Slovic, and T. Malmfors. 1999. How Exposed Is Exposed Enough? Lay Inferences about Chemical Exposure. Risk Analysis 19(4):649-659.

Morgan, K., M.L. DeKay, P.S. Fischbeck, M.G. Morgan, B. Fischhoff, and H.K. Florig. 2001. A Deliberative Method for Ranking Risks (II): Evaluation of Validity and Agreement among Risk Managers. Risk Analysis 21(5):923-938.

Morgan, M.G., B. Fischhoff, A. Bostrom, and C.J. Atman. 2002. Risk Communication: A Mental Models Approach. New York: Cambridge.

Morgan, M.G. and M. Henrion. 1990. Uncertainty: A Guide to Dealing with Uncertainty in Quantitative Risk and Policy Analysis. Cambridge University Press, New York.

NRC (National Research Council. 1989. Improving Risk Communication. Washington D.C.: National Academy Press.

Physician’s Desk Reference> (PDR). 1993. 47^th Edition.Montvale, New Jersey: Medical Economics Data.

Pinker, S. 1984. Language Learnability and Language Development. Cambridge, MA: Harvard University Press.

Raynor, S. 1992. Cultural Theory and Risk Analysis. Chapter 4 in Social Theories of Risk, S. Krimsky and D. Golding (eds.), Praeger, Westport, Connecticut.

Renn, O. 1992. The Social Arena Concept of Risk Debates. Chapter 7 in Social Theories of Risk, S. Krimsky and D. Golding (eds.), Praeger, Westport, Connecticut.

Shepard, R.N. 1992. The Three-dimensionality of Color: An Evolutionary Accommodation to an Enduring Property of the World? In J.H. Barkow, L. Cosmides, and J. Tooby (eds.), The Adapted Mind: Evolutionary Psychology and the Generation of Culture. New York: Oxford University Press.

Sjoberg, L. 1998. World Views, Political Attitudes and Risk Perception. Risk: Health, Safety and Environment 9:137-152.

Slovic, P. 1987. Perception of Risk. Science 236:280-285.

Slovic, P. 1992. Perception of Risk: Reflections on the Psychometric Paradigm.Chapter 5 in Social Theories of Risk, S. Krimsky and D. Golding (eds.), Praeger, Westport, Connecticut.

Slovic, P. 1999. Trust, Emotion, Sex, Politics, and Science: Surveying the Risk-assessment Battlefield. Risk Analysis 19(4):689-701.

Slovic, P. and E.U. Weber. 2002. Perception of Risk Posed by Extreme Events. Paper prepared for discussion at the conference “Risk Management Strategies in an Uncertain World,” Palisades, New York, April 12-13.

Sokal, R.R. and F.J. Rohlf. 1994. Biometry (3rd Edition). Freeman and Company, New York.

Weber, E.U. 2003. Origins and Functions of Perceptions of Risk. Presented at the NCI Workshop on Conceptualizing and Measuring Risk Perceptions, February 13-14.

Willis, H.H., M.L. DeKay, M.G. Morgan, H.K. Florig, and P.S. Fischbeck. 2004. Ecological Risk Ranking: Development and Evaluation of a Method for Improving Public Participation in Environmental Decision Making. Risk Analysis 24(2):363-378.

Glossary

Adverse effect: A harm, such as a headache, a blood pressure reading, a liver function test result, a death, etc. due to a hazard.

Adversity: The measured amount of harm caused by an adverse effect. Adversity may be measured on an ordinal or rational scale.

Affect: A positive or negative emotional response to a hazard.

Aggregation: A mathematical operation performed to characterize a group of estimates with a single quantity. Common aggregations include an average (mean), a median, or a mode.

Average: An aggregation operation calculated by summing estimates and dividing by the number of estimates. Average estimates a central tendency of the estimates, but is sensitive to outlying extreme estimates. See also Mean.

Attitudes towards uncertainty: Quantified parameters specifying a relationship between uncertainty and perception of risk. The attitudes quantified in RAMAS Risk Imaging are Burden of proof, Dispute tolerance, and Uncertainty display.

Best possible bound: An uncertainty bound that is guaranteed to enclose the true frequency or the true adversity but which is no wider than is necessary given the stated uncertainty.

Bound: An upper bound of a set of real numbers is a real number that is greater than or equal to every number in the set. A lower bound is a number less than or equal to every number in the set. If an upper bound cannot be any smaller, or a lower bound cannot be any larger, it is called a best possible bound.

Burden of proof: A quantified attitude that relates the perception of risk to uncertainty regarding the best estimate or central tendency of risk data. Burden of proof ranges from evidentiary to precautionary. A preference for evidentiary burden of proof requires evidence that there is a harm before risk is perceived. A preference for precautionary burden of proof requires that risk is perceived unless evidence for no harm exists.

Categorical scale: A scale that gives a label to individual data points. No natural order exists for these labels and they cannot be sorted from smallest to largest. A categorical scale is also known as a nominal scale.

Central tendency: The value or values around which a series of values varies. Central tendency is often measured with the mean, median, or mode.

Comprehensive bound: A bound around frequency, adversity, or risk that is guaranteed to completely enclose the true value.

Confidence interval: A range of values that contains a parameter value with given probability. A 99% confidence interval gives a range that contains the true value with 99% confidence.

Confidence limits: See Confidence interval.

Consensus: An attitude towards uncertainty that requires a single value or a restricted range of values to represent a larger range of estimates. A consensus can be achieved through negotiation or through aggregation or weighted aggregation. The opposite of consensus is inclusion.

Dependence: A relationship between two or more events or random variables such that the occurrence or value of a particular event or variable gives some information regarding the occurrence or value of another.

Dispute tolerance: A quantified attitude that relates the perception of risk to uncertainty regarding the magnitude of adversity. Uncertainty in adversity may be due to differences in opinion and judgment, differences in models, and differences in information regarding. Dispute tolerance ranges from consensus to inclusion. A Risk perceiver inclined toward consensus feels that the median, average, or modal adversity is the adversity perceived. An individual inclined towards inclusion perceives the disagreement between estimates or opinions to be a part of the risk.

Equity: An emotional and rational concept of fairness regarding the distribution of risk exposure and the distribution of benefits from risk exposure.

Focus: The use of attitudes regarding uncertainty to narrow a risk image and visualize a particular risk perception.

Fréchet uncertainty bounds: Comprehensive bounds that are guaranteed to enclose the true frequency no matter what dependence exists between harms. Fréchet bounds on a joint distribution H(x,y), specified by having marginal distributions F(x) and G(y), given by max(F(x) + G(y) – 1,0) ≤ H(x,y) ≤ min (F(x), G(y)). Also known as Fréchet-Hoeffding limits.

Fréchet inequalities: Equations making it possible to bound joint events using only the marginal probabilities and no information about dependence. The resulting bounds are both comprehensive and best possible in the absence of dependence information.

Frequency: Counts of event occurrences, often expressed as proportions of occurrences to a count of all members of a reference class at risk of occurrence.

Harm: A bad outcome or adverse effect of a hazard. Hazards must have at least one, and may have many, harms.

Hazard: Anything presenting the possibility of danger or risk. Adverse effects due to hazards are called harms.

Image: A graphical representation of digital data.

Incertitude: Uncertainty due to ignorance or imperfect of knowledge. Also known as epistemic uncertainty, ignorance, subjective uncertainty, Type II or Type B uncertainty, reducible uncertainty, and state-or-knowledge uncertainty.

Inclusion: An attitude towards uncertainty and risk that requires that variability in estimates, opinions, or judgments be maintained. Average estimates or opinions are not preferred because there is no reason to believe that the commonness of an opinion increases the likelihood that it is true.

Independence: Two or more variables are independent if knowing the value of one variable tells you nothing about the value of another.

Interval: A segment of the real line existing between a minimum and a maximum value. Closed intervals have specified minima and maxima, open or half-open intervals do not. In RAMAS Risk Imaging, the term “interval” is also used to denote a range of ordinal values between a minimum and a maximum.

Justice: An emotional and rational concept requiring the impartial assignment of benefits or costs based upon individual merit.

Lower limit: A value of frequency or of adversity which is less than or equal to the true but unknown frequency or adversity. Also called a lower bound.

Mean: A common measure of central tendency. The arithmetic mean is the sum of the values divided by the number of values in the sample. The median is preferred to the mean as a measure of central tendency if the distribution of values is skewed.

Median: A measure of the central tendency of a series of values. The median is the value that splits the distribution of the sorted sample in half.

Mode: A measure of central tendency. The mode is the most common value in a series of values.

Ordinal: Ordered numerically in a series, where values may be ranked from least to most but the distances between the ranked values are arbitrary or otherwise unknown.

Ordinal ranking: An ordinal value given to a data point that specifies its value relative to other ordinally valued data, but which does not specify an arithmetic distance between values.

Ordinal scale: A scale in which values can be rank ordered, but in which the distances between points are arbitrary or otherwise unknown.

Point value: A completely certain value assigned to an estimate.

Precautionary principle: An attitude that relates uncertainty to risk perception by specifying that unknown risk should be assumed harmful until proven safe.

Probability: The chance an event will occur, expressed on a scale from 0 (impossible) to 1 (certain), or as a percentage between 0 and 100%

Profile: See Risk profile.

Ranking: See Ordinal ranking.

Rational scale: A scale of measurement that allows values to be ranked from smallest to largest, and the distance between values is a meaningful measure of how much greater or lesser one value is relative to any other value.

Risk: In RAMAS Risk Imaging, risk is the frequency that harmful events are expected to occur multiplied by the expected harm.

Risk image: An image or display of digital data describing the risk of harm from one or more hazards. In RAMAS Risk Imaging, the risk image includes the uncertainty regarding both the expected frequency and the expected magnitude of each hazard.

Risk image display: The main graph in RAMAS Risk Imaging where the risk image is shown.

Risk perception: A conclusion regarding actual or potential risk based upon risk data and attitudes towards uncertainty and risk. Individuals perceive risks and groups of individuals with similar attitudes and exposed to similar risk data perceive similar risks.

Risk profile: An image of risk due to all of the potential harms associated with a hazard. A risk profile may be a series of point values if the risk perceiver’s attitudes require complete disregard of uncertainty. Otherwise, a risk profile is an area in frequency/adversity space enclosed by uncertainty bounds.

Risk threshold line: A line specified by regulations, standards, or norms, that is drawn on the risk display for the purpose of comparing with risk profiles. A Basic Safety Objective (BSO) is an example of a risk threshold line.

Severity: The magnitude of adversity or harm. Severity may be measured on an ordinal or a rational scale.

Stereotype: A particular set of attitudes towards uncertainty and risk that describe an individual’s or an interest group’s risk perception.

Trust: An emotional and rational concept linking inferred motives to requirements for equity, justice, and competence. Trust affects attitudes towards uncertainty and risk, which in turn affect risk perception.

Uncertainty: The absence of perfectly detailed knowledge. Uncertainty includes incertitude (the exact value is not known) and variability (the value is changing). Uncertainty may also include other forms such as vagueness, ambiguity and fuzziness (in the sense of border-line cases).

Uncertainty display: A quantified attitude that relates the perception of risk to uncertainty regarding both the uncertain magnitude of a harm and the uncertain frequency with which it may occur.

Uncertainty bound: A bound around frequency, adversity, or risk that is intended to enclose the true but unknown value.

Upper limit: A value of frequency or of adversity that is greater than or equal to the true but unknown frequency or adversity. Also called an upper bound.

Variability: The fluctuation or variation due to randomness or stochasticity. Variability is also associated with aleatory uncertainty, stochastic uncertainty, Type I or Type A uncertainty, irreducible uncertainty, and objective uncertainty.

Visualization: The result of focusing a risk image to view only a particular set of risk perceptions. A risk perception is visualized by specifying attitudes towards uncertainty and risk.