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Risk Estimation

by: Daniel Kewski

In simplified terms, risk (R) may be defined by the formula R = P x C, where the term P denotes the probability of an adverse event occurring, and the term C denotes the consequence of that event.  This definition demonstrates that a high risk can occur because of either high probability P, or high consequences C, or both.  The special case of low probability/high consequence (LP/HC) events refer to situations such as a major earthquake, tsunami, or nuclear reactor failure, in which the occurrence of a rare event can lead to disastrous consequences.

Experts in risk science may employ a broader version of the above definition of risk in their work (Kaplan & Garrick, 1981).   In its most general form, the symbol  ‘x’ does not necessarily denote multiplication; rather, it is intended to denote a more general operator that combines probability and consequences in some appropriate manner that is specific to the risk issue under consideration.  In this broader context, experts may describe risk in the form of a probability distribution, showing a range of possible consequences and the probability of each.  The expected value of this distribution of risk provides a summary measure of risk that is consistent with the simplified formula, R = P x C.    
When the consequences are understood to be fixed, discussions about risk often focus on the probability dimension of risk.  For example, the probability of developing a particular adverse health outcome, such as heart disease, may be calculated, and compared with the probability of another outcome, such as cancer.   In western countries, the lifetime probability of dying from heart disease is approximately 1 in 3, whereas the lifetime probability of dying from cancer, 1 in 4, is slightly lower. 

To be precise, other characteristics of the population at risk need to be specified.  Are we concerned about the risk to the entire population, or a subset of the population defined in terms of age, gender, or ethnicity? For example, the annual risk of dying from heart disease will be notably different for males between 85 and 90 years of age (one in 15) than for males 25 to 30 years of age (one in 21,000) (Thomas and Hrudey, 1996).  Are we concerned about the population of an entire country, or a city or province within that country?  And are there genetically susceptible subpopulations, for which the probability of developing a particular health outcome may be notably higher than in the general population?

Risk can vary appreciably among individuals in a population, and may be assessed at both the individual and population level.  Risk estimates for individuals will be more accurate if the individual factors that affect risk including age, gender, genetics, and lifestyle factors – are taken into account.  Population level risk estimates take into account individual variability in risk by effectively averaging individual risks across the population.

Epidemiologists have developed useful measures of risk to describe the impact of a particular hazard of the population of interest.  The population attributable risk (PAR), or attributable fraction (AF), represents the percentage of the disease burden in that population that would be avoided if the hazard were eliminated (Last, 2001).   For example, the World Health Organisation has estimated that about 10% of all lung cancer cases worldwide would be avoided if exposure to radon in homes were eliminated (World Health Organization, 2009).   
As a second example, researchers have recently estimated that the global fraction of adult mortality due to fine particulate air pollution generated through human activity to be approximately 8% for cardiopulmonary disease, 13% for lung cancer, and 9% for ischemic heart disease (Evans et al., 2012).  These estimates were obtained by using advanced satellite imaging techniques to predict air pollution levels in 192 countries included in the study.  Such analyses are useful in evaluating the global burden of disease associated with a range of health hazards, and in setting priorities for risk mitigation (World Health Organization, 2010).

Population level risk can also be measured in terms of the reduction in life expectancy due to a particular risk factor.   In the United States, a moderate increase in fine particulate air pollution levels of 10 µg/m3 in urban air has also been estimated to reduce life expectancy by about 6 months (Pope et al., 2009).  A more refined measure of the impact of a given risk factor on population health is the reduction in quality adjusted life expectancy (QUALY), which takes into account both quality of life and loss of life.

The total number of years of life lost – referred to as person-years of life lost (PYLL) – due to exposure to a particular risk factor can also be used to characterize risk at the population level.  As with life expectancy, quality of life can also be incorporated into the calculation of the PYLL, in measures such as disability-adjusted years of life lost (DALYs) or health-adjusted years of life lost (HALYs).

Risk can be expressed in relative terms, in the form of a ratio of the risk under one set of circumstances to the risk under another set of circumstances.  For example, the risk of a motor vehicle accident while using a cellular telephone while driving is 4 times greater than the risk of an accident when not using a cellular telephone, for a relative risk of 4-fold (McEvoy et al., 2007). Stated another way, the risk of a motor vehicle accident is increased by 400% when using a cellular telephone while driving. 

Because people are exposed to a number of different hazards, the notion of the cumulative risk from a set of similar hazards is of interest (U.S. National Research Council, 2009). Hazardous air pollutants present in ambient air, such as particulate matter, ozone, and volatile organic pollutants, each carry some degree of risk; from the population health perspective, it is important to seek to minimize the cumulative risk associated with all of the pollutants present in ambient air combined.

When assessing the risk associated with multiple hazards, consideration needs to be given to possible interactions among those hazards. A synergistic interaction occurs when the combined risk associated with two or more hazards is greater than the sum of the risks associated with the individual hazards.  An example of this is provided by tobacco smoking and occupational exposure to radon in underground mines (Moolgavkar et al., 1993).  Whereas a heavy cigarette smoker or an underground miner exposed to high levels of radon that existed in the past before effective mine ventilation may each be at a 12-fold increased risk of lung cancer, the relative risk of lung cancer in a heavy smoking miner also exposed to high radon levels is over 50-fold, much higher than the sum (12 + 12 = 24-fold) of the individual risks of lung cancer for tobacco smoking and occupational radon exposure alone.  In this example, risk is expressed in relative terms, with the 12-fold increase in lung cancer risk associated with either radon or tobacco smoking representing the relative risk (RR) of these exposures, defined as the lung risk in the presence of exposure divided by the lung cancer risk in the absence of exposure.  

The most appropriate measure of risk to use in a particular risk assessment application will depend on the risk context in which the assessment is being done.  Risk analysts will consider the nature of question they have been asked to consider, usually within the broader risk management context, and choose one or more measures of risk that will help address that question. 


Evans, J., van Donkelaar, A., Martin, R. V., Burnett, R., Rainham,D. G., Birkett, N. J., and Krewski, D. 2012. Estimates of global mortality due to particulate air pollution using satellite imagery. Environ. Res.

Kaplan, S., and Garrick, B. J. 1981. On the quantitative definition of risk. Risk Anal. 1:11-27 
Last, J. M., ed. 2001. A Dictionary of Epidemiology. New York: Oxford University Press, Inc.

McEvoy, S. P., Stevenson, M. R., and Woodward, M. 2007. The contribution of passengers versus mobile phone use to motor vehicle crashes resulting in hospital attendance by the driver. Accid. Anal. Prev. 39:1170-1176.

Moolgavkar, S. H., Luebeck, E. G., Krewski, D., and Zielinski, J. M. 1993. Radon, cigarette smoke, and lung cancer: a re-analysis of the Colorado Plateau uranium miners' data. Epidemiology 4:204-217.
Pope, C. A. III., Ezzati, M., Dockery, D. W. 2009. Fine-particulate air pollution and life expectancy in the United States. N. Engl. J. Med. 360:376-386.

Thomas, S. P., and Hrudey, S. E., eds. 1997. Risk of Death in Canada: What We Know and How We Know It. Edmonton: The University of Alberta Press.

U.S. National Research Council. 2009. Science and Decisions: Advancing Risk Assessment. Washington, D.C : The National Academies Press. Available at

World Health Organization. 2010. Preventing disease through healthy environments – Exposure to air pollution: A major public health concern. Geneva: WHO Document Production Services. Available at

World Health Organization. 2009. WHO Handbook on Indoor Radon: A Public Health Perspective.  Geneva: WHO Press. Available at

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