Journal Logo


Population attributable risk: implications of physical activity dose


Author Information
Medicine and Science in Sports and Exercise: June 2001 - Volume 33 - Issue 6 - p S635-S639
  • Free


In epidemiology, relative risk (RR) and similar measures are used to assess the strength of a relationship between a particular exposure and the incidence of a particular disease (or outcome), thus establishing causality and magnitude of risk of exposed individuals compared with unexposed individuals. The public health or societal impact of an exposure, however, depends not only on the magnitude of the relative risk but on the prevalence of the risk factor in the population. Population attributable risk (PAR) can be calculated from estimates of the RR and the population prevalence of the risk factor to provide an estimate of how much of a particular disease could be prevented if exposure to the risk factor were eliminated (1,11,13). A measure such as PAR takes into account both the strength of the association (RR associated with the exposure) and the prevalence of the exposure. Using this approach, the effect of eliminating various risk factors can be compared. For example, PAR estimates have been used to identify physical inactivity as one of the most important modifiable risk factors for coronary heart disease (CHD) (1). Because PAR is a useful tool in assessing the consequences of modifying the prevalence of risky exposures, this article explores how PAR could be used in conjunction with varying doses of physical activity and details some of the problems inherent in its interpretation. For simplicity, CHD will be the only outcome used in the following examples. The estimates presented here are derived from currently available data and will naturally change as new information emerges.


PAR is calculated by using the prevalence (P) of a risk factor and the RR of that risk factor with a particular outcome (PAR = (P*(RR − 1))/(P*(RR − 1) + 1)). It is often expressed as a percentage by multiplying by 100. PAR is a theoretical calculation rather than an empirical assessment of the effect of modifying a particular risk factor. Although useful from both conceptual and pragmatic perspectives, PAR has important limitations. A discussion of these limitations will assist in the overall interpretation of the measure. We describe six categories of limitations: 1) PAR is a useful but imaginary concept; 2) independently calculated PARs of different risk factors for the same outcome cannot be added; 3) PAR assumes that known and unknown risk factors are randomly distributed in the population; 4) RR, and therefore PAR, may differ for disease incidence, morbidity, and mortality; 5) physical activity has been measured and categorized differently in general population surveys and in observational studies of relative risk; and 6) different effects of vigorous and moderate activity on health outcomes have not been sufficiently clarified to know the most appropriate manner by which to incorporate them into calculations of PAR.

PAR is a useful but imaginary concept.

It predicts health outcomes in an imaginary world in which people change their physical activity level and nothing else. The prevalence of other behaviors and risk factors such as blood pressure and blood cholesterol remain constant in PAR calculations. To the extent the prevalence of these risk factors is expected to change as activity changes, PAR underestimates probable changes in health outcomes.

Independently calculated PARs of different risk factors for the same outcome cannot be added.

As just noted, independent calculations of PAR assume that nothing else changes. Although we know that most chronic diseases have multiple causes and can be affected by several risk situations, PAR evaluates one risk factor at a time and the calculation assumes that the prevalences of the other risk factors are held constant. When information is available for several risk factors (e.g., smoking, physical inactivity, high blood pressure, high serum cholesterol as related to CHD), separate PAR estimates can be calculated for each, but these estimates cannot be added together. For example, summing the PAR estimates for physical inactivity and for high blood pressure will overestimate the effect on CHD when both physical inactivity and high blood pressure were removed simultaneously. The PAR estimate for each risk factor can be evaluated separately and may prove useful for program planning or for comparing potential risk factor interventions, but adding them together gives an inaccurate picture of the combined effect of changing several risk factors at the same time.

PAR assumes other risk factors are randomly distributed in the population.

If risk factors are clustered within individuals, PAR is an overestimate. If risk factors are unclustered within individuals, PAR is an underestimate. This concept is illustrated in Figure 1 using three pie charts each displaying different distributions of two risk factors while holding the prevalence and the RR of each risk factor constant (Fig. 1). In this example, the RR for Risk Factor 1 is 3.0; the RR for Risk Factor 2 is 6.0; and the RR for having both risk factors (Risk Factor 12) is 18.0. For each pie in the example, the prevalence of Risk Factor 1 is 50% and the prevalence of Risk Factor 2 is 40%. In this hypothetical situation, the PAR varies for Risk Factor 1 from 20% when the risk factors are not clustered to 71% when they are clustered. The PAR when the risk factors are randomly distributed (the assumed situation) is 50%. Therefore, when interpreting the PAR for a given disease outcome, attention should be given as to how specific risk factors combine or interact to affect the disease process. Because CHD risk factors do cluster within individuals, PAR may overestimate the effect of a single risk factor such as physical inactivity. The extent to which this overestimate would be counterbalanced in reality by changes induced in other risk factors (e.g., if physical activity increases and blood pressure decreases) could be modeled and calculated.

Population attributable risk percentages for Risk Factor 1 (RF1) with different distributions of Risk Factor 1 and Risk Factor 2 (RF2). In all cases, prevalence of RF1 = 50% and RF2 = 40%. RR for RF1 = 3, RF2 = 6, and RF12 = 18.

RR, and therefore PAR, may differ for disease incidence, morbidity, and mortality.

In the case of CHD, there is sufficient information to suggest that increasing physical activity reduces the risk of developing CHD (incidence), dying from CHD (mortality), and incurring associated disability (morbidity) for persons with CHD. However, the relationship between dose and response may be different for incidence, morbidity, and mortality. The same may be true for other chronic diseases.

Physical activity has been measured and categorized differently in general population surveys and in observational studies of RR.

As a result, national PAR estimates are of questionable accuracy because relative risks from specific studies and national physical activity prevalence estimates may not correspond. For a given RR, different prevalence estimates yield different PAR estimates as shown in Figure 2. The larger changes in PAR occur at lower prevalences. Ideally, the RR measures and the population-wide prevalence estimates would come from the same research. Less than ideal, but an improvement over the status quo, would be use of the same physical activity measures and categories in national surveys and in etiologic studies.

Population attributable risk by selected values of relative risk and prevalence.

The different effects of vigorous and moderate activity on health outcomes have not been sufficiently clarified to know the most appropriate manner by which to incorporate them into calculations of PAR.

Vigorous and moderate activity could be considered as independent risk factors (similar to serum cholesterol level and family history of early myocardial infarction), or they could be considered different levels of a continuous or categorical risk factor, or they may be independent but interacting variables (e.g., a set dose of moderate physical activity may have different health effects if spiced with a dose of vigorous or hard physical activity). For simplicity, we have assumed a continuous or categorical relationship. The appropriate classification of physical activity intensity remains, however, an important unresolved issue. A closely related issue of special importance for this article is that many of the RR estimates available for various outcomes (CHD, diabetes, obesity), as well as the “best” measures of exposure (e.g., moderate intensity, vigorous intensity), may change as new scientific knowledge emerges. Even using existing information has problems because there is not agreement among studies on the definition of “moderate” or “vigorous” activity, or even “inactivity.” Furthermore, many individuals who are classified as doing “moderate” levels of physical activity may actually do both moderate and vigorous activity.

Prevalence of Physical Activity in the General Population

Surveillance of physical activity in the United States is conducted annually by the National Center for Health Statistics in the National Health Interview Survey (NHIS) ( Respondents are asked about frequency and duration of self-determined intensities of leisure-time physical activity. These questions are used to track health objectives for “no” leisure-time activity and moderate- or vigorous-intensity activity ( Participation in activities that increase heart rate or breathing are asked, but no examples of specific activities are provided. Those who report no participation in either moderate or vigorous activities are considered “inactive”; those who participate in vigorous activities for at least 20 min on 3 or more d·wk-1 are considered “vigorously active”; those who participate in moderate-intensity activities for at least 30 min on 5 or more d·wk-1 are considered “moderately active.” Another category, “recommended” levels of physical activity, includes those who meet the frequency and duration criteria for either moderate- or vigorous-intensity activity.

The Behavioral Risk Factor Surveillance System (BRFSS) collects state data on physical activity periodically ( Questions used from 1984–2000 ask for a description of the type, duration, and frequency of the respondent’s two most common activities in the previous month. Intensity is calculated on the basis of age- and sex-adjusted metabolic expenditure values for each activity (4,9). Comparisons of the 1998 NHIS data and the 1998 BRFSS data are shown in Table 1. As noted in Table 1 and in other publications (2,12,14), the prevalence of physical activity can vary substantially depending on the measurement source, conceptual interpretation of the questions, and cut points or algorithms used to classify physical activity into intensity-related categories on the basis of presumed health effects.

Table 1
Table 1:
Variations in the prevalence of physical activity United States adults, 1998.

The prevalence estimates of physical activity obtained from surveillance systems may not be appropriate for the calculation of PAR when using RR estimates derived from a specific study population, because the definitions are rarely the same. In these situations, using the prevalence estimates for the various levels of physical activity of the study population itself may provide more accurate PAR estimates.

Relative Risk

In addition to prevalence estimates, the other component of PAR, the RR, is also subject to variation from study to study. A summary of the relationship between physical activity (or inactivity) and the risk of CHD has been reviewed in several publications (10,14) that have generally found that active adults have about half the risk for CHD mortality compared with inactive adults. Included among the identified health benefits of moderate-intensity activity are reduced risk for all-cause mortality or CHD events among those who engage in moderate-intensity activity compared with inactive individuals (3,5). Although it is clear that there is a dose-response relationship between physical activity and CHD, what is not yet known is whether the shape of the dose-response curve is linear or curvilinear. Examples of the range of RR (displayed so that the most active groups are the reference groups) from two studies using different definitions of physical activity are shown in Table 2. In the study of CHD events among female nurses (5), there appears to be a larger difference in the RR between the least active group and the next active group for both total physical activity and for walking without including vigorous activity (quintiles of MET hours per week), suggesting that the nature of the curve is not linear. To a lesser extent, this is also observed in the Lee and Paffenbarger study of all-cause mortality among Harvard Alumni (3).

Table 2
Table 2:
Examples relative risks for physical inactivity from selected epidemiology studies.

Population Attributable Risk

PAR estimates for physical activity and CHD have ranged from 23% to 46%, with the best estimate at around 35%(6). Although these estimates apply to general populations, they are limited because they have usually assumed only two categories of physical activity. Several studies have estimated the PAR of CHD associated with various intensities and types of physical activity (3,5,7). For example, in the Harvard Alumni cohort, the PAR for sedentary living habits such as not walking at least 9 miles·wk-1, not climbing at least 20 flights of stairs·wk-1, and not participating in a moderately vigorous sports activity were calculated for the entire category (sedentary living) and for each component (7). The PAR (expressed as a percentage) for sedentary living habits was 13.2%. When examining the components of sedentary living, not participating in moderately vigorous sports activity was found to be more important than the others, with a PAR of 12% compared with 9.7% for walking less than 9 miles·wk-1 and 8.8% for climbing less than 20 flights of stairs·wk-1. In this analysis, all estimates were adjusted for age as well as for other risk factors for mortality (e.g., cigarette smoking, hypertension, overweight, early parental mortality). Whether using crude or adjusted estimates, the RR and the prevalence estimates for the physical activity categories, as well as the PAR, are specific to this study.

Other studies have created categories of physical activity by calculating volume or total energy expenditure (sometimes combining several intensities) and dividing the groups into quintiles (5) or other using other cut points (3). The RRs for each quintile (or other cut point) are adjusted for other factors, but not necessarily the same factors throughout various studies. Within a particular study the PAR may be useful for comparing the effect of modifying physical activity dose within that study population, but may not be practical for more general use.

In spite of the difficulties of calculating and interpreting PAR estimates for general populations, there is sufficient information to make some informed estimates of the effect of the shape of the dose-response curve. Using theoretical estimates of RR and assuming a fixed prevalence (quintiles), PAR estimates that might be applicable to general populations with these characteristics can be calculated. In these examples, the reference group (RR = 1.0) is the most active 20% of the population and the highest risk group (RR = 2.0) is the least active 20%. The RR for the other quintiles varies depending on the shape of the dose-response relationship. In Figure 3, a linear relationship is assumed, and the RR for each quintile increases by 0.25 as activity decreases (1.0, 1.25, 1.50, 1.75, 2.0). The overall PAR is 33%, and each quintile’s contribution to the overall PAR is shown (Fig. 3). About 70% of the overall PAR is attributable to the least active quintiles. In Figure 4, the same prevalence estimates are applied, but the RR increases in a nonlinear manner as activity decreases (1.0, 1.125, 1.25, 1.5, 2.0). In this example, the overall PAR is 27% and about 82% is attributable to the two least active quintiles. Understanding the shape of the dose-response relationship between physical activity and target health outcomes can provide improved estimates of the effect of changes in physical activity patterns on a population level.

Prevalence distribution and PAR contribution: energy expenditure by quintiles, linear RR decline.
Prevalence distribution and PAR contribution: energy expenditure by quintiles, exponential RR decline.

In summary, PAR can be a useful tool to understand the public health burden of physical inactivity and to further quantify the implications of different doses of physical activity. However, its usefulness would be improved if the following recommendations were implemented:

  • Develop prevalence and relative risk estimates that can be applied to the entire population by using consistent definitions of physical activity intensity in both research and surveillance settings.
  • Develop methods to model the benefits of the combined health effects of different doses or intensities of physical activity on health outcomes.

Address for correspondence: Caroline A. Macera, Ph.D., Centers for Disease Control and Prevention, Physical Activity and Health Branch (PAHB), Division of Nutrition and Physical Activity (DNPA), 4770 Buford Highway, N.E., Atlanta, GA 30341; E-mail:


1. Centers for Disease Control and Prevention. Physical activity and the prevention of CHD. Morb. Mortal. Wkly. Rep. 42: 669–672, 1993.
2. Jones, D. A., B. E. Ainsworth, J. B. Croft, C. A. Macera, E. E. Lloyd, and H. R. Yusuf. Moderate leisure-time physical activity: who’s meeting the public health recommendations? A national cross-sectional study. Arch. Fam. Med. 7: 285–289, 1998.
3. Lee, I.-M., and R. S. Paffenbarger Associations of light, moderate, and vigorous intensity physical activity with longevity. Am. J. Epidemiol. 151: 293–299, 2000.
4. Macera, C. A., and M. Pratt Public health surveillance of physical activity. Res. Q. Exerc. Sport 71: 97–103, 2000.
5. Manson, J. E., F. B. Hu, J. W. Rich-Edwards, et al. A prospective study of walking as compared with vigorous exercise in the prevention of CHD in women. N. Engl. J. Med. 341: 650–658, 1999.
6. Newschaffer, C. J., C. A. Brownson and L. J. Dusenbury Cardiovascular disease. In: Chronic Disease Epidemiology and Control, 2nd Ed., C. Brownson, P. L. Remington, J. R. Davis (Eds.). Washington, DC: American Public Health Association, 1998,
7. Paffenbarger, S. R., Jr, R. T. Hyde A. L. Wing I.-M. Lee D. L. Jung and J. B. Kampert The association of changes in physical activity level and other lifestyle characteristics with mortality among men. N. Engl. J. Med. 328:538–545, 1993.
8. Pate, R. R., M. Pratt, S. N. Blair, et al. Physical activity and public health: a recommendation from the Centers for Disease Control and Prevention and the American College of Sports Medicine. JAMA 273: 402–407, 1995.
9. Pereira, M. A., S. J. Fitzgerald, E. W. Gregg, et al. A collection of physical activity questionnaires for health-related research. Med. Sci. Sports Exerc. 29: S146–S152, 1997.
10. Powell, K. E., P. D. Thompson, C. J. Caspersen, and J. S. Kendrick. Physical activity and the incidence of CHD. Ann. Rev. Public Health 8: 253–287, 1987.
11. Powell, K. E., and S. N. Blair. The public health burdens of sedentary living habits: theoretical but realistic estimates. Med. Sci. Sports Exerc. 26: 851–856, 1994.
12. Sarkin, J. A., J. F. Nichols, J. F. Sallis, and K. J. Calfas. Self-report measures and scoring protocols affect prevalence estimates of meeting physical activity guidelines. Med. Sci. Sports Exerc. 32: 149–156, 2000.
13. Stephenson J., A. Bauman T. Armstrong B. Smith and B. Bellew The Costs of Illness Attributable to Physical Inactivity in Australia: A Preliminary Study Canberra, Australia: Population Health Division Publications, Publication #2704, 2000.
14. U.S. Department of Health and Human Services Physical Activity and Health: A Report of the Surgeon General. Atlanta, GA: Centers for Disease Control and Prevention, S/N 017–023– 00196–5:1996.


© 2001 Lippincott Williams & Wilkins, Inc.