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00005768-200712000-0001700005768_2007_39_2226_everett_production_12miscellaneous-article< 101_0_17_3 >Medicine & Science in Sports & Exercise©2007The American College of Sports MedicineVolume 39(12)December 2007pp 2226-2233Training for Old Age: Production Functions for the Aerobic Exercise Inputs[APPLIED SCIENCES: Physical Fitness and Performance]EVERETT, MICHAEL D.1; KINSER, ANN M.2; RAMSEY, MICHAEL W.21Departments of Economics and Finance, and 2Kinesiology, Leisure, and Sport Sciences, East Tennessee State University, Johnson City, TNAddress for correspondence: Michael D. Everett, Ph.D., Department of Economics and Finance, East Tennessee State University, PO Box 70686, Johnson City, TN 37614; E-mail: for publication February 2007.Accepted for publication July 2007.ABSTRACTPurpose: This paper attempts to develop production functions (PF) between aerobic exercise inputs and long-run health outputs. Future studies could use such PF for estimating the benefits and costs (broadly defined) of different exercise programs to help develop optimal (utility maximizing) ones.Methods: To develop the PF, the paper reviewed the biomedical literature for the major dose-response relations between health, physical fitness, and exercise. Where relevant, the paper converted the dose-response relationships from relative risks to absolute probabilities and standardized terminology and units of measures.Results: The paper develops a clear set of biological PF that illustrate, quantitatively, how increases in peak cardiorespiratory (CR) fitness as measured by a short stress test reduce the probability of all-cause mortality; how increasing intensities of short (approximately 30 min, three to five times a week) exercise sessions increase peak CR fitness or retard its age-related decline; and how consistent exercise reduces the risk of myocardial infarctions (MI).Conclusions: The exercise-long-run health PF developed in this paper should provide a useful framework for other studies to estimate the broadly defined costs and benefits of different exercise programs and to help develop optimal ones.Preparing for old age involves investing in long-run health as well as investing in financial portfolios (11). Consistent lifelong aerobic exercise training constitutes a powerful input for producing a broad range of positive long-run health benefits or outputs such as reduced probability of cardiovascular diseases (CVD), diabetes, some types of cancers, and all-cause mortality (ACM) (1,6,19). The aerobic exercise input may also entail high time (in terms of other immediately foregone opportunities) and effort costs. Utility (satisfaction)-maximizing individuals and their medical and financial advisors need to weigh those costs against the expected benefits of different exercise programs to develop optimal (utility maximizing) ones (11). This requires solid biomedical data (6). For example, what are the long-run health benefits to training at the recommended moderate exercise levels (5), and what additional benefits might accrue to higher levels of training? Do higher levels of training entail longer or harder exercise sessions? Should master athletes age gracefully by reducing their levels of exercise? What is the risk of an exercise-induced heart attack (or, technically, a myocardial infarction (MI))?The exercise science literature holds clear answers to some of these questions, but substantial uncertainty, controversy, or confusion, particularly for laypersons, surround others. The American College of Sports Medicine (ACSM) latest (2005) guidelines (1) provide an extensive review and interpretation of the exercise-fitness-health literature but few clear quantifiable dose-response relationships for directly calculating the costs of exercise inputs and the benefits of the resulting health outputs. Exercise committee reports and recommendations have tended to emphasize moderate exercise as a "public health recommendation," which would appeal to sedentary adults (5). These reports have some small, dose-response graphs between fitness levels and reductions in ACM (22), but they do not clearly specify the additional benefits of higher levels of fitness that other exercise science professionals have advocated (32). Also, these recommendations and the underlying literature use relative risk of ACM instead of the actual probabilities needed to estimate broadly defined economic benefits. Moreover, terminology and definitions for exercise and fitness levels often vary between studies, and some studies have started to use more technical terminology such as percent of heart rate reserve (26). Finally, substantial controversy exists among exercise science professionals over the biologically optimal levels of exercise for long-run health (3).Thus, a need exists for easier-to-read summary relationships between the full range of exercise intensity inputs and long-run health outputs in terms of actual probabilities that analysts can use for benefit-cost analysis. This paper will attempt to develop such production functions (PF), as they are called in economics. Easy-to-read PF, along with benefit-cost estimates based on them, should help proactive individuals and their medical and financial advisors develop more effective, efficient, and optimal exercise strategies and programs in both technical biological and utility-maximizing terms.METHODOLOGY AND DEFINITIONSPF equal dose-response functions between productive inputs (e.g., exercise) and desired outputs (e.g., long-run health). Economists generally express these with variables measurable in broad monetary terms. The monetary cost of the exercise input would include the monetary value individuals put on the alternative activities they could undertake instead of spending time on exercise. The monetary benefits of reduced ACM would include the implicit values individuals put on their lives, such as requiring higher incomes for riskier occupations. Monetary measures allow comparison of input costs to output benefits for utility-maximizing decisions. Utility maximization refers to maximizing one's overall satisfaction with life. Engaging in a major activity or purchase only if the expected increase in utility (benefits) exceeds the expected increase in disutility (costs) represents one approach to maximizing satisfaction.This study attempts to develop clear biological PF for future benefit-cost analyses from various dose-response functions in the literature. First, we performed exploratory research in the biomedical literature, which identified a number of key articles on four basic exercise-long-run health relationships: fitness and long-run health (4,14,17,19), exercise inputs to increase or maintain fitness levels (26,27), the impact of age on fitness levels (7,28,34), and the risk of exercise-induced MI (16,24,30,33). Then, we attempted to convert those four key relationships into PF with variables and terminology that a wide range of professionals and proactive individuals could efficiently understand and use for benefit-cost valuations and optimal decision making. This involved detailed study and analysis of the key reviews and many of the underlying articles that the reviews cite. These conversions included relative risk of ACM and exercise-induced MI to the actual probabilities needed for benefit estimates in monetary terms; percentage of heart rate reserve or recovery to percentage of maximum heart rate (max HR that can be estimated with the formula, 220 minus age, although individual variations exist), which individuals can use to monitor exercise sessions; and V˙O2 uptake to metabolic units (METs), where 1 MET equals 3.5 L of oxygen per minute per kilogram of body weight (many gyms have equipment with MET meters). The results and discussion sections describe the specific development of each PF.The study also standardizes the definitions of key variables such as exercise intensities and fitness levels, using Table 1-1 of the ACSM latest guidelines (1). That table defines exercise intensity levels in terms of percentage of max HR (very light, < 50 percent; light, 50-63; moderate, 64-76; hard, 77-93). That table also sets the ranges for peak cardiorespiratory (CR) fitness levels found in the PF graphs. Note that in the table and studies, fitness means peak CR capacity as measured by a short stress test, such as a Bruce protocol (12) consisting of a 10- to 20-min treadmill test.RESULTSThe literature review and analysis resulted in solid PF and PF graphs (PFG) in three of the key relationships-increased fitness and reduced ACM, exercise inputs to increase fitness, and the impact of age on exercise and fitness. The study could develop only a tentative PF for the relationship between consistency of exercise and reductions in the probability of exercise-induced MI.PF for the fitness-long-run health relationships.Recent large studies indicate that peak CR fitness levels constitute the strongest predictor of ACM through a wide range of ages (4,14,17,19). Increasing fitness is more powerful than, and independent of, reducing other well-known risk factors such as smoking, hypertension, and being overweight (4,19). Moreover, increased fitness reduces some of those risk factors and morbidities such as heart and vascular disease (32), colon cancer, obesity, adult-onset diabetes (1), and loss of functionality in daily living (28). However, only the literature on peak fitness and ACM lends itself to a PFG for quantitative estimates of exercise benefits. PFG 1 shows the relationship between fitness level and the reduced probability of ACM outputs on the basis of Myers et al. (19) and corroborated by other key reviews (4,14,17) and data from U.S. vital statistics (Fig. 1).FIGURE 1-PFG 1: Risk of all-cause mortality for the next 10 yr for middle-aged males as a function of their initial level of peak cardiorespiratory fitness in metabolic equivalent units (METs).The horizontal axis in PFG 1 represents the peak CR capacity levels (METs) that middle-aged men exhibited in a short exercise stress test at the start of one of the studies (19). The vertical axis shows the probabilities (percentage of the men who died) during a 10-yr follow-up period. The solid curve in PFG 1 shows estimates of how increases in or maintenance of fitness reduces the probability of ACM for normal (asymptomatic) men in their mid-50s (average 55 yr, SD ± 12 yr) and, thus, the potential benefits to training for long-run health. The ACM probability drops from more than 40% for the very-low-fit group (< 6 METs peak capacity) to under 10% for the very-high-fit group (> 12 METs). However, the rate of ACM probability reduction diminishes particularly after the mid-fit level. The dotted lines in PFG 1 represent the 95% confidence interval in which the true relationship may lie. At least one large study involving women (17) indicates that the general relationship would also apply to middle-aged women, but with lower ACM risk for each fitness level. Increased fitness also relates strongly with decreased mortality for men with known heart disease (19). The men with CVD disease had similar ACM risk as "normal" men at each initial peak CR capacity level. The actual probabilities in PFG 1 are similar to the relative risk in (19) because that study used the highest-fit group as the norm, and that group had an approximately 10% probability of ACM during a 10-yr follow-up period, which apparently was extrapolated from the study's 7-yr follow-up period.Exercise PF for increasing cardiorespiratory fitness.Exercise inputs to increase CR fitness have several principle exercise variables: duration, frequency, and intensity. Duration and frequency inputs required approximately 30-40 min·d−1, three to six times per week, according to numerous studies and reviews dating back more than half a century (1,2,5,26,27,31). Exercise sessions include warm-up, work at target intensity, and cool-down. Two small but well-designed studies suggest that effective light to moderate exercise can be broken into three 10-min sessions per day (10,18). Supplemental inputs include stretching several major muscle groups twice for at least 15 s and minimal resistance training of one set of 3-23 repetitions per major muscle group at least two times a week (1). These reduce the risk of injury and increase the ability to perform the desired exercise intensity over the long run.The intensity levels and effort input costs remain more complex. The present review uses Swain's (26) analysis of 37 small exercise studies plus our analysis of numerous other studies, such as that of Warburton et al. (31), to develop a relatively clear PF graph between the full range of exercise intensity inputs and increasing fitness levels (PFG 2). The vertical axis represents initial or current fitness levels. The horizontal axis represents threshold exercise intensities (percentage of max HR) needed to increase those fitness levels. As an individual's current fitness increases, during several months of training at his or her threshold level, that threshold level would also increase. For example, low-fit, middle-aged individuals with initial fitness of 6-8 METs would need intensities of approximately 65-75% of max HR to increase their fitness to mid-fit levels (8-10 METs). Once they reached those mid-fit levels, they would need intensities of approximately 75-90% of max HR to increase their fitness to high-fit (10-12 METs) and very-high-fit levels (> 12 METs). Table 1-1 of ACSM's 2005 guidelines (1) describe these percentages of max HR as moderate and hard, respectively. A few studies indicate that individuals can effectively use interval training instead of one constant intensity, at least for higher-intensity exercise levels (26,31). These studies generally used 5-10 intense intervals ranging from approximately 2 to 5 min, during which effort rises to and peaks in the range of 80-90% of max HR or higher. Then, subjects reduced intensity to comfortable levels for approximately 2 min. Studies also indicate that individuals have to specifically train different muscle groups to use them for achieving threshold exercise levels needed to increase peak CR fitness (1) (Fig. 2).FIGURE 2-PFG 2: An exercise-fitness production function: threshold exercise intensities needed to raise peak CR capacity for different levels of initial peak CR capacity.Threshold exercise can produce measurable increases in peak CR fitness quickly. Our analysis of data from 37 small but well-controlled exercise programs presented in the study by Swain and Franklin (27), plus other studies such as that of Warburton et al. (31), suggest that average individuals in the successful moderate-threshold exercise programs, including those divided into 10-min segments, increased fitness approximately by 0.1 METs per week. The successful hard-threshold-intensity programs increased fitness by 0.2 METs per week for healthy, active individuals. Thus, individuals can raise their fitness levels by at least one fitness category (about 2 METs) in 3-6 months. However, wide variations among individual responses exist, and some of the studies do not demonstrate statistically significant gains (27) or differences between moderate and hard programs (5). The literature did not provide data for making confidence intervals around this PFG.PF and age-related fitness declines.The PF so far tend to emphasize short- to medium-run variables such as threshold exercise to increase fitness in less than a year and the benefits of reduced ACM during the following 10 yr. The PF in this section combine those short-run relations with the inevitable long-run decline in peak fitness capacity during an adult life. The three solid lines in PFG 3 developed from (7,34) demonstrate the relationship between age and the peak fitness for three exercise groups (light/very light, moderate/light, hard/moderate), using cross-sectional data. These curves assume that each group reduces its exercise intensity by one level from age 30 to 70 (7). The solid lines demonstrate that each group experiences approximately the same rate of decrease in peak fitness with age. Most studies find that the hard/moderate group drops somewhat faster than does the light/very light group. Nevertheless, the top two groups begin with sufficiently high fitness that, by their 50 to 70s, they still have as much peak fitness as do sedentary 20- to 30-yr-olds, respectively. The literature suggests that this may translate into comparable work and living functionalities (31) (Fig. 3).FIGURE 3-PFG 3: Decline of peak METs with age for groups with different levels of exercise.The dotted lines demonstrate that moving to different exercise groups can change peak fitness by multiple levels. The retrain lines suggest that even middle-aged and older, low- to mid-fit individuals can train up one or two levels of fitness within a year. The detraining line suggests that they can drop from very-high-fit and moderately fit to the lowest-fit levels within 10 yr of reducing exercise to light/very light levels (basically becoming sedentary). The dotted line for the continued hard group suggests that high- and very-high-fit, middle-aged men who can sustain consistent, hard-threshold exercise can substantially retard their age-related fitness declines, at least for the medium run (approximately 10 yr) (23).PF for reducing the risk of an exercise-induced MI.The risk of an exercise-induced MI may constitute a cost to continued or renewed exercise in middle and old age that, theoretically, should be subtracted from the long-run health benefits of exercise. Four small studies (approximately 10-50 MI) on exercise-induced MI (16,24,30,33) indicate that exercise or physical exertion at 6 METs or more does increase the immediate risk of nonfatal and fatal MI. Six METs falls in the moderate to hard exercise intensity level for mid-fit individuals in ACSM's Table 1-1. One key study (16) reported in the early 1990s that of the approximately 1.7 million MI per year in the United States, 75,000 (< 5%) were exercise related, with 25,000 fatal and 50,000 nonfatal. That study provides a very clear bar graph that shows that increased exercise consistency (sessions per week) dramatically reduces the relative risk of a nonfatal exercise-induced MI (33), and it provides corroborating data. A "sedentary" middle-aged man who engages in a bout of physical exertion of 6 METs or more has more than 100 times the risk of an MI than at other times. Men who have exercised consistently several times a week for a year or more have much lower increased risk (approximately 20 times for one to two sessions per week; 8 times for three to four sessions; and only 2.4 times for five sessions). Another key study (24) provides a table that indicates that fatal MI, which occur less frequently, follow a similar drop with exercise consistency.This review found it difficult to convert those relative risks to a graph with probabilities of an exercise-induced MI during 10 yr for comparison with the reduced ACM benefits of exercise. A thorough analysis would fall outside the scope of this study. Our tentative analyses found that the actual probability of an exercise-induced MI (nonfatal and fatal) for a middle-aged man who engaged in moderate to hard exercise three times per week would equal less than 0.1% per year and 1% for 10 yr (0.06% nonfatal + 0.02% fatal = 0.08% total per year and 0.77% for 10 yr). The probability for a low- to very-low-fit man undertaking a moderate exercise program to increase his fitness could approximate 1% during just the year it takes to increase fitness and establish a period of consistent exercise (more than 10 times the thrice-weekly exerciser). If the per-year risk dropped to the consistent exercise level for the remaining 9 yr, the overall 10-yr risk would approximate 2%. For such individuals who start and stop exercise programs several times, the cumulative risk of an exercise-induced MI could be 3% or higher for a 10-yr period. Recall that PFG 1 indicates potential benefits to exercise programs that increased fitness from low- to mid-fit levels, reducing the probability of ACM during 10 yr by approximately 20 percentage points. Thus, the net benefit of moderate to hard exercise into middle and at least early old age should remain high.DISCUSSIONMost of the PF that this study developed from a rigorous review of the biomedical literature are solid enough for benefit-cost analysis to help develop optimal long-run exercise programs and strategies. The more speculative PF on exercise-induced MI need further development, along with PF on exercise and MI in general (32); however, this would require another study.Discussion of PF relating fitness levels to long-run health.The literature indicates that increased CR fitness is a powerful input for long-run health in terms of reductions in the probabilities of a wide range of morbidities and functionalities (28), which individuals can at least weigh qualitatively against the costs of increasing fitness levels. PFG 1 on the increased fitness-reduced probability of ACM provides a solid basis for more precise quantitative benefit estimates based on various measures of the value of a life. The biological data for this PFG seem reliable for moving from the low-fit to high-fit range, given the many large studies (4,14,17,19). Some questions exist over the extreme ends of the PFG, and some analysts suggest it may be more linear (32). First, PFG 1 may overestimate the benefits of moving from lower-fit to mid-fit categories. Many persons in the very-low-fit category may have genetic characteristics, undetected disease, or overweight problems that both restrain their peak CR capacity and predispose them toward higher mortality risks. Even though the large studies have tried to control for this bias in various ways, it may increase the ACM probability for the entire very-low-fit group. Second, PFG 1 may underestimate the benefits of very-high-fit levels. Most of the underlying studies only measure fitness levels at the beginning of the study and do not monitor fitness during the follow-up period. Because many high- and very-high-fit middle-aged men reduce or cease their physical activity as they age, as PFG 3 and the exercise reduction with age graph in (34) indicate, they may drop toward mid-fit levels during the follow-up period. Even if diminishing returns exist for moving to high- and very-high-fit categories, some proactive individuals might find a 2.5-5% reduction in the probability of ACM attractive. Many people voluntarily expend scarce resources to reduce the probability of less catastrophic events such as losing a house to fire, which probably remains considerably less than 2.5% during 10 yr.Discussion of PF to increase fitness.The PF in this area clearly indicate the most biologically effective and efficient combination of exercise inputs to increase fitness, and, thus, they provide a solid basis for estimating exercise costs. For example, the relative fixed duration and frequency inputs suggest at least an hour per session with some clothes changing and 3-5 h·wk−1, or at least 150 per 200 h·yr−1, which analysts can convert to a monetary value. However, producing exercise as a by-product of a more immediately desired output, such as walking or cycling for transportation, or labor-intensive yard work, could generate threshold exercise at a much lower cost. Traveling to gyms and sports facilities could increase time costs substantially. Increasing intensity does not have to take more time, but individuals might find fewer opportunities to produce it as a low-cost by-product. Perceived effort costs should increase, but high-fit individuals may enjoy higher-intensity exercise, or they at least may be able to reduce the effort cost with interval training and social competition.The biologically most effective and efficient combination of exercise inputs rest on solid biomedical data consisting of numerous small, well-controlled, often clinical studies dating back at least to the 1960s. Strong consensus seems to exist on the duration and frequency inputs for training peak CR fitness, as defined above. Some exercise recommendations have indicated that longer duration could substitute for intensity, but this seems to hold only at the very low levels of fitness (26) and for weight control (1). PFG 2 complements the existing exercise literature by combining the low-intensity exercise approaches with the traditional aerobic training intensities of 75-85% of max HR in one continuous PF. Consensus seems to exist that mid- to high levels require threshold intensities, as PFG 2 indicates. Uncertainty may exist regarding the lower intensity levels that Swain and Franklin (27) think might fall in the 50% of max HR range. The maximum exercise intensities for training peak competitive CR fitness involve uncertainties over the role of anaerobic and lactate thresholds.Uncertainties also stem from individual variations in abilities (genetic and trained) to exercise at higher intensity levels and in genetic capacity to respond to higher intensities with higher fitness. Although the Swain (26) and Swain and Franklin (27) reviews that underlie PFG 2 do not provide measures of individual variations, our analysis of many of the underlying controlled clinical exercise program groups has revealed some cases where individual responses varied widely from the average (31). These possible variations in program and individual responses to exercise, and the low correlations between individuals' self reports of exercise levels and objectively measured fitness levels (32), suggest that individuals should monitor their exercise programs to make sure they are increasing or maintaining their target fitness levels. Monitoring can range from formal stress tests with exercise professionals in human performance labs to informal personal time and distance performance benchmarks, such as how long it takes to walk a mile or run a 5-km race.Discussion of PF related to age.The PF that relate age as well as exercise to fitness levels reinforce the benefits of consistent, lifelong exercise. PFG 3 indicates that 60-yr-old moderate to hard exercisers can enjoy fitness, and perhaps functionality, levels higher than the general adult population at any age. Although the functionality benefits remain difficult to quantify, PFG 3 may help individuals and analysts make reasonable assumptions about the value of the ability to earn more and enjoy a more active life style in middle and early old age. PFG 3 also conveys how quickly master athletes and other high- to moderate-intensity exercisers can lose their fitness benefits if they lower their training with age or give up consistent exercise. Thus, the value of continued hard training for this group could be quite high. Although the dotted retraining lines suggest that individuals could wait until middle age to start consistent threshold exercise and still reap much of the benefit, that strategy must entail risks of exercise-limiting morbidities, loss of functionality, and injuries, and exercise-induced MI.Although these age-related drops in peak fitness with age rest on several large studies, some of the variables in those studies did not coincide with data underlying the other PFG and ACSM Table 1-1 (1). Thus, we used judgment, based on an analysis of the literature (7,23,28,34) and standard terminology in ACSM Table 1-1, to create groups and placement of the some lines in PFG 3. For example, we lowered the line for the "sedentary group" in the key reviews (7,34) so that the 50- to 60-yr-olds in that group, which we call light/very light would fall into the low- or very-low-fit category in PFG 3. We also created a new moderate/light group and line, positioning it in the middle of the graph on the basis of ACSM Table 1-1 and the key reviews' active line. The hard/moderate line coincides with those lines in the key reviews (7,34). These adjustments should increase the clarity of PFG 3 without introducing potentially serious numeric biases, because PFG 3's purpose is to provide a more qualitative overview. All the curves in PFG 3 and the key underlying reviews (7,28,34) suggest that continued exercise at the moderate to hard levels into middle and old age can keep fitness levels as high as those for typical 30- and 40-yr-olds who remain sedentary (the light/very light intensity line).The major age-related drops in fitness studies generally do not focus on the role of exercise for retraining fitness or retarding its age-related decline. Thus, the retrain PF in PFG 3 rests on the extensive literature underlying PFG 2, which indicates that exercise training into the 60s and later can raise peak CR fitness for sedentary and moderately active people (1,25,27). The continued hard dotted line rests on longitudinal data in one review of 20 studies on master athletics (23), which indicates that some middle-aged endurance athletes who maintain their high levels of exercise can substantially retard the drop in their peak capacity. Most of the underlying studies in that review generally do not clearly specify whether drops in intensity or volume of training explain the general decline for master athletes through middle age. However, at least one small (N = 40) study (13) found that running pace (i.e., exercise intensity) correlated strongly with peak CR capacity (r = 0.81, P = 0.02), whereas miles run per week had a low correlation (r = 0.25, P = 0.29). Also note that the large review by Wilson and Tanaka (34) seems to deny the role of exercise in retarding fitness declines, but they recant that position in their conclusion.Discussion of possible PF for reducing risk of an exercise-induced MI.The fear of an exercise-induced MI into middle and, particularly, old age may constitute a major perceived exercise risk or cost to many individuals (29). Our analysis of that risk, and the consensus of the key articles in the area, suggest that the risk remains very small relative to the long-run exercise benefits. Thus, attempting to net the MI exercise-induced risk out of the long-run exercise benefits probably involves misplaced precision. The benefits of consistent exercise at the moderate to hard (approximately 6 METs) level approximate a 20 percentage point drop in ACM, whereas the costs approximate a 1 percentage point increase in the risk of a fatal or nonfatal MI during a 10-yr period for consistent exercisers. MI probabilities do increase significantly to the 2-3% or higher level during 10 yr for middle-aged persons attempting to increase their fitness levels, and particularly for persons who start and stop exercise programs multiple times or who only engage in one or two exercise sessions per week. Also, we do not have good data on the risks for high-intensity exercisers in their 70s and older.Nevertheless, expert panels have developed recommendations for reducing the risks of exercise-induced MI for these groups, and other inputs can help reduce the overall MI probabilities. Sedentary, middle-aged persons initiating exercise programs can reduce the MI risk by undergoing screening and, where appropriate, using supervised exercise programs to work up from very light levels of exercise intensity, as depicted in PFG 2 (20). Such programs are routinely prescribed after MI or heart surgery, and for elderly people (1). Another panel of experts (15) recommends screenings for master athletes that may reduce their exercise-related MI risk. Other inputs, such as diet and social support (21), and assessing the need for cholesterol-lowering drugs (9), should also lower the risk because exercise does not prevent accumulation of arterial plaque, which autopsies of well-conditioned individuals have demonstrated (8).CONCLUSIONThis literature review has yielded a set of clear biological PF between exercise inputs and long-run health outputs that analysts can use to estimate the costs and benefits of different exercise programs for developing optimal ones. According to the biological PF, long-run health, defined as reductions in ACM and a wide range of morbidities and loss of functionalities, depends on peak CR fitness as measured by a short stress test. Increasing peak fitness or retarding its inevitable age-related decline depends on relatively short (30- to 40-min) exercise sessions at threshold-intensity levels (approximately 60-85% of max HR) three to five times per week. This model answers many of the questions posed in the introduction on using the exercise input. Moderate exercise and mid-level fitness generate large benefits (20 percentage point reductions in the probability of ACM) for previously sedentary individuals. Higher intensities and fitness levels can produce a further reduction of 5-10 percentage point. Increased fitness depends on relatively short exercise sessions rather than long, marathon-type training sessions. Master athletes who reduce their levels of training to low intensity levels drop their fitness to low levels and lose the benefits of reduced probability of ACM, other morbidities, and superior functionality in everyday living. The risk of an exercise-induced MI remains very low relative to the benefits of exercise. Consistent exercise and recommendations from expert panels and other inputs such as diet and stress reduction and cholesterol-lowering drugs, where needed, can reduce the risk even further.The biological PF also provide a basis for benefit-cost analysis of different exercise levels and programs to help develop optimal ones. The discussion in the paper seems to reinforce the moderate exercise approach with the apparent diminishing returns to increased fitness (PFG 1) and apparent increasing costs of higher levels of exercise (PFG2). Nevertheless, some individuals might find another 5-10 percentage point reduction in ACM probability attractive and can find ways of lowering the costs of consistent, higher-intensity exercise. 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