Chapter 5 Cardiorespiratory Fitness and Mortality: the Epidemiological Evidence and Its Limits

Three landmark studies

Cardiorespiratory fitness is usually measured as maximal oxygen uptake (VO₂max) or as the metabolic equivalents (METs) reached on a treadmill exercise test, where 1 MET is roughly a resting oxygen uptake of 3.5 millilitres per kilogram of body mass per minute. Over more than thirty years, many cohort studies have found a strong inverse association between fitness and all-cause mortality. The three studies below are the most cited.

Evidence

Blair and colleagues, 1989. 10,224 men and 3,120 women examined at a preventive medicine clinic in Dallas, Texas, who had a maximal treadmill exercise test, were followed for an average of just over 8 years, during which 283 died (Blair et al. 1989). Grouped by fitness quintile, age-adjusted all-cause mortality fell as fitness rose, the least fit group having several times the death rate of the most fit; after statistical adjustment for age, smoking, cholesterol, systolic blood pressure, fasting glucose and parental history of coronary heart disease, low fitness remained associated with higher mortality. It was one of the first large cohorts to study all-cause mortality using objectively measured fitness rather than self-reported activity.

Evidence

Kodama and colleagues’ 2009 meta-analysis. Pooling 33 studies, the all-cause mortality analysis included 102,980 people and 6,910 deaths and the coronary and cardiovascular analysis 84,323 people and 4,485 events (Kodama et al. 2009). Each 1-MET higher maximal aerobic capacity (roughly 1 km/h faster running speed) was associated with a pooled relative risk of 0.87 for all-cause death (95 % confidence interval 0.84–0.90) and 0.85 (0.82–0.88) for coronary and cardiovascular events, that is about 13 % and 15 % lower. Compared with high fitness (10.9 METs or more), low fitness (below 7.9 METs) carried a relative risk of all-cause death of 1.70.

Evidence

Mandsager and colleagues, 2018. 122,007 consecutive adult patients who underwent clinically indicated, symptom-limited treadmill exercise testing at the Cleveland Clinic between 1991 and 2014 were followed for a median of 8.4 years, about 1.1 million person-years, with 13,637 deaths (Mandsager et al. 2018). Groups were defined by fitness percentile for age and sex: low (below the 25th percentile), below average (25th–49th), above average (50th–74th), high (75th–97.6th) and elite (97.7th and above). After adjustment, the hazard ratio for low versus elite fitness was 5.04 (4.10–6.20); elite versus high was 0.77 (0.63–0.95); below average versus above average was 1.41 (1.34–1.49). In the same model, smoking had a hazard ratio of 1.41 (1.36–1.46), diabetes 1.40 (1.34–1.46) and coronary artery disease 1.29 (1.24–1.35). The authors concluded that the adjusted risk associated with reduced cardiorespiratory fitness was “comparable to or greater than traditional clinical risk factors”, and that the inverse association with long-term mortality showed “no observed upper limit of benefit”.

Note

How to read “worse than smoking”. The 5.04 compares two extreme groups (bottom 25 % against top 2.3 %), whereas smoking’s 1.41 is a binary comparison; the comparison of like is below versus above average, also 1.41, which is why the paper says “comparable to or greater than”. Participants were patients referred for clinical reasons, and fitness was estimated from treadmill workload; “no observed upper limit” means only that within these data the elite group still did better than the high group, not that training ordinary people to elite levels would bring the same difference.

From hazard ratios to “years on the mortality curve”

Hazard ratios are hard to grasp intuitively. The Gompertz curve of Chapter 1 offers a conversion: if a group’s hazard is $HR$ times that of a reference group at every age, its hazard curve equals the reference curve shifted by some number of years.

Calculation

Derivation. Let the reference group have $\mu(t) = R e^{\alpha t}$ and the comparison group $HR \cdot \mu(t)$ . Setting $HR \cdot R e^{\alpha t} = R e^{\alpha (t + \Delta t)}$ gives

$\Delta t = \frac{\ln HR}{\alpha} = \frac{\ln HR}{\ln 2}\,\mathrm{MRDT}.$

When $HR < 1$ , $\Delta t < 0$ : the group’s risk is “as if $|\Delta t|$ years younger”. The conversion rests on four assumptions: (1) a Gompertz curve with the Makeham term ignored; (2) the same hazard ratio at all ages (proportional hazards); (3) a causal hazard ratio; and (4) ages between about 30 and 90 (Chapter 1). The program converts several published hazard ratios and uses the Gompertz–Makeham life table of Chapter 1 to check the effect on life expectancy at age 50.

Calculation

# HR on a Gompertz curve = shift of dt = ln(HR) / alpha years. Assumes no Makeham term, proportional
# hazards and a causal HR. HRs: Kodama et al. 2009; Mandsager et al. 2018 (adjusted).
import math

HRS = [("per 1 MET higher fitness (Kodama 2009)", 0.87),
       ("below vs above average fitness (Mandsager 2018)", 1.41),
       ("smoking (Mandsager 2018)", 1.41), ("diabetes (Mandsager 2018)", 1.40),
       ("low vs elite fitness (Mandsager 2018)", 5.04)]
print(" comparison                                       |  HR  | years, MRDT 7 / 8 / 9 y")
for label, hr in HRS:
    shifts = [math.log(hr) / (math.log(2) / m) for m in (7, 8, 9)]
    print(f" {label:48s} | {hr:4.2f} | " + " / ".join(f"{s:+5.1f}" for s in shifts))

# Check with a Gompertz-Makeham life table (program 1's parameters): life expectancy at 50
ALPHA = math.log(2) / 8; R = 0.004 / math.exp(ALPHA * 50); A = 0.0005
def e50(hr=1.0, dt=0.01):
    s, e = 1.0, 0.0
    for i in range(int(75 / dt)):
        e += s * dt; s *= math.exp(-hr * (A + R * math.exp(ALPHA * (50 + i * dt))) * dt)
    return e
base = e50()
print(f"life expectancy at 50, reference hazard: {base:.1f} y")
for label, hr in (("0.87 (1 MET)", 0.87), ("0.87^3 (3 METs)", 0.87 ** 3), ("1 / 5.04", 1 / 5.04)):
    print(f"  hazard x {label:16s}: {e50(hr):5.1f} y ({e50(hr) - base:+.1f})")
# If only half of the observed log-HR were causal (the rest confounding):
half = math.exp(math.log(0.87) / 2)
print(f"half of ln(0.87) causal -> HR {half:.3f}, {math.log(half) / ALPHA:+.2f} y per MET,"
      f" life expectancy at 50 {e50(half) - base:+.1f} y")
#  comparison                                       |  HR  | years, MRDT 7 / 8 / 9 y
#  per 1 MET higher fitness (Kodama 2009)           | 0.87 |  -1.4 /  -1.6 /  -1.8
#  below vs above average fitness (Mandsager 2018)  | 1.41 |  +3.5 /  +4.0 /  +4.5
#  smoking (Mandsager 2018)                         | 1.41 |  +3.5 /  +4.0 /  +4.5
#  diabetes (Mandsager 2018)                        | 1.40 |  +3.4 /  +3.9 /  +4.4
#  low vs elite fitness (Mandsager 2018)            | 5.04 | +16.3 / +18.7 / +21.0
# life expectancy at 50, reference hazard: 30.5 y
#   hazard x 0.87 (1 MET)    :  31.9 y (+1.4)
#   hazard x 0.87^3 (3 METs) :  34.8 y (+4.3)
#   hazard x 1 / 5.04        :  47.9 y (+17.4)
# half of ln(0.87) causal -> HR 0.933, -0.80 y per MET, life expectancy at 50 +0.7 y

With an MRDT of 8 years, the hazard ratio of 0.87 per MET corresponds to shifting the mortality curve by about 1.6 years; with an MRDT of 7 or 9 years the shift is between 1.4 and 1.8 years. In the life table, multiplying the hazard at every age after 50 by 0.87 raises remaining life expectancy at 50 from 30.5 to 31.9 years (+1.4); multiplying by $0.87^3$ (3 METs higher) adds 4.3 years.

The same conversion applied to Mandsager and colleagues’ figures: below versus above average (1.41) and smoking (1.41) both correspond to about 4 years, and low versus elite (5.04) to about 19 years. This last figure shows the limits of the conversion. Dividing the hazard by 5.04 in the life table adds 17.4 years to remaining life expectancy at 50, from about age 80 to about age 98, far beyond anything seen in intervention studies, which suggests that much of the difference between the extreme groups is not caused by “fitness itself”. If only half of the log hazard ratio per MET were causal, the shift would be about 0.8 years and the gain in life expectancy about 0.7 years.

What observational studies cannot show

All of these numbers come from observational studies and show only that fitness and mortality are associated. At least three biases can make the observed association larger than the causal effect: reverse causation (undiagnosed disease both lowers exercise capacity and raises the risk of death; excluding early deaths deals with this only in part); genetic and constitutional confounding (see the next section and Book 22 of this series); and healthy-user bias (fit people also differ in diet, sleep, medical care and socio-economic circumstances).

Calculation

A synthetic cohort of 200,000 adults followed for 10 years. Assumptions: a genetic or constitutional factor $G$ raises fitness by 0.8 MET per standard deviation and independently lowers the risk of death (hazard ratio 0.85); 8 % of people have undiagnosed disease that lowers measured fitness by 1.5 METs and triples the risk of death for the first 2 years; and the true causal effect of fitness is a hazard ratio of 0.94 per MET. The hazard ratio per MET is estimated by Poisson regression. Finally the program computes the E-values of two published hazard ratios: an E-value is how strongly an unmeasured confounder would have to be associated with both the exposure and the outcome (on the risk-ratio scale) to explain away the observed association completely (VanderWeele and Ding 2017).

Calculation

# Synthetic cohort, 200,000 adults, 10 years (fixed seed). G raises fitness 0.8 MET/SD and lowers
# hazard (HR 0.85/SD); 8 % hidden disease: -1.5 MET, hazard x3 in years 0-2. True HR 0.94/MET.
# Poisson regression (Newton-Raphson); E-values after VanderWeele & Ding 2017.
import math, random

rng, TRUE, rows = random.Random(30), math.log(0.94), []
for _ in range(200_000):
    g = rng.gauss(0, 1); z = rng.random() < 0.08
    met = 9 + 0.8 * g + rng.gauss(0, 1.8) - (1.5 if z else 0)
    base = 0.008 * math.exp(TRUE * (met - 9) + math.log(0.85) * g)
    t1 = rng.expovariate(base * (3 if z else 1))
    t = t1 if t1 < 2 else 2 + rng.expovariate(base)
    rows.append((met, g, min(t, 10.0), int(t < 10)))

def poisson_hr(data, use_g):            # data: (MET, g, years, died); returns exp(slope on MET)
    k = 3 if use_g else 2
    b = [math.log(sum(r[3] for r in data) / sum(r[2] for r in data))] + [0.0] * (k - 1)
    for _ in range(12):
        G = [0.0] * k; Hm = [[0.0] * k for _ in range(k)]
        for x, g, y, d in data:
            v = (1.0, x - 9, g)[:k]; m = y * math.exp(sum(bi * vi for bi, vi in zip(b, v)))
            for i in range(k):
                G[i] += (d - m) * v[i]
                for j in range(k): Hm[i][j] += m * v[i] * v[j]
        for i in range(k):                  # Gauss-Jordan: solve Hm * step = G
            piv = Hm[i][i]; Hm[i] = [h / piv for h in Hm[i]]; G[i] /= piv
            for j in range(k):
                if j != i:
                    f = Hm[j][i]; G[j] -= f * G[i]
                    Hm[j] = [a - f * c for a, c in zip(Hm[j], Hm[i])]
        b = [bi + s for bi, s in zip(b, G)]
    return math.exp(b[1])

late = [(m, g, t - 2, d) for m, g, t, d in rows if t > 2]      # follow-up from year 2
print(f"deaths: {sum(r[3] for r in rows)} of {len(rows)}; true causal HR per MET: 0.940")
print(f"observed HR per MET, all follow-up:             {poisson_hr(rows, False):.3f}")
print(f"observed, deaths in the first 2 years excluded: {poisson_hr(late, False):.3f}")
print(f"adjusted for G (unmeasurable in practice):      {poisson_hr(rows, True):.3f}")
print(f"adjusted for G, early deaths excluded:          {poisson_hr(late, True):.3f}")
def e_value(rr):
    rr = 1 / rr if rr < 1 else rr
    return rr + math.sqrt(rr * (rr - 1))
print(f"E-values: HR 0.87 per MET -> {e_value(0.87):.2f}; HR 5.04 low vs elite -> "
      f"{e_value(5.04):.2f}")
# deaths: 16263 of 200000; true causal HR per MET: 0.940
# observed HR per MET, all follow-up:             0.894
# observed, deaths in the first 2 years excluded: 0.905
# adjusted for G (unmeasurable in practice):      0.921
# adjusted for G, early deaths excluded:          0.934
# E-values: HR 0.87 per MET -> 1.56; HR 5.04 low vs elite -> 9.55

The true effect is 0.940, but the direct estimate is 0.894, whose log hazard ratio is about 1.8 times the true value. Excluding deaths in the first 2 years gives 0.905, correcting only a small part; adjusting for $G$ gives 0.921; only doing both comes close to the true value (0.934). In real studies, $G$ is exactly the part that cannot be measured.

The E-value gives another angle. The E-value of the hazard ratio of 0.87 per MET is 1.56: an unmeasured factor associated about 1.56-fold with both fitness and death would be enough to explain the association away, and such a factor is not hard to imagine. The E-value of the low-versus-elite 5.04 is 9.55, so explaining it away completely would require very strong confounding; but this only means that the association is unlikely to be entirely due to confounding, not that a hazard ratio of 5.04 is causal.

Evidence

The only large randomised trial. Norway’s Generation 100 study randomised 1,567 older adults born in 1936–1942 (aged about 70–77) to high-intensity interval training twice a week (400 people), moderate-intensity continuous training twice a week (387) or a control group following national physical-activity guidelines on their own (780), and followed them for 5 years (Stensvold et al. 2020). Mortality in the control group was 4.7 %; the two training arms combined did not differ from control in all-cause mortality. The hazard ratio for high-intensity intervals was 0.63 (0.33–1.20) against control and 0.51 (0.25–1.02) against moderate-intensity training, neither statistically significant. The authors noted that many in the control group did a good deal of high-intensity activity of their own accord, narrowing the differences between groups.

The trial does not deny the importance of fitness (its control group was itself active, its participants healthy and deaths few), but it is a reminder that inferring “how many years starting to train will bring” from observational hazard ratios is a large leap.

The genetic component of fitness and heterogeneity of the training response

Evidence

The HERITAGE Family Study. After a standardised 20-week training programme, sedentary adults increased their maximal oxygen uptake by an average of 384 mL/min, with a standard deviation of 202 mL/min and individual changes ranging from almost nothing to about 1,000 mL/min (720 participants who completed the programme and complied with it); in white families, the variance between families was about 2.5 times that within families (Bouchard and Rankinen 2001). Bouchard and colleagues (2011) estimated the heritability of the VO₂max training gain at about 47 % (473 white adults from 99 families); 21 single-nucleotide polymorphisms that they selected explained about 49 % of the variance in the training response in the same sample, with partial replication in other cohorts (Bouchard et al. 2011). Predictive power estimated in the same sample used for selection overstates performance in new samples, so this figure should be treated with caution.

“Training without benefit” is often put down to “non-responders”, but observed changes include measurement error and day-to-day variation.

Calculation

Atkinson and Batterham (2015) pointed out that the true standard deviation of individual responses should be estimated from the difference between the standard deviations of change in the intervention and control groups: $SD_\text{true} = \sqrt{SD_\text{intervention}^2 – SD_\text{control}^2}$ (Atkinson and Batterham 2015). HERITAGE had no non-training control group, so the control standard deviations below are assumptions. The second part of the program compares, in 100,000 synthetic participants, the proportions with an “observed gain below 100 mL/min” and a “true gain below 100 mL/min”.

Calculation

# True response SD = sqrt(SD_trained^2 - SD_control^2) (Atkinson & Batterham 2015). HERITAGE:
# mean gain 384, SD 202 mL/min (Bouchard & Rankinen 2001); control SDs are assumptions.
import math, random

MEAN, SD_OBS = 384.0, 202.0
print(" assumed SD of change without training | implied SD of true response | true CV")
for sd_ctrl in (0, 80, 120, 160):
    sd_true = math.sqrt(SD_OBS ** 2 - sd_ctrl ** 2)
    print(f"              {sd_ctrl:3d} mL/min               |        {sd_true:5.0f} mL/min"
          f"         |  {sd_true / MEAN:4.0%}")

rng = random.Random(30)
print(" assumed control SD | observed 'non-responders' | true gain < 100 | of observed, truly")
for sd_ctrl in (80, 120, 160):
    sd_true = math.sqrt(SD_OBS ** 2 - sd_ctrl ** 2)
    obs_nr = true_nr = both = 0
    for _ in range(100_000):
        true = rng.gauss(MEAN, sd_true); obs = true + rng.gauss(0, sd_ctrl)
        obs_nr += obs < 100; true_nr += true < 100; both += (obs < 100) and (true < 100)
    print(f"      {sd_ctrl:3d} mL/min    |          {obs_nr / 1000:4.1f} %          |"
          f"     {true_nr / 1000:4.1f} %     |       {both / max(obs_nr, 1):4.0%}")
print("heritability of the VO2max gain in HERITAGE: about 47 % (Bouchard et al. 2011)")
#  assumed SD of change without training | implied SD of true response | true CV
#                 0 mL/min               |          202 mL/min         |   53%
#                80 mL/min               |          185 mL/min         |   48%
#               120 mL/min               |          162 mL/min         |   42%
#               160 mL/min               |          123 mL/min         |   32%
#  assumed control SD | observed 'non-responders' | true gain < 100 | of observed, truly
#        80 mL/min    |           7.9 %          |      6.2 %     |        61%
#       120 mL/min    |           8.0 %          |      4.0 %     |        34%
#       160 mL/min    |           8.2 %          |      1.1 %     |         7%
# heritability of the VO2max gain in HERITAGE: about 47 % (Bouchard et al. 2011)

If the standard deviation of change without training were 120 mL/min, the standard deviation of true responses would be about 162 mL/min, still large (a coefficient of variation of about 42 %): individual differences in the training response are real. But “observed non-responders” and “true non-responders” are different things. About 8 % of people have an observed gain below 100 mL/min, and only about a third of them also have a true gain below 100; with larger measurement error (a standard deviation of 160) that share falls to 7 %. A single before-and-after measurement is therefore not enough to classify someone as a “non-responder”, still less to conclude that the person is “born unable to improve”.

Hypothesis · not established

Genetic confounding explains a substantial part of the fitness–mortality association (not established). If genetic factors affect both fitness and the risk of death, then among identical twins, the reduction in the risk of death of the fitter twin relative to the co-twin should be clearly smaller than the reduction seen between unrelated individuals. This could be tested in large twin cohorts with objective fitness measurements; if the hazard ratio within identical pairs is similar to that in the population, genetic confounding is not the main explanation and the hypothesis is weakened.

Chapter summary

Blair 1989, Kodama 2009 and Mandsager 2018 agree that cardiorespiratory fitness is strongly and inversely associated with all-cause mortality: about 13 % lower risk per MET, and adjusted hazard ratios of up to 5 between the lowest and highest fitness groups. As the paper puts it, the risk of reduced fitness is “comparable to or greater than” traditional risk factors, and the like-for-like comparison is below versus above average (1.41) against smoking (1.41). On the Gompertz curve, 0.87 is roughly a 1.6-year shift, but only if the hazard ratio is causal and proportional across ages; a synthetic cohort shows that reverse causation and genetic confounding can nearly double the observed log hazard ratio, and the only large randomised trial found no reduction in mortality from organised training over 5 years. Individual differences in the training response are real and about half heritable, but a single measurement cannot identify a “non-responder”. The next chapter discusses how to train: intensity distribution, Zone 2 and impulse–response models.

References

Atkinson, Greg, and Alan M. Batterham. 2015. “True and False Interindividual Differences in the Physiological Response to an Intervention.” Experimental Physiology 100 (6): 577–88. https://doi.org/10.1113/EP085070.

Blair, Steven N., III Kohl Harold W., Jr. Paffenbarger Ralph S., Debra G. Clark, Kenneth H. Cooper, and Larry W. Gibbons. 1989. “Physical Fitness and All-Cause Mortality: A Prospective Study of Healthy Men and Women.” JAMA 262 (17): 2395–401. https://doi.org/10.1001/jama.1989.03430170057028.

Bouchard, Claude, and Tuomo Rankinen. 2001. “Individual Differences in Response to Regular Physical Activity.” Medicine & Science in Sports & Exercise 33 (6 Suppl): S446–51.

Bouchard, Claude, Mark A. Sarzynski, Treva K. Rice, et al. 2011. “Genomic Predictors of the Maximal O

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Uptake Response to Standardized Exercise Training Programs.” Journal of Applied Physiology 110 (5): 1160–70. https://doi.org/10.1152/japplphysiol.00973.2010.

Kodama, Satoru, Kazumi Saito, Shiro Tanaka, et al. 2009. “Cardiorespiratory Fitness as a Quantitative Predictor of All-Cause Mortality and Cardiovascular Events in Healthy Men and Women: A Meta-Analysis.” JAMA 301 (19): 2024–35. https://doi.org/10.1001/jama.2009.681.

Mandsager, Kyle, Serge Harb, Paul Cremer, Dermot Phelan, Steven E. Nissen, and Wael Jaber. 2018. “Association of Cardiorespiratory Fitness with Long-Term Mortality Among Adults Undergoing Exercise Treadmill Testing.” JAMA Network Open 1 (6): e183605. https://doi.org/10.1001/jamanetworkopen.2018.3605.

Stensvold, D., H. Viken, S. L. Steinshamn, et al. 2020. “Effect of Exercise Training for Five Years on All Cause Mortality in Older Adults—the Generation 100 Study: Randomised Controlled Trial.” BMJ 371: m3485. https://doi.org/10.1136/bmj.m3485.

VanderWeele, Tyler J., and Peng Ding. 2017. “Sensitivity Analysis in Observational Research: Introducing the E-Value.” Annals of Internal Medicine 167 (4): 268–74. https://doi.org/10.7326/M16-2607.

Fan, Y. (2026). Ageing Kinetics, the mTOR-AMPK Autophagy Switch and Hormesis: From the Gompertz Mortality Law and Mitohormesis to Cardiorespiratory Fitness Epidemiology, Read Beside Classical Chinese Longevity Philosophy [衰老动力学、mTOR-AMPK自噬开关与毒物兴奋效应的生物数学模型] (Version 1.0.0). 5D Library. https://doi.org/10.5281/zenodo.23770092 · Licensed under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0).