Cross-Sectional Age Comparisons Understate Individual Performance Decline in Endurance Athletes: A Within-Runner Analysis of 264,213 Boston Marathon Finishes

<title>Abstract</title> <p>Background. Almost everything known about how endurance performance declines with age comes from comparing older athletes with younger ones at a single point in time. That design cannot distinguish ageing from selective attrition: if slower athletes stop competing sooner, the older age groups that remain are progressively enriched with the most durable performers, and the apparent age gradient is flattened. Whether this materially biases published age curves has rarely been tested, because it requires following the same athletes over many years. Methods. We assembled 280,817 Boston Marathon finish records from 2001–2014, a single unchanged course. Runners were linked across years by name, sex, country and a stable implied birth cohort, yielding a panel of 15,465 runners observed in three or more races (65,490 finishes). Age gradients were estimated two ways: cross-sectionally across runners, and within runners using runner fixed effects. Because age, period and cohort are exactly collinear within a person, race-year effects were estimated in the full cross-section — where age varies within every year — and subtracted before fitting the fixed-effects models. Selective attrition was examined directly by modelling whether a runner returned to a later race. Results. The two designs diverged, and the divergence grew with age. At age 45 the cross-sectional gradient was 1.28 min/year versus 1.62 min/year within runners; at 55, 2.13 versus 3.05; and at 65, 2.98 versus 4.48 (95% CI 4.31 to 4.65) — a within-runner decline 50% steeper than the cross-sectional estimate. Attrition ran in the direction required to produce this gap: runners in the slowest quartile of their race were markedly less likely to return than the fastest (77.3% versus 84.0%), and the probability of returning fell by 0.29 percentage points per year of age. Within-runner decline was steeper in men than women at every age. Results were unchanged when the extreme-heat 2012 race was excluded and when analysis was restricted to runners with five or more finishes. Conclusions. Cross-sectional age comparisons understate how fast individual endurance performance actually declines, by roughly half at age 65, and the error compounds with age. Published age-graded standards and masters performance curves derived from cross-sectional data are therefore likely to be optimistic about the trajectory any given athlete should expect. Longitudinal designs, or explicit correction for differential dropout, are needed wherever individual decline is the quantity of interest.</p>