Methods and caveats

Hazard shape is not stability

Zones on the marker explorer describe the shape of a mortality curve. A steep stretch is a candidate barrier, not a demonstrated one. Stability is a property of how people move, so instability is claimed only from within-person drift or from recovery after a challenge.

Cross-sectional versus within-person

NHANES measures each person once: it shows where people are and how risk changes across them. It cannot show how a person moves. Within-person questions use cohorts that measure the same people repeatedly, such as the Health and Retirement Study, and challenge studies that follow recovery minute by minute.

Regression to the mean

Measurement error alone makes people measured high appear to fall and people measured low appear to rise, which looks like a stable point at the mean. In HRS, readings repeated within one visit make a measure look steadier than it is over years, so each point is tested under both the weakest and the strongest noise correction and reported only if it holds under the stricter one. In ELSA, three or more visits per person give the long-term reliability directly (Heise's three-wave method), and visit pairs that may reflect a laboratory change are flagged and rerun without them.

Treatment-created density modes

Treatment moves people: blood-pressure and glucose-lowering drugs pile people up near treatment targets and can create a second peak in a distribution. The density layer leaves out treated people where a treatment flag exists, and any mode among the diagnosed may still be made by treatment.

Survivor bias in HRS

People enter the Health and Retirement Study in later life and must survive to be measured again. Those on the steepest descent are the most likely to be missing from the second measurement, so drift estimates describe survivors and understate decline.

Flexible versus four-knot curves

The main curves use a four-knot restricted cubic spline, which is straight beyond its outer knots and so cannot show a plateau at the extremes. Every curve except daily movement (from wrist accelerometry) was refitted on a penalised B-spline with the penalty chosen by AIC; the comparison is on each marker's page.

Recovery time from period averages

MIDUS records one average per period of its stress protocol: two halves of a seated baseline, a maths task, a Stroop task, a recovery period after each, and a standing challenge. There is no recovery curve to fit. Recovery time on the mountainside page is therefore computed from group means: the response is the mean of the two tasks minus the first baseline half; the shortfall is the mean of the two recovery periods minus the same baseline; the recovery fraction is one minus shortfall over response; and τ is the time constant of an exponential return whose average over the recovery window equals the shortfall over the response. When the fraction is one or more the window held the whole return and τ is reported as full recovery; when it is zero or less, as no recovery. Intervals resample people within each group.

τ is a ratio, so it is sensitive to the response. If recovery settles a fixed amount above baseline whatever the response, a smaller response gives a longer τ with no change in how fast anyone recovers. A simulation with the measured noise of one period's average shows the size of that bias; the page shows it. Group comparisons therefore also use the shortfall at equal response: a regression of each person's shortfall on group membership and on the response measured against the second baseline half, whose noise is independent of the shortfall's. Equivalence is judged against a stated smallest effect of interest, the extra shortfall that a slowing of one minute would add at the reference group's response; the model itself gives no size without placing groups on its demand axis. The code is the recovery-robustness script in the project's MIDUS folder.