The countdown paradox: time-varying analysis of biomarker-clock age and symptom onset

Research focused on Alzheimer's disease (AD) 'biomarker clocks' seeks to identify ages at which AD pathological landmarks occur (e.g., initiation of amyloid accumulation) and are meaningfully related to disease outcomes (e.g., symptom onset). However, the statistical approach for assessing the association between age at biomarker-clock event and remaining time to clinical symptom onset can create a structural artifact. We term it here the 'countdown paradox', because the remaining time to symptom onset shrinks as the age at biomarker-clock event increases, which may result in inaccurate associations between age at biomarker-clock event and the remaining time. We conducted analyses to examine this issue with simulation studies and theoretical results, and also examined it empirically using five biomarkers in two longitudinal AD-related cohorts (BIOCARD and ADNI): (1) CSF Aβ42/Aβ40, (2) CSF p-tau181, (3) plasma p-tau181, (4) amyloid PET, and (5) plasma p-tau217. As an alternative analytic approach to the standard approach, we used a time-varying effect analysis that evaluates the association between biomarker-clock events and symptom onset on the 'age' time scale, avoiding the structural coupling between predictor and outcome. This analytic approach generates clinically relevant insights on the prognostic value of biomarker-clock events. Under simulated null scenarios in which the biomarker was generated independent of symptom onset, the standard analysis produced false-positive rates up to 100% and hazard ratios above 1, regardless of the true effect direction, whereas the time-varying analysis maintained type I error near the nominal 5%. Moreover, in analyses of both the BIOCARD and ADNI cohorts, the standard analysis produced uniformly significant associations for ages at biomarker-clock events, based on all five biomarkers (hazard ratios 1.94-3.34, all P < 0.01), comparable to the pattern predicted by the countdown paradox and reported in the literature. The time-varying analysis showed a different pattern for the effect of age at biomarker-clock events: for all biomarkers investigated, a younger age at biomarker-clock events is associated with a higher hazard for symptom onset on the age scale, conveying the opposite prognostic message implied by the standard analysis. These findings suggest that the standard biomarker-clock analysis may generate inaccurate associations and even reverse the apparent direction of the age effect, inverting the resulting prognostic message. A time-varying effect analysis avoids this by relating the age at a biomarker-clock event to clinical onset, with important implications for interpreting prior biomarker-clock studies.