Transition rates between amyloid and neurodegeneration biomarker states and to dementia: a population-based, longitudinal cohort study

Abstract

Background: In a 2014 cross-sectional analysis, we showed that amyloid and neurodegeneration biomarker states in participants with no clinical impairment varied greatly with age, suggesting dynamic within-person processes. In this longitudinal study, we aimed to estimate rates of transition from a less to a more abnormal biomarker state by age in individuals without dementia, as well as to assess rates of transition to dementia from an abnormal state.

Methods: Participants from the Mayo Clinic Study of Aging (Olmsted County, MN, USA) without dementia at baseline were included in this study, a subset of whom agreed to multimodality imaging. Amyloid PET (with (11)C-Pittsburgh compound B) was used to classify individuals as amyloid positive (A(+)) or negative (A(-)). (18)F-fluorodeoxyglucose ((18)F-FDG)-PET and MRI were used to classify individuals as neurodegeneration positive (N(+)) or negative (N(-)). We used all observations, including those from participants who did not have imaging results, to construct a multistate Markov model to estimate four different age-specific biomarker state transition rates: A(-)N(-) to A(+)N(-); A(-)N(-) to A(-)N(+) (suspected non-Alzheimer's pathology); A(+)N(-) to A(+)N(+); and A(-)N(+) to A(+)N(+). We also estimated two age-specific rates to dementia: A(+)N(+) to dementia and A(-)N(+) to dementia. Using these state-to-state transition rates, we estimated biomarker state frequencies by age.

Findings: At baseline (between Nov 29, 2004, to March 7, 2015), 4049 participants did not have dementia (3512 [87%] were clinically normal and 537 [13%] had mild cognitive impairment). 1541 individuals underwent imaging between March 28, 2006, to April 30, 2015. Transition rates were low at age 50 years and, with one exception, exponentially increased with age. At age 85 years compared with age 65 years, the rate was nearly 11-times higher (17.2 vs 1.6 per 100 person-years) for the transition from A(-)N(-) to A(-)N(+), three-times higher (20.8 vs 6.1) for A(+)N(-) to A(+)N(+), and five-times higher (13.2 vs 2.6) for A(-)N(+) to A(+)N(+). The rate of transition was also increased at age 85 years compared with age 65 years for A(+)N(+) to dementia (7.0 vs 0.8) and for A(-)N(+) to dementia (1.7 vs 0.6). The one exception to an exponential increase with age was the transition rate from A(-)N(-) to A(+)N(-), which increased from 4.0 transitions per 100 person-years at age 65 years to 6.9 transitions per 100 person-years at age 75 and then plateaued beyond that age. Estimated biomarker frequencies by age from the multistate model were similar to cross-sectional biomarker frequencies.

Interpretation: Our transition rates suggest that brain ageing is a nearly inevitable acceleration toward worse biomarker and clinical states. The one exception is the transition to amyloidosis without neurodegeneration, which is most dynamic from age 60 years to 70 years and then plateaus beyond that age. We found that simple transition rates can explain complex, highly interdependent biomarker state frequencies in our population.

Funding: National Institute on Aging, Alexander Family Professorship of Alzheimer's Disease Research, the GHR Foundation.

Figure 1. Diagram of the multi-state transition model

Each node denotes one of the six states in the model. Node shapes denote the type of state. Ovals represent the four different A/N biomarker states among non-demented participants. The rounded box represents dementia. The rectangular box represents death. The six arrows represent the six forward transition rates between states that were estimated in our model. All states were allowed to transition to death in the model; however, for the sake of readability we do not show the arrows corresponding to transitions to death. Our model allowed each transition rate to vary by age and so we estimated the transition rate corresponding to each arrow for a specified age. While theoretically subjects should only move from less abnormal to more abnormal states, in reality, some “backward” transitions were observed in our data. These backward transitions were rare and likely due to misclassification, but to accommodate them, the model included a single estimated transition rate from a more abnormal to a less abnormal biomarker state (0.025) that did not vary by age (arrows not shown).

Figure 2. Estimated biomarker transition rates by age

The A−N− to A+N− transition rate was allowed to vary non-linearly on the log scale with age by modeling it with restricted cubic splines with knot as ages 55, 65, 75, and 90. All other transitions were modeled with linear (on the log-scale) age effects. Blue shades indicate transitions from A− to A+. Green shades indicate transitions from N− to N+. Red shades indicate transitions to dementia.

Figure 3. Confidence intervals for estimated biomarker transition rates plotted on log scale

Note the difference in the scale between Fig 2 (arithmetic scale) and Fig 3 (log scale). The data in Fig 3 are plotted on log scale to demonstrate variance around the regression line for each rate in terms of coefficient of variation. Shaded areas indicate 95% pointwise confidence intervals. Confidence intervals were obtained by first randomly generating 10,000 multivariate normal variates centered at the maximum likelihood estimates with the variance-covariance matrix equal to the inverse of the negative of the Hessian matrix. Age-specific rates were calculated for each of the 10,000 variates and the 95% pointwise CIs were calculated as the 2.5^th and 97.5^th quantiles of these simulated age-specific rates.

Figure 4. Estimates and 95% confidence intervals for differences between transition rates for selected transitions

We interpret 95% CIs that do not include the null value of zero as significantly different at p<0.05. Confidence intervals for the difference in rates were obtained as described for Figure 3 except that the 2.5^th and 97.5^th quantiles were calculated not from the distribution of simulated rates but from the distribution of the difference in simulated rates (i.e., the 2.5^th and 97.5^th quantiles of the 10,000 simulated rate differences at each age).

Figure 5. Transition rates among the four biomarker states within non-demented participants and to dementia at ages 65, 75, and 85 years

Rates are expressed as number of transitions per 100 person-years (95% CI).

Figure 6. Estimated frequency of states by age

Assuming a cohort of non-demented A−N− participants aged 50, we used the transition rates to estimate what the frequency of each state will be as these participants age from 50 to 90. Panel A shows the estimated frequency of non-demented (cognitively normal for age and MCI) participants, participants with dementia, and participants who have died by age. Panel B shows the estimated frequency of participants in each of the four biomarker groups by age among those participants who remain alive and non-demented.