Though aging and the apolipoprotein E (APOE) ε4 allele are two established factors advancing Alzheimer’s disease (AD) progression,¹ how these factors advance successive occurrences of AD pathophysiological events remains largely unclear. This study aims to quantitatively determine the effects of age and the APOE ε4 allele on AD developmental processes.

We utilized Alzheimer’s Disease Neuroimaging Imitative (ADNI) 2 datasets, which included 144 subjects (of which there were 45 cognitively normal [CN], 74 mild cognitive impairment [MCI], and 25 mild AD). We employed the event-based probabilistic (EBP) model to estimate the optimal temporal ordering sequence (S^o) among brain function and structure, cerebrospinal fluid, and neurocognition biomarkers during the AD progression. Specifically, we selected the following 10 well-studied biomarkers: two cerebrospinal fluid (CSF) biomarkers of Aβ1-42 and p-tau levels; three global mean functional connectivity strength indices of hippocampus, posterior cingulate cortex, and fusiform gyrus; two gray matter concentration indices of hippocampus and fusiform gyrus; and three neurocognitive test scores, including those from the Mini-Mental State Examination (MMSE), modified 13-item Alzheimer’s Disease Assessment Scale-Cognitive Subscale (ADAS-Cog), and Rey Auditory Verbal Learning Test (AVLT). The S^o was estimated according to the EBP model,²

$$ p(X│S)=∏_{j=1}^J∑_{k=0}^Np(k)\left[∏_{i=1}^kp(x_{ij}│E_i ) ∏_{i=k+1}^Np(x_{ij}│¬E_i )\right] $$

Where $$$p(X│S)$$$ is the likelihood of the whole dataset $$$X$$$ given the sequence $$$S$$$; E_i, =1…N, represents corresponding biomarker events; $$$j$$$ represents the subjects which $$$j$$$=1…J; $$$∏_{i=1}^kp(x_{ij}│E_i )$$$ and $$$∏_{i=k+1}^Np(x_{ij}│¬E_i )$$$ are overall likelihood of measurements given that corresponding events have occurred and have not occurred, respectively; and $$$p(k)$$$ is the likelihood of being at stage $$$k$$$, which means events E₁ to E_k have occurred and events E_k+1to E_N have not occurred.

Each subject’s AD risk (stage k) was identified according to the equation below.

$$ argmax_k P(k)=∏_{i=1}^kp(x_{ij}│E_{S^o (i)} ) ∏_{i=k+1}^Np(x_{ij}│¬E_{S^o (i)} ) $$

Where implications of $$$∏_{i=1}^kp(x_{ij}│E_{S^o (i)})$$$ and $$$∏_{i=k+1}^Np(x_{ij}│¬E_{S^o (i)})$$$ refer to those in the first equation with the optimal sequence, S^o. To differentiate AD risk stages from clinical AD stages, we define the former as “scores” on the index for characterizing Alzheimer’s disease risk events, or “CARE index.”

We employed the sigmoidal model below to fit the aging trajectory of the CARE index in three clinical groups, respectively. We further investigated the aging trajectory of the CARE index in APOE ε4 carriers and noncarriers with the same sigmoidal model.

$$ CARE(x)=10e^{-a(x+c)^b}+1 $$

where x represents age.

The S^o showed that hippocampal and posterior cingulate cortex network biomarkers occur first, followed by aberrant CSF Aβ1-42 and p-tau levels, cognitive deficit, and finally regional gray matter loss and functional connectivity abnormality in the fusiform network (Figure 1A). The CARE index score was the highest in AD patients, followed in turn by MCI and CN groups (Figures 1B and 1C). We found that this among-group difference pattern remains across the mid-late life span, as well as that the CARE index scores increased with advancing age in all of the three groups (Figure 2). The APOE ε4 allele shifted the aging trajectory of the CARE index toward a higher value, which corresponds to a younger age, for all subjects; ε4 carriers relative to noncarriers showed higher CARE index scores within each age group (Figure 3). This study measures longitudinal AD progression as a function of age and APOE status across the whole AD spectrum, by associating the CARE index scores derived from 10 biomarkers with these two AD risk modulators. The aging-related increase in CARE index scores and its exacerbation by the APOE ε4 allele demonstrated in this study agree with current knowledge concerning the contributions of aging and the APOE ε4 allele on AD progression, thus justifying application of the CARE index approach in staging AD risk and underlining the necessity of age adjustment on the CARE index norm in future applications. These findings provide a surrogate to quantitatively assess aging and the APOE ε4 allele modulations on AD progression.