Y. εHC1. εHC2. εHC3. εAD1. εAD2. εAD3. P1(a1, yHC1). P2(a2, yHC2). P3(a3, yHC3) ... LME. y0, vertical y-intercept value of healthy population. Blue and red ...
S1 Fig.
^ y HC0
LME Modelling:
Inferred:
Observations: AD
AD
HC
HC
HC population
Population regression line (slope βa)
PLSR model:
^ y 0
!"#$% = '(!")#$% )
P1(a1, yHC1)
εHC1
Population regression line (slope βa)
^ y AD0
P1(a1, yHC1) ^ ^ P1(a1, y HC1) P2(a2, yHC2)
P1(a1, yAD1)
^ ^ P1(a1, y HC1)
^ y AD0
^ ^ P2(a2, y HC2)
^ ^ P1(a1, y AD1)
εAD1
εHC3 ^ ^ P3(a3, y HC3)
εAD1 ^ ^ P2(a2, y HC2)
P3(a3, yHC3)
P1(a1, yAD1)
Y
^ ^ P1(a1, y AD1)
Y
P3(a3, yHC3)
εHC2
^ y 0
εHC2
P2(a2, yHC2)
εHC1
^ y HC0
^ ^ P2(a2, y AD2)
εHC3
^ ^ P2(a2, y AD2)
^ ^ P3(a3, y HC3)
P2(a2, yAD2)
!" = !"- + /0 + = ! − !"
εAD2 P2(a2, yAD2)
^ ^ P3(a3, y AD3)
εAD2
εAD3
^ ^ P3(a3, y AD3)
εAD3 P3(a3, yAD3)
P3(a3, yAD3)
0
0 0
a1
a2
a3
0
Age
a1
a2
a3
Age
Variant ROI (vr)
Quasi-variant ROI (qvr)
Fig 1. Example of LME modelling for hypothetical variant (vr) and quasi-variant(qvr) ROIs. HC and AD are hypothetical subjects. P1 , P2 and P3 are observations of each ROI y at three different ages (a1 , a2 and a3 ). Black lines, healthy population regression line calculated from LME. yˆ0 , vertical y-intercept value of healthy population. Blue and red lines, individual regression lines estimated by assuming both as healthy. Points Pˆ1 , Pˆ2 and Pˆ3 , inferred yˆ’s for the three ages.ˆ yHC0 and yˆAD0 , the subject-specific y-intercepts estimated for HC and AD subjects, respectively. yˆHC0 and yˆAD0 of vr ROI are inferred from the yˆHC0 and yˆAD0 of qvr ROI through PLSR model. a , slope or rate change of the standard deviation of ROI per unit of age. ✏HC1 , ✏HC2 , ✏HC3 , ✏AD1 , ✏AD2 and ✏AD3 , the residuals of each observation with respect to the estimated individual regression lines.
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