Random change point model for joint modeling of cognitive decline and dementia

Abstract

We propose a joint model for cognitive decline and risk of dementia to describe the pre-diagnosis phase of dementia. We aim to estimate the time when the cognitive evolution of subjects in the pre-dementia phase becomes distinguishable from normal evolution and to study whether the shape of cognitive decline depends on educational level. The model combines a piecewise polynomial mixed model with a random change point for the evolution of the cognitive test and a log-normal model depending on the random change point for the time to dementia. Parameters are estimated by maximum likelihood using a Newton-Raphson-like algorithm. The expected cognitive evolution given age to dementia is then derived and the marginal distribution of dementia is estimated to check the log-normal assumption.

Figure 1. Expected BVRT score given the age at acceleration of cognitive decline (and 95% confidence interval)

plain line: high educational level and changepoint at 85 years short dashed line: 95% confidence interval long dashed line: low educational level and changepoint at 70 years dotted line: 95% confidence interval

Figure 2. Expected BVRT score in the years before the diagnosis given age at dementia

plain line: high educational level, dementia at 75 years long dashed line: high educational level, dementia at 90 years short dashed line: low educational level, dementia at 75 years dotted line: low educational level, dementia at 90 years

Figure 3. Observed mean of the BVRT score at each visit (and 95% confidence interval) for incident cases of dementia and average of the expected BVRT score given the age at dementia computed for cases with available measure at the visit

Horizontal bar with plain line: observed means for highly educated cases Square with dashed line: observed means for less educated cases Cross: predicted means

Figure 4. Risk function for the marginal distribution of the age at dementia estimated by the joint model and non-parametrically

plain line: high educational level, joint model short dashed line: high educational level, non parametric estimation (with confidence bands) long dashed line: low educational level, joint model dotted line: low educational level, non parametric estimation (with confidence bands)