Statistical analysis

The descriptive statistics for continuous variables are presented by median and inter-quartile range (IQR, 1st quartile, 3rd quartile) due to the non-normality of variables (Table ​(Table1).1). The Shapiro Wilk test was used to test the normality. Categorical variables were summarized by frequencies and percentages. The pattern of CDR-SB scores was examined using a spaghetti plot (Fig. 3A).

Disease progression modeling of CDR-SB in Alzheimer’s disease. (A) The pattern of CDR-SB values longitudinally observed in each of the three groups. (B) The smoothed line and the scatter plot with transformed CDR-SB using natural log in each of the three groups. (C) The estimated CDR-SB and the corresponding time for SCI and AMCI cohort to start to overlap. (D) The estimated CDR-SB and the corresponding time for AMCI and ADD cohort to start to overlap. (E) The AMCI cohort shifted by the time of 116.5 months and the ADD cohort shifted by 172.7 (= 116.5 + 56.2) months. (F) A disease progression model from SCI to the end stage of ADD. ADD: Alzheimer’s disease dementia; AMCI: amnestic mild cognitive impairment; CDR-SB: clinical dementia rating sum of boxes; SCI: subjective cognitive impairment.

The entire disease continuum model was developed using the following three processes: (1) modelling for each disease cohort, (2) calculating the time for CDR-SB of the two consecutive disease cohorts to start to overlap, (3) constructing an entire disease continuum model. First, for the estimation of the model for longitudinal data, the mixed-effect model with a random effect for the patient and a fixed effect for the time was applied to each set of disease cohort data. CDR-SB with skewed distribution was transformed by the natural log after adding 0.5 to all scores because zero scores occur in CDR-SB. Time effect was fitted using a linear term or a quadratic term in each model after testing the significance of the quadratic term. For the diagnosis of the estimated model, studentized residuals were used to examine model assumptions and to detect outliers for each model. The observations with absolute studentized residuals greater than 3 were considered outliers and the model was re-estimated after excluding outliers from the data (Fig. 3B). The improvements in the goodness of fits to the model after excluding outliers were evaluated using Akaike information criterion (AIC), Bayesian information criterion (BIC), and AIC with a correction for finite sample size (AICC). Second, using the estimated model of each cohort, the point estimates and 95% confidence intervals (CI) of CDR-SB at the time measured for each patient were calculated. If a point estimate of CDR-SB in AMCI fell within 95% CIs of CDR-SB in SCI, this point estimate was considered as an overlapped CDR-SB between the two cohorts, SCI and AMCI. We found the smallest score among the overlapped CDR-SB in the AMCI cohort and substituted this score into the estimated model of the SCI cohort to calculate the corresponding time to this CDR-SB (Fig. 3C). Then, we shifted the data of the AMCI cohort to start from this time (Fig. 3E). Also, the same procedure was performed for the two consecutive AMCI and ADD cohort data points. (Fig. 3D,E). Finally, we constructed a single model using whole data from the three cohorts using a mixed-effect model. (Fig. 3F). To examine the effect of education level on disease progression, another disease progression model of the entire ADD continuum was developed in lower- and higher-education groups using mixed effect models. The time from SCI to AMCI and the time from AMCI to ADD were also calculated with this model. For all tests, a p-value < 0.05 was considered statistically significant. Statistical analysis was performed using SAS 9.4 (SAS Institute Inc, Cary, NC) and R 3.5.1 (Vienna, Austria) ggplot2 package.