Personalized predictive modeling for patients with Alzheimer’s disease using an extension of Sullivan’s life table model

We used L-GoM to characterize the natural history of AD in a cohort of 229 participants (91 men, 138 women) over 21 semiannual examinations (spanning 10 years) in the Predictors 2 Study cohort (1997–2011),¹ the second of two highly coordinated cohort studies designed to investigate the natural history of AD and to develop improved prediction models [21]. The Predictors 2 Study cohort was representative of patients with AD with mild disease severity at the time of enrollment at three specific study sites specializing in AD—Columbia University College of Physicians and Surgeons, Johns Hopkins University School of Medicine, and Massachusetts General Hospital—but was not necessarily representative of the general AD population. An essential requirement for the present analysis was that the data adequately covered the full range of patient outcomes over the 21 examinations, and this was met by selecting study sites with different disciplinary specializations: neurology at Columbia, psychiatry at Johns Hopkins, and geriatric neurobehavior at Massachusetts General Hospital. All subjects were diagnosed with “probable AD” on the basis of 1984 National Institute of Neurological and Communicative Disorders and Stroke-Alzheimer’s Disease and Related Disorders Association criteria, equivalent to “probable AD dementia” on the basis of 2011 National Institute on Aging-Alzheimer’s Association criteria [22, 23]. Date of death was reported for 186 of the 229 participants, and AD was confirmed in 96% of available postmortem diagnostic evaluations [24]. Almost all participants had mild dementia at the time of recruitment into the study. Of 226 participants with complete Clinical Dementia Rating (CDR) data [25, 26], only 9 scored > 1; of 219 participants with complete Mini Mental State Examination (MMSE) [27] results, only 4 scored < 16; and of 217 participants with complete CDR and MMSE scores, only 1 crossed both of the indicated thresholds.

A total of 119,115 distinct data points (i.e., responses) for the 229 participants were available for model fitting for the 79 covariates listed in Table 1; 6 were fixed at the intake examination, and 73 were time-varying. All 79 covariates had p < 0.05 based on Wilks’ chi-square test [28]; 19 others (including education) with nonsignificant p values were excluded from the model. The 73 time-varying covariates spanned 11 measurement domains: (1) behavior, (2) cognition, (3) functioning, (4) dependence, (5) eyesight/hearing problems, (6) acute medical treatments/conditions, (7) psychiatric/psychotic symptoms, (8) alcohol use, (9) motor signs/symptoms, (10) depression/agitation, and (11) dementia with Lewy body symptoms.

Because the SLT/L-GoM model is a new synthesis of the SLT [13] and L-GoM [7, 8, 29] models, this section provides a self-contained nontechnical explanation for readers interested in understanding the model and interpreting its results. The mathematics underlying this synthesis are provided separately in Additional file 1 at a level of detail sufficient to reproduce our results and apply the model to similar data.

The four disease subtypes and their trajectories were determined using procedures detailed in Additional file 1: Table A.2 (see Additional file 1: Appendix) displays the Kullback-Leibler information statistics [37] used to assess the relative importance of each covariate for each of the four AD subtypes. Additional file 1: Table A.3 displays the corresponding λ parameters. Additional file 1: Table A.5 displays the corresponding pure-subtype trajectories. The statistics in Additional file 1: Tables A.2 and A.3 are summarized in Table 2 below in a form that characterizes the four subtypes according to the size and direction of the effects exhibited by the 35 most salient covariates in the model. Each combination of subtype and covariate was coded as exhibiting low (L), medium (M), or high (H) severity, but only if the associated λ parameters exhibited relatively large differences from the corresponding marginal probabilities for randomly selected patients with AD (i.e., computed by averaging over all completed examinations, not just examination 1). Operationally, the L-M-H designation was made only if the Kullback-Leibler information statistic [37] was > 0.50 (see Additional file 1: Appendix); otherwise, the covariate severity remained unclassified for the subtype. The M designation was used only for covariates with three or more severity levels, and only if an unambiguous H or L designation could not be made.

The severity patterns in Table 2 show that the subtypes are quite distinct. Subtype 1 had the largest number of covariates exhibiting low severity (n = 17). Subtype 2 had low severity for 5 of the same 17 covariates. Subtype 3 showed no overlap in severity designations with subtype 1 or 2. Subtypes 3 and 4 had high severity on 11 and 17 covariates, respectively, but the high-severity designations did not overlap. Subtypes 3 and 4 had medium and high severity, respectively, on the equivalent institutional care variable (number 53, the only covariate for which both subtypes had severity codes), on the basis of their respective use of adult home care vs. FTC. Equivalent institutional care was the top-ranked covariate (based on p values).

Subtype 4, representing the terminal endpoint of the AD process, had high patient dependence, moderate extrapyramidal symptoms, poor cognition, and highly impaired functioning. Subtype 3 was the only subtype with any severity designations on items within domains 1, 7, and 10 (behavior, psychiatric/psychotic symptoms, and depression/agitation), and it was the only subtype with high severity on the personality items within domain 3 (Blessed Dementia Rating Scale [BDRS]). Hence, psychiatric and behavioral symptoms, personality changes, and depression were strongly exhibited only by subtype 3. Subtype 1 had low initial severity on 17 items, slow AD progression (Additional file 1: Table A.5), and the best prognosis. Subtype 2 had low initial severity on five items, fast AD progression (Additional file 1: Table A.5), and the worst prognosis. Compared with subtype 1, subtype 2 was more likely to be female, be older, score lower on the MMSE, and be homozygous for the apolipoprotein E (ApoE) ε4 allele.

We evaluated the assumption that overall severity increased over subtypes by applying the LMH severity coding procedure to five summary measures: CDR [25], MMSE score [27], BDRS score [38, 39], Dependence Scale score [40], and psychiatric symptoms [41, 42] (Table 2). The severity codes for subtypes 1 and 2 were indistinguishable on four of the five summary measures, the exception being MMSE, with subtype 1 coded low (L) and subtype 2 unclassified. The severity for subtype 3 was higher than for subtype 1 on all five summary measures and higher than for subtype 2 for all but MMSE. Thus, the results for the summary measures exhibited monotonic severity patterns, which confirmed the assumed overall ordering of the subtypes; moreover, taken as a set, the severity codes were consistent with the labeling of the subtypes as mild, mild-moderate, moderate, and severe.

A finding of great prognostic significance was that the rate of AD progression was substantially faster for subtype 2 than for subtype 3, which, in turn, was substantially faster than for subtype 1 (Additional file 1: Table A.5). The ordering reversal between subtypes 2 and 3 was maintained throughout the 10-year study period, with the fourth component of the pure-subtype trajectories reaching final values of 0.58, 0.99, and 0.93, respectively, for subtypes 1–3.

The relationships between the three prognostic subtypes and the five subgroups can be visualized using the scatterplot on the left side of Fig. 1. Except for ten subjects located at the subtype 1 vertex and three subjects at the subtype 2 vertex, the scatterplot shows no evidence of clustering of the subjects. The subtype 3 vertex was unoccupied (because the highest GoM score for subtype 3 was 0.89); moreover, the nearby regions were thinly populated. The five subgroups are color-coded in Fig. 1; they were constructed to be cleanly separated and substantially more homogeneous than the overall sample (see Additional file 1: Table A.7). In contrast, the scatterplot on the right side of Fig. 1 shows that, although the sex effect was highly significant (p = 0.00007) (Additional file 1: Table A.2), males and females were distributed throughout the plot with no clean separation. Females, however, had their highest relative concentrations near subtype 2 and between subtypes 1 and 2. Males had their highest relative concentrations between subtypes 1 and 3 and between subtypes 2 and 3; seven males were located at the subtype 1 vertex.

The basic 6-month mortality probabilities (λ parameters) were 0.6% and 16.0% for subtypes 1 and 4, respectively, and zero for subtypes 2 and 3 (Additional file 1: Table A.3), indicating that individual mortality was determined by subtypes 1 and 4 alone, constrained to the range 0–16.0%, with the rate at time t primarily determined by an individual’s time-varying GoM score on subtype 4 (maximum 16.0%). Figure 2 displays the observed vs. estimated survival curves for all participants, males and females, and subgroups 0–4. The estimates were almost all within the simultaneous 95% confidence bands around the observed values, the sole exceptions being subgroup 2 at 3.5–4.5 years.

FTC represents “around-the-clock supervision of personal care, safety, or medical care” [40], as measured by the top-ranked covariate, equivalent institutional care. The basic disability probability (λ parameter) was 83.2% for subtype 4 and zero for subtypes 1–3 (Additional file 1: Table A.3), with the rate at time t fully determined by an individual’s time-varying GoM score on subtype 4. Figure 3 displays the observed vs. estimated FTC rates for all participants, males and females, and subgroups 0–4. The estimated FTC rates increased over time for both sexes and all subgroups. The fits to the observed FTC rates were excellent; all but three estimated values (both sexes and females at 6 years and subgroup 2 at 6.5 years) were within the pointwise 95% confidence bands around the observed values.

Figure 4 displays the overall survival curves (left side) and the corresponding FTC disability-free survival curves (right side) for all participants and subgroups 0–4. Both sets of survival curves decreased monotonically over time and were strongly separated by subgroup. Subgroup 2 crossed over subgroup 0 at 2.5 and 1.5 years, respectively, implying that the underlying hazards were not proportional.

Table 3 displays the means, 95% CIs, and ranges of the 10-year TLEs, DFLEs, and DLEs for all participants and subgroups 0–4, assuming that survival beyond year 10 (examination 21) was censored. The TLEs and DFLEs are the areas under the respective plots in Fig. 3. Whereas the DFLEs varied widely across subgroups, the DLEs did not; the relative variation of the TLEs was intermediate between that of the DFLEs and DLEs. Mean 10-year TLE differed widely across subgroups: range 3.57–7.98 years, average 6.09 years. Mean 10-year DFLE differed relatively even more widely across subgroups: range 1.23–6.47 years, average 4.03 years. Mean 10-year DLE was relatively much closer: range 1.51–2.34 years, average 2.06 years. Subgroup 4 was distinguished by its relatively short DFLE (1.23 years) and subgroup 1 by its relatively long DFLE (6.47 years). Among the subgroups most closely related to the prognostic subtypes (1–3), subgroup 2 had the shortest DFLE and the longest DLE at 2.85 and 2.33 years, respectively.