A viewpoint on change point modeling for cognitive aging research: Moving from description to intervention and practice

Journal Pre-proof A viewpoint on change point modeling for cognitive aging research: Moving from description to intervention and practice Briana N. Sprague

PII:

S1568-1637(19)30117-5

DOI:

https://doi.org/10.1016/j.arr.2019.101003

Reference:

ARR 101003

To appear in:

Ageing Research Reviews

Received Date:

17 April 2019

Revised Date:

8 November 2019

Accepted Date:

23 December 2019

Please cite this article as: Sprague BN, A viewpoint on change point modeling for cognitive aging research: Moving from description to intervention and practice, Ageing Research Reviews (2019), doi: https://doi.org/10.1016/j.arr.2019.101003

This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier.

1 A viewpoint on change point modeling for cognitive aging research: Moving from description to intervention and practice Briana N. Sprague The Pennsylvania State University, 119 Health and Human Development Building, 16802, University Park, PA, [email protected] Highlights Change point models (CPMs) are useful for event-based time conceptualization.



CPMs can evaluate compression of cognitive morbidity in intervention studies.



More basic and applied research should use CPMs for cognitive aging research.

-p

ro

of



re

Chronological age is a commonly-used time metric, but there may be more relevant time measures in older adulthood. This paper reviews change point modeling, a type of analysis

lP

increasingly common in cognitive aging research but with limited application in applied research. Here, we propose a new application of such models for cognitive training studies.

ur na

Change point models have the potential to assess intervention outcomes such as compression of morbidity or reduced decline after an event (e.g., reduced cognitive decline after a dementia diagnosis) as well as changes in outcome trajectories across different intervention dosages (e.g.,

Jo

initial vs. booster training). Through change point modeling, we can better understand how interventions impact cognitive aging trajectories. 1. The Problem with Age Chronological age is an intuitive, easily assessed, meaningful measure of the passage of time. Despite its ubiquity, “age” may be a proxy for a variety of cognitive, biological, or neurological changes and conflate “true aging” with such processes (Kim & Jazwinski, 2015;

2 Ram, Gerstorf, Fauth, Zarit, & Balmberg, 2010). For example, 65- and 75-year-olds may perform substantially differently on cognitive tasks; however, are differences driven by aging alone or subclinical pathology in the 75-year-old? Additionally, older age is marked by increased cognitive heterogeneity (Mella, Fagot, & de Ribaupierre, 2016; Stone, Lin, Dannefer, & KelleyMoore, 2017), reducing the utility of mean performance in older ages. Furthermore, variability exists between cognitive domains in how they decline (Singer, Verhaeghen, Ghisletta,

of

Lindenberger, & Baltes, 2003; Sprague, Hyun, & Molenaar, 2017). For example, processing

ro

speed and memory do not decline simultaneously or at the same rate across older adulthood.

Complicating matters is the overreliance on cross-sectional data, which are appropriate

-p

for age-related differences but not changes. The age convergence assumption (Sliwinski,

re

Hoffman, & Hofer, 2010) states that cross-sectional and longitudinal results would converge on a common trajectory. This is infrequently observed in practice, demonstrated by the failure to

lP

consistently replicate cross-sectional findings underlying cognitive aging theories such as processing speed (Salthouse, 1996) or common cause theory (Christensen, Mackinnon, Korten,

ur na

& Jorm, 2001) in longitudinal datasets. This assumption violation is relevant because it obscures how cognition changes across age and may over- or underestimate age effects. In fact, chronological age may not be the most appropriate way to model developmental trajectories in older adults (Gerstorf, Ram, Lindenberger, & Smith, 2013; Ram et al., 2010).

Jo

To address this, researchers increasingly rely on alternative time metrics and longitudinal

approaches to disentangle between- and within-person cognitive aging processes and better describe cognitive trajectories (Hoffman, 2012; Ram et al., 2010; Sliwinski et al., 2010; Sliwinski & Mogle, 2008). Briefly, researchers compare multilevel models with different time metrics (e.g., age, time since baseline, dementia, death) and evaluate which models have better

3 statistical fit (e.g., AIC or BIC; Hoffman, 2012). Also known as event-based modeling, this has been applied to cognitive aging research for the last 20 years (e.g., Joseph et al., 1999) but has proliferated in the last decade (e.g., Wilson, Leurgans, Boyle, & Bennett, 2011; Wilson, Segawa, Hizel, Boyle, & Bennett, 2012; L. Yu et al., 2013). Event-based modeling is well-equipped to identify antecedents and moderators of both normative and non-normative cognitive trajectories. 2. Change Point Models

of

The event-based modeling technique most frequently used in cognitive aging research is

ro

change point modeling. Change points, also called turning points (McArdle & Wang, 2008),

break points (Muggeo, 2008), bent-cable (Chiu, Lockhart, & Routledge, 2006), or broken stick

-p

models (White, Muniz-Terrera, & Matthews, 2018), are instances when trajectories may be

re

disrupted by some event, marked by a possible change in slope post-event (van den Hout, Muniz-Terrera, & Matthews, 2013). Change point models can estimate the slope of cognitive

lP

function before and after a pre-specified event, such as retirement (Finkel, Andel, Gatz, & Pedersen, 2009), mild cognitive impairment diagnosis (MCI; e.g., Buracchio, Dodge, Howieson,

ur na

Wasserman, & Kaye, 2010; Silbert et al., 2012; Wilson et al., 2011) or dementia diagnosis (e.g., Grober et al., 2008; Johnson, Storandt, Morros, & Galvin, 2009; Li, Dowling, & Chappell, 2015; Thorvaldsson et al., 2011). Change point research that specifies a change point a priori generally asks: (1) which cognitive domains decline before the specified change point, (2) which cognitive

Jo

domains undergo accelerated decline after the change point, and (3) can moderators predict either the change point location or pre- and post-event declines (i.e., slopes)? Change point models can also be used to determine the change point of a specific

outcome of interest by allowing the model to determine the change point, such as time to death (or terminal) drops (e.g., Batterham, Mackinnon, & Christensen, 2011; MacDonald, Hultsch, &

4 Dixon, 2011; Muniz-Terrera, Minett, Brayne, & Matthews, 2014; Sliwinski et al., 2006; L. Yu et al., 2013). Models that allow the data to specify a change point aim to identify when a terminal drop begins and if the timing of the terminal drop varies for different cognitive domains. Modeldriven change point analyses can provide a data-driven approach to identify hidden events in longitudinal data (e.g., terminal drops). For example, time to death models could uncover terminal drops without a priori hypothesizing when the terminal drop period occurs. This is a

of

unique strength compared to other methods such as latent growth curve models, where change

ro

points are a priori hypothesized (e.g., Sternäng et al., 2016). It should be noted, however, that both methods are appropriate for evaluating slopes around a known change point, such as age or

-p

diagnosis. While other methods such as time-varying effects modeling (TVEM) also allow free

re

estimation of such turning points (e.g., Tan, Shiyko, Li, & Li, 2012), such techniques answer fundamentally different research questions. TVEM, for instance, could answer whether the

lP

strength of the relationship between two variables differs as a function of one’s nearness to death, but it does not answer questions about the slope of one variable. That is, change point

ur na

models are able to combine strengths of other analytic approaches while answering substantively meaningful questions. These questions are important for understanding how late-life cognitive function changes before and after meaningful events, as well as what risk and resilience factors affect the timing and tempo of cognitive change.

Jo

2.1 Unresolved issues of change point models in cognitive aging There remain unresolved issues limiting our understanding of late-life cognitive

trajectories. While longitudinal research consistently demonstrates that speed of processing is the first cognitive domain to decline across older adulthood (Schaie, 1989; Zaninotto, Batty, Allerhand, & Deary, 2018), the temporal order of cognitive decline with non-age-based time

5 anchors is unknown in the cases of MCI and death (e.g., it is unknown whether speed of processing declines significantly earlier than other cognitive domains when time to MCI conversion is the time anchor) or tentatively accepted in the case of probable Alzheimer’s disease (Karr, Graham, Hofer, & Muniz-Terrera, 2018). The role of moderators in the change point process has also not yet been established. For

of

instance, individuals with higher education have slower rates of cognitive decline prior to a dementia diagnosis, but they are more likely to experience accelerated cognitive decline

ro

afterward (Karr et al., 2018). Moderators of cognitive decline include physical health/function

-p

(Muniz-Terrera, van den Hout, Piccinin, Matthews, & Hofer, 2013; Wilson, Segawa, Buchman, et al., 2012), genetic/neurological risk factors (Boyle et al., 2013; Wilson, Segawa, Hizel, et al.,

re

2012; L. Yu et al., 2013), baseline cognitive function/impairment (Muniz-Terrera et al., 2013; Sliwinski et al., 2006; Wilson, Segawa, Hizel, et al., 2012), education (Muniz-Terrera et al.,

lP

2014), and personality (Wilson et al., 2015). The impact of moderators on either the change point or the slopes have been inconsistent across studies and cognitive domains (Karr et al., 2018), so

ur na

it remains unclear which moderators are important for which cognitive domains. This is important as a better understanding of such moderators will enable more precise models across multiple groups of individuals thus enhancing our ability to detect declines earlier (e.g., early identification). Related, some such moderators are modifiable which may allow for candidate

Jo

behavioral interventions for cognitive morbidity compression. Taken together, cognitive decline is not uniform across age and alternative event-based

time metrics should be considered to determine the best way to conceptualize time. Although event-based models may be more statistically informative, it remains unclear how these findings can be used for interventions or other applied settings.

6 3. Moving from Description to Practice To our knowledge, change point modeling is primarily used with observational data but could easily be implemented in experimental research designs. To illustrate, one study from the Advanced Cognitive Training for Independent and Vital Elderly (ACTIVE) trial (Jobe et al., 2001) found that processing speed training reduced dementia risk by 29% across ten years compared to a no-contact control group (Edwards et al., 2017). While this is one of the most

of

promising interventions to date, the training did not work (in terms of preventing dementia) for

ro

8.5% (n = 59) of participants who converted to dementia. However, those who experienced

dementia conversion in the processing speed group may still have received benefits from training

-p

such as cognitive and everyday functioning improvements (Edwards et al., 2017; Rebok et al.,

re

2014; Ross et al., 2016; Ross, Freed, Edwards, Phillips, & Ball, 2017; Willis et al., 2006), even if preventing dementia conversion was unsuccessful among this subsample of 8.5% of participants.

lP

If one was interested in subanalyses examining those who converted to dementia (i.e., those who converted to dementia in spite of receiving the intervention), receiving processing

ur na

speed training could be included as a moderator on the intercept and slopes. These analyses would answer whether processing speed training delayed conversion to dementia or attenuated post-diagnosis decline, respectively. Figure 1 presents a hypothetical comparison of trajectories across ten years of a control group that did not receive the training (A) and a subsample of the

Jo

processing speed training group that did not respond to the training as indicated by converting to dementia (B). Group A and Group B start out with the same pre-dementia diagnosis slope on some measure of cognitive function. Using change point modeling with time to dementia diagnosis as the event-based change point, one could assess whether processing speed training impacts the change point location (dashed line) and the post-change point slope. If training

7 conferred benefits but participants still converted to dementia, their trajectories may look like that presented in Figure 1B. Specifically, while a subsample of participants in the processing speed group converted to dementia, they still benefitted from the training as indicated by a less steep post-diagnosis cognitive decline compared to the control group. Unlike other approaches such as hazard ratios (Edwards et al., 2017), this approach provides information about people who do not receive the dementia prevention benefit and could identify incremental benefits such

of

as delayed dementia diagnosis or decelerated post-diagnosis cognitive decline, even if dementia

ro

prevention was unsuccessful.

Conceptually, change point models can also address complex dosage delivery designs.

-p

For example, the ACTIVE trial included an initial training of ten sessions after baseline followed

re

by further randomization of compliant participants who could receive an additional four sessions prior to the annual 1 and annual 3 assessments (Jobe et al., 2001). Thus, compliant participants

lP

could receive up to 18 sessions if randomized to additional booster training or 10 sessions if not randomized to additional booster sessions. Change point models enable us to examine if slopes

ur na

not only differ by intervention group assignment but also by dosage assignment (e.g., intention to treat (ITT) or treatment received models). For example, Figure 2 illustrates a hypothetical comparison of a processing speed training arm assigned to receive the initial 10 sessions, as well as the booster doses at Annual 1 and Annual 3, against a no-contact control group. This approach

Jo

would address whether booster sessions sustained intervention-related gains in cognitive function.

3.1. Research Design Considerations Change point models have a number of requirements that should be considered in

intervention design. First, intervention sample sizes should be large enough and followed for

8 enough time for participants to experience the pre-event slope, event itself, and post-event slope. For example, if the study sample is those at risk of conversion to dementia, more intensive assessments in the beginning of the trial would be warranted to capture the conversion process. Additionally, more intensive assessments immediately after the event occurs would be appropriate for the post-event slope as well. While change point models have been implemented on samples as small as 37 (Carlson et

of

al., 2008), the average sample size of studies included in a recent review were 448 (Karr et al.,

ro

2018). Similar to traditional growth curve models (Curran, Obeidat, & Losardo, 2010), sample sizes greater than 100 are more common and likely produce more reliable parameter estimates. A

-p

larger sample size is necessary when the change point is unknown (Kwok, Luo, & West, 2010).

re

If the event is uncommon and the sampling procedures draw from community-dwelling older adults, recruitment procedures such as oversampling those with a higher likelihood of

lP

experiencing the event should be implemented.

Alternatively, if the sample is healthy and one is interested in time to death analyses,

ur na

participants must be followed long enough to ensure a sufficient number of deaths are observed. The number of timepoints necessary will vary depending on whether the change point time is known, but at least four or five timepoints are recommended for an efficient yet reliable study design (Wu, Jia, Kinai, & Little, 2017). Notably, some change point model simulations were

Jo

implemented on seven (Ning & Luo, 2017) or eight (Kwok et al., 2010) timepoints, highlighting the large number of assessments optimal for such models. Not only would there need to be enough timepoints, but there would also need to adequate time between assessments to capture an event with an unknown timing such as death and MCI diagnosis. Previous studies on change point models ranged from nine to 30 years of follow-up (Karr et al., 2018), but there is no

9 standard or recommended length of time for follow-up, as long as the event of interest is captured. That is, the interval between assessments should be long enough for an event to occur (e.g., not multiple assessments over one week if the event is expected to occur over months or years), but not so long as to miss the event (e.g., assessing such that at baseline no participants have dementia but at follow-up every participant has dementia with no assessment of when

of

diagnosis occurred). Multiple follow-up assessments also present the issue of retest effects, particularly on

ro

pre-change point slopes. To overcome this, one study adjusted for the number of timepoints as a

-p

proxy of retest effects and found that change points occurred further from death in psychomotor speed, learning, memory, and language but not executive function (Dodge, Wang, Chang, &

re

Ganguli, 2011). Including the number of assessments as a covariate may address concerns of retest effects on change points and their slopes. Prior work illustrating various scenarios such as

lP

unknown change points and budget constraints provides example sampling procedures to aid in efficient research design (Wu et al., 2017).

ur na

A limitation of change point models is that the event of interest may never occur over the study period for some participants. One option is to remove participants who did not experience the event, such as not including participants who did not die in time-to-death models (van den

Jo

Hout et al., 2013) and participants who did not convert to MCI or dementia (Wilson et al., 2011; Li et al., 2015). Another option is to use model-specified change points. For example, verbal memory declines before a probable Alzheimer’s disease diagnosis by several years, whereas executive function declines occur a few months prior to diagnosis (Karr et al., 2018). This suggests that verbal memory assessments could be used to indicate prodromal Alzheimer’s disease, whereas executive function assessments may not be as sensitive to indicate a prodromal

10 period. Even if Alzheimer’s disease diagnosis does not occur within the study period, a decline in verbal memory specified by a change point model could be a sensitive marker of cognitive decline before an official diagnosis occurs. Notably, these analyses would be dependent on a sufficient sample of those experiencing the event, i.e., converting to dementia. If change point models cannot be implemented, other analytic techniques examining classes of responders could be implemented if the research questions are appropriate for such statistical approaches. For

of

example, one could assess responders to treatment or nonresponders using latent class analysis

ro

(see J. Yu & Tatia, 2018 for an applied cognitive aging example). Latent class analysis could answer questions such as predictors of response class but could not answer when change points

-p

occur.

re

In addition to design limitations, there is a complementary computational limitation to change point models. While fixed effect models are computationally simpler to implement, this

lP

group-based approach assumes that all participants have the same initial value, pre- and postchange point slope, and change point occurrence. It is likely this assumption is not tenable, so

ur na

random change point models are ideal to better capture such between-person variability (Dominicus, Ripatti, Pedersen, & Palmgren, 2008). It is possible to model random effects for the (1) intercept, (2) change point, and (3) pre- and (4) post-change point slopes with an unstructured covariance matrix (Brilleman, Howe, Wolfe, & Tilling, 2017). These series of effects would

Jo

answer whether there was significant between-person variability in (1) initial status, (2) location of the change point, (3) pre-change point slope, and (4) post-change point slope. While substantively interesting, this is computationally intensive. Specifically, four random variances and six random covariances would need to be freely estimated, and models of this complexity may not converge (e.g., MacDonald et al., 2011 for a brief discussion of random effects in

11 change point models). There is no consensus on how to best address this limitation, but Bayesian approaches appear to be most commonly implemented in random change point models (Karr et al., 2018). Cognitive aging research presents a few unique challenges worth remarking upon as well. For instance, one may be interested in examining terminal drops prior to death but does not have an a priori prediction of when the change point occurs (e.g., does the terminal drop period begin

of

three years prior to death?). Traditionally, change points would be a priori hypothesized and the

ro

resultant models would be evaluated using fit indices. However, simulation studies demonstrate that while the omnibus model fit tests suggest acceptable model fit, the estimated change point

-p

parameter would be misspecified. That is, the change point would be incorrectly identified, but

re

the model fit would suggest that the change point is correctly identified (Ning & Luo, 2017). To address this, newer techniques allow for the change point to be freely estimated without

lP

requiring a priori predictions of where the change occurs (Ning & Luo, 2017). As stated above, this is computationally intensive and requires a sufficient sample size.

ur na

4. Conclusions and Future Recommendations

Although cognitive interventions aim to maintain cognitive and everyday function, there is currently no effective way to completely prevent dementia for all people (Alzheimer's Association, 2017). Even delaying cognitive impairment by five years is expected to cut the

Jo

prevalence and cost by about 40% each (Zissimopoulos, Crimmins, & St. Clair, 2014). Using change point models to analyze intervention effects provides more nuance than other analytic strategies like hazard ratios, growth curve modeling, and time-varying effects modeling. Even if individuals convert to MCI or dementia, change point models may reveal that their conversion is

12 delayed or their rate of cognitive deterioration is slowed which is a highly meaningful outcome for the individuals, their families, and the public. Relatedly, change point models are useful in quantifying compression of morbidity, or shortening the duration of disability and the “fixed occurrence of death” (Fries, 1980). Although frequently used to describe physical disability (e.g., Crimmins & Beltrán-Sánchez 2011), compression of cognitive morbidity could be conceptualized as reducing the prevalence of MCI,

of

incident dementia, or reducing terminal cognitive decline. Only one study has found compression

ro

of cognitive morbidity across two older adult cohorts (Langa et al., 2008), where fewer older adults reach cognitive impairment but experience accelerated cognitive decline when

-p

approaching death compared to previous cohorts. Using change point modeling, future research

re

can examine whether behavioral interventions ameliorate post-impairment declines. If older adults are less impaired immediately prior to death, there are positive implications for clinically-

lP

meaningful outcomes like and healthcare expenditures (Allen et al., 2017). Change point modeling provides the opportunity to examine clinically meaningful

ur na

representations of time beyond chronological age. When applied to cognitive training, researchers can use change point modeling to elucidate nuanced training effects beyond delay of dementia diagnosis, such as less steep declines in function post-diagnosis or the impact of different dosing schedules. The requirements of change point models create specific design

Jo

considerations that make them not appropriate for all research studies. As others note (Karr et al., 2018), the utility of change point models may be unclear since they rely on the event to have occurred and collection of post-event data. Especially in time to death modeling, practical use is undercut because terminal drop periods cannot be identified until the individuals have died. Large-scale observational datasets traditionally used in change point modeling have enough

13 participants but this will present a challenge for implementing such models with intervention research, particularly pilot studies with small sample sizes. If change point models are inappropriate for one’s dataset, other research questions could be asked that do not rely on change point models, such as the impact of training on everyday function or other outcomes. Subanalyses could be analyzed on those who do convert, if there are any. Despite the fact that immediate applicability is unknown, basic research using change

of

point models is critical as there is no consensus on cognitive trajectories of MCI or death (Karr et

ro

al., 2018). Chief among these is the unknown temporal ordering of domain decline with non-age metrics (as the decline in normative aging is well-established). Particularly in time to MCI

-p

models, it is unclear which cognitive domains are affected earlier in the disease timecourse. By

re

identifying temporal ordering of cognitive domains in these alternative time metrics, domains that are the first to decline could be used as screening tools to identify older adults most

lP

susceptible to future decline and disease conversion. Researchers could also identify moderators of both when the change point occurs and the post-change point slope. Ultimately, we argue that

ur na

both basic and applied research are necessary to maximize the utility of change point models for cognitive aging research.

Because there are no completely effective prevention programs for MCI, dementia, or death, compression of morbidity is essential to ensuring quality of life in the final years. Future

Jo

research should examine: (1) cognitive decline rates prior to meaningful events to identify early signs of future impairment, (2) (modifiable) moderators of change point locations and post-event slope, and (3) behavioral interventions’ impact on change points with the goal of delaying the event and attenuating post-event declines. Delaying or reducing the rate of cognitive dysfunction is critical as the number of those with dementia is expected to rise to over 13 million by 2050

14 (Alzheimer's Association, 2017). Funding agencies are interested in dementia-related research (Department of Health and Human Services, 2017), particularly work that identifies prodromal risk and resilience factors of cognitive decline and dementia (National Institutes of Health, 2018). As resources explaining how to implement change point models become more ubiquitous across myriad statistical programs such as (but not limited to) SAS (SAS Institute Inc.), Mplus (Ning & Luo, 2017), R (Killick, Eckley, Fearnhead, & Lee, 2016), SPSS (SPSS Statistics

of

Support, 2018) and Stan (Brilleman et al., 2017), such models will be vital to identify cognitive

ro

interventions that reduce time spent with cognitive dysfunction and attenuating cognitive decline after disability onset. Once the timing and tempo of cognitive decline are documented, we will

Jo

ur na

lP

re

-p

have better benchmarks to evaluate intervention effectiveness.

15 Figure 1. Hypothetical Comparison of a (A) Control and (B) Processing Speed Intervention Subgroup Analysis.

-2.5

00

2.5

re

‡Time since baseline (years)

-5

0

2.5

5

5

7.5

10

lP

†Time to dementia (years)

-p

ro

of

Cognitive Function

(A)

Jo

Cognitive Function

ur na

(B)

†Time to dementia

-7.5

‡Time since baseline 0

-5

-2.5

2.5

5

0

2.5

7.5

10

16

Jo

ur na

lP

re

-p

ro

of

Note. The hypothetical analysis would be a subgroup analysis completed only on those who eventually converted to dementia during the follow-up period. The pre-diagnosis slopes for both groups are the same. The dashed line indicates where the diagnosis occurs. The post-diagnosis slope for the control group is accelerated, indicating accelerated cognitive decline after diagnosis compared to the processing speed group. In this example, the time to the average dementia diagnosis in years are different (as indicated by the first x-axis, or †), but the years since baseline are the same (as indicated by the second x-axis, or ‡).

17

Posttest

Annual 1

Annual 2

Annual 3

Annual 4

re

Baseline

-p

ro

of

Cognitive Function

Figure 2. Hypothetical Comparison of Processing Speed Group with Booster Against No-Contact Control Subgroup Analysis.

ur na

lP

Note. The hypothetical analysis would be a subgroup analysis completed only on those who assigned to receive the initial processing speed training and booster sessions at Annual 1 and Annual 3 compared to the no-contact control. The thick solid line represents the processing speed group, and the thick dashed line represents the no-contact control group. The dashed lines at posttest, Annual 1, and Annual 3 represent the assessments immediately after the processing speed training delivery.

FUNDING

Briana N. Sprague received support by the Albert and Lorraine Kligman Graduate Fellowship,

Jo

The Pennsylvania State University. CONFLICT OF INTEREST

All authors have no conflicts of interest.

Annual 5

18

Jo

ur na

lP

re

-p

ro

of

References Allen, N. B., Zhao, L., Liu, L., Daviglus, M., Liu, K., Fries, J., . . . Lloyd-Jones, D. M. (2017). Favorable cardiovascular health, compression of morbidity, and healthcare costs. Circulation, 135(18), 1693-1701. doi:10.1161/CIRCULATIONAHA.116.026252 Alzheimer's Association. (2017). 2017 Alzheimer's disease facts and figures. Alzheimer's & Dementia, 13(4), 325-373. doi:10.1016/j.jalz.2017.02.001 Batterham, P. J., Mackinnon, A. J., & Christensen, H. (2011). The effect of education on the onset and rate of terminal decline. Psychology and Aging, 26(2), 339-350. doi:10.1037/a0021845 Boyle, P. A., Wilson, R. S., Yu, L., Barr, A. M., Honer, W. G., Schneider, J. A., & Bennett, D. A. (2013). Much of late life cognitive decline is not due to common neurodegenerative pathologies. Annals of Neurology, 74(3), 478-489. doi:10.1002/ana.23964 Brilleman, S. L., Howe, L. D., Wolfe, R., & Tilling, K. (2017). Bayesian piecewise linear mixed models with a random change point: An application to BMI rebound in childhood. Epidemiology, 28(6), 827-833. doi:10.1097/EDE.0000000000000723 Buracchio, T., Dodge, H. H., Howieson, D., Wasserman, D., & Kaye, J. (2010). The trajectory of gait speed preceding mild cognitive impairment. Archives of Neurology, 67(8), 980-986. doi:10.1001/archneurol.2010.159 Carlson, N. E., Moore, M. M., Dame, A., Howieson, D., Silbert, L. C., Quinn, J. F., & Kaye, J. A. (2008). Trajectories of brain loss in aging and the development of cognitive impairment. Neurology, 70(11), 828-833. doi:10.1212/01.wnl.0000280577.43413.d9 Chiu, G., Lockhart, R., & Routledge, R. (2006). Bent-cable regression theory and applications. Journal of the American Statistical Association, 101(474), 542-553. doi:10.1198/016214505000001177 Christensen, H., Mackinnon, A. J., Korten, A., & Jorm, A. F. (2001). The "common cause hypothesis" of cognitive aging: Evidence for not only a common factor but also specific associations of age with vision and grip strength in a cross-sectional analysis. Psychology and Aging, 16(4), 588-599. doi:10.1037/0882-7974.16.4.588 Crimmins, E. M., & Beltrán-Sánchez , H. (2011). Mortality and morbidity trends: Is there compression of morbidity? The Journals of Gerontology, Series B: Psychological Sciences and Social Sciences, 66B(1), 75-86. doi:10.1093/geronb/gbq088 Curran, P. J., Obeidat, K., & Losardo, L. (2010). Twelve frequently asked questions about growth curve modeling. Journal of Cognitive Development, 11(2), 121-136. doi:10.1080/15248371003699969 Department of Health and Human Services. (2017). President's HHS FY 2017 budget factsheet. Washington, D.C.: HHS Headquarters Retrieved from https://www.hhs.gov/about/budget/fy2017/budget-factsheet/index.html Dodge, H. H., Wang, C. N., Chang, C. C., & Ganguli, M. (2011). Terminal decline and practice effects in older adults without dementia: The MoVIES Project. Neurology, 77(8), 722730. doi:10.1212/WNL.0b013e31822b0068 Dominicus, A., Ripatti, S., Pedersen, N. L., & Palmgren, J. (2008). A random change point model for assessing variability in repeated measures of cognitive function. Statistics in Medicine, 27(27), 5786-5798. doi:10.1002/sim.3380 Edwards, J. D., Xu, H., Clark, D. O., Guey, L. T., Ross, L. A., & Unverzagt, F. (2017). Speed of processing training results in lower risk of dementia. Alzheimer's & Dementia:

19

Jo

ur na

lP

re

-p

ro

of

Translational Research & Clinical Interventions, 3(4), 603-611. doi:10.1016/j.trci.2017.09.002 Finkel, D., Andel, R., Gatz, M., & Pedersen, N. L. (2009). The role of occupational complexity in trajectories of cognitive aging before and after retirement. Psychology and Aging, 24(3), 563-573. doi:10.1037/a0015511 Fries, J. F. (1980). Aging, natural death, and the compression of morbidity. The New England Journal of Medicine, 303(3), 130-135. doi:10.1056/NEJM198007173030304 Gerstorf, D., Ram, N., Lindenberger, U., & Smith, J. (2013). Age and time-to-death trajectories of change in indicators of cognitive, sensory, physical, health, social, and self-related functions. Developmental Psychology, 49(10), 1805-1821. doi:10.1037/a0031340 Grober, E., Hall, C. B., Lipton, R. B., Zonderman, A. B., Resnick, S. M., & Kawas, C. (2008). Memory impairment, executive dysfunction, and intellectual decline in preclinical Alzheimer's disease. Journal of the International Neuropsychological Society, 14(2), 266-278. doi:10.1017/S1355617708080302 Hoffman, L. (2012). Considering alternative metrics of time: Does anybody really know what "time" is? In J. R. Harring & G. R. Hancock (Eds.), Advances in longitudinal methods in the social and behavioral sciences (pp. 255-287). Charlotte, NC: Information Age Publishing. Jobe, J. B., Smith, D. M., Ball, K., Tennstedt, S. L., Marsiske, M., Willis, S. L., . . . Kleinman, K. (2001). ACTIVE: A cognitive intervention trial to promote independence in older adults. Controlled Clinical Trials, 22(4), 453-479. doi:10.1016/S0197-2456(01)00139-8 Johnson, D. K., Storandt, M., Morros, J. C., & Galvin, J. E. (2009). Longitudinal study of the transition from healthy aging to Alzheimer disease. Archives of Neurology, 66(10), 12541259. doi:10.1001/archneurol.2009.158 Joseph, L., Wolfson, D. B., Bélisle, P., Brooks, J. O., III, Mortimer, J. A., Tinklenberg, J. R., & Yesavage, J. A. (1999). Taking account of between-patient variability when modeling decline in Alzheimer's disease. American Journal of Epidemiology, 149(10), 963-973. Karr, J. E., Graham, R. B., Hofer, S. M., & Muniz-Terrera, G. (2018). When does cognitive decline begin? A systematic review of change point studies on accelerated decline in cognitive and neurological outcomes preceding mild cognitive impairment, dementia, and death. Psychology and Aging, 33(2), 195-218. doi:10.1037/pag0000236 Killick, R., Eckley, I., Fearnhead, P., & Lee, J. (2016). Package 'changepoint'. Kim, S., & Jazwinski, S. M. (2015). Quantitative measures of healthy aging and biological age. Healthy Aging Research, 4. doi:10.12715/har.2015.4.26 Kwok, O.-M., Luo, W., & West, S. G. (2010). Using modification indexes to detect turning points in longitudinal data: A Monte Carlo study. Structural Equation Modeling, 17(2), 216-240. doi:10.1080/10705511003659359 Langa, K. M., Larson, E. B., Karlawish, J. H., Cutler, D. M., Kabeto, M. U., Kim, S. Y., & Rosen, A. B. (2008). Trends in the prevalence and mortality of cognitive impairment in the United States: Is there evidence of a compression of cognitive morbidity? Alzheimer's & Dementia, 4(2), 134-144. doi:10.1016/j.jalz.2008.01.001 Li, C., Dowling, N. M., & Chappell, R. (2015). Quantile regression with a change-point model for longitudinal data: An application to the study of cognitive changes in preclinical Alzheimer's disease. Biometrics, 71(3), 625-635. MacDonald, S. W. S., Hultsch, D. F., & Dixon, R. A. (2011). Aging and the shape of cognitive change before death: Terminal decline or terminal drop? The Journals of Gerontology.

20

Jo

ur na

lP

re

-p

ro

of

Series B, Psychological Sciences and Social Sciences, 66(3), 292-301. doi:10.1093/geronb/gbr001 McArdle, J. J., & Wang, L. (2008). Modeling age-based turning points in longitudinal life-span growth curves of cognition. In P. Cohen (Ed.), Applied data analytic techniques for turning point research. New York, NY: Routledge/Taylor & Francis Group. Mella, N., Fagot, D., & de Ribaupierre, A. (2016). Dispersion in cognitive functioning: Age differences over the lifespan. Journal of Clinical and Experimental Neuropsychology, 38(1), 111-126. doi:10.1080/13803395.2015.1089979 Muggeo, V. M. (2008). Modeling temperature effects on mortality: Multiple segmented relationships with common break points. Biostatistics, 9(4), 613-620. doi:10.1093/biostatistics/kxm057 Muniz-Terrera, G., Minett, T., Brayne, C., & Matthews, F. E. (2014). Education associated with a delayed onset of terminal decline. Age and Ageing, 43(1), 26-31. doi:10.1093/ageing/aft150 Muniz-Terrera, G., van den Hout, A., Piccinin, A. M., Matthews, F. E., & Hofer, S. M. (2013). Investigating terminal decline: Results from a UK population-based study of aging. Psychology and Aging, 28(2), 377-385. doi:10.1037/a0031000 National Institutes of Health. (2018). Towards implementing novel training methods to enhance cognition in aging (RFA-AG018-031). In: National Institutes of Health. Ning, L., & Luo, W. (2017). Specifying turning point in piecewise growth curve models: Challenges and solutions. Frontiers in Applied Mathematics and Statistics, 3, 19. doi:10.3389/fams.2017.00019 Ram, N., Gerstorf, D., Fauth, E., Zarit, S., & Balmberg, B. (2010). Aging, disablement, and dying: Using time-as-process and time-as-resources metrics to chart late-life change. Research in Human Development, 7(1), 27-44. doi:10.1080/15427600903578151 Rebok, G. W., Ball, K. K., Guey, L. T., Jones, R. N., Kim, H.-Y., King, J. W., . . . Willis, S. L. (2014). Ten year effects of the advanced cognitive training for independent and vital elderly cognitive training trial on cognition and everyday functioning in older adults. Journal of the American Geriatrics Society, 62, 16-24. doi:10.1111/jgs.12607 Ross, L. A., Edwards, J. D., O'Connor, M. L., Ball, K. K., Wadley, V. G., & Vance, D. E. (2016). The transfer of cognitive speed of processing training to older adults' driving mobility across 5 years. The Journals of Gerontology, Series B: Psychological Sciences and Social Sciences, 71(1), 87-97. doi:10.1093/geronb/gbv022 Ross, L. A., Freed, S. A., Edwards, J. D., Phillips, C. B., & Ball, K. (2017). The impact of three cognitive training programs on driving cessation across 10 years: A randomized controlled trial. The Gerontologist, 57(5), 838-846. doi:10.1093/geront/gnw143 Salthouse, T. A. (1996). The processing-speed theory of adult age differences in cognition. Psychological Review, 103(3), 403-428. doi:10.1037/0033-295X.103.3.403 SAS Institute Inc. SAS/STAT(R) 13.1 user's guide: The MCMC procedure. Retrieved from http://support.sas.com/documentation/cdl/en/statug/66859/HTML/default/viewer.htm#sta tug_mcmc_examples18.htm Schaie, K. W. (1989). Perceptual speed in adulthood: Cross-sectional and longitudinal studies. Psychology and Aging, 4(4), 443-453. doi:10.1037/0882-7974.4.4.443 Silbert, L. C., Dodge, H. H., Perkins, L. G., Sherbakov, L., Lahna, D., Erten-Lyons, D., . . . Kaye, J. A. (2012). Trajectory of white matter hyperintensity burden preceding mild cognitive impairment. Neurology, 79(8), 741-747. doi:10.1212/WNL.0b013e3182661f2b

21

Jo

ur na

lP

re

-p

ro

of

Singer, T., Verhaeghen, P., Ghisletta, P., Lindenberger, U., & Baltes, P. B. (2003). The fate of cognition in very old age: Six-year longitudinal findings in the Berlin Aging Study (BASE). Psychology and Aging, 18(2), 318-331. doi:10.1037/0882-7974.18.2.318 Sliwinski, M. J., Hoffman, L., & Hofer, S. M. (2010). Evaluating convergence of within-person change and between-person age differences in age-heterogeneous longitudinal studies. Research in Human Development, 7(1), 45-60. doi:10.1080/15427600903578169 Sliwinski, M. J., & Mogle, J. (2008). Time-based and process-based approaches to analysis of longitudinal data. Handbook on Cognitive Aging: Interdisciplinary perspectives. Thousand Oaks, CA: Sage Publications, N/A(N/A), 477-491. Sliwinski, M. J., Stawski, R. S., Hall, C. B., Katz, M., Verghese, J., & Lipton, R. B. (2006). Distinguishing preterminal and terminal cognitive decline. European Psychologist, 11(3), 172-181. doi:10.1027/1016-9040.11.3.172 Sprague, B. N., Hyun, J., & Molenaar, P. C. M. (2017). Revisiting measurement invariance in intelligence testing in aging research: Evidence for almost complete metric invariance across age groups. Journal for Person-Oriented Research, 3(2), 86-100. doi:10.17505/jpor.2017.08 SPSS Statistics Support. (2018). Spline regression (a.k.a. piecewise polynomials or segmented regression). In. IMB Support: IBM. Sternäng, O., Reynolds, C. A., Finkel, D., Ernsth-Bravell, M., Pedersen, N. L., & Dahl Aslan, A. K. (2016). Grip strength and cognitive abilities: Associations in old age. The Journals of Gerontology, Series B: Psychological Sciences and Social Sciences, 71(5), 841-848. doi:10.1093/geronb/gbv017 Stone, M. E., Lin, J., Dannefer, D., & Kelley-Moore, J. A. (2017). The continued eclipse of heterogeneity in gerontological research. Journals of Gerontology: Social Sciences, 72(1), 162-167. doi:10.1093/geronb/gbv068 Tan, X., Shiyko, M. P., Li, R., & Li, Y. (2012). A time-varying effect model for intensive longitudinal data. Psychological Methods, 17(1), 61-77. doi:10.1037/a0025814 Thorvaldsson, V., MacDonald, S. W. S., Fratiglioni, L., Winblad, B., Kivipelto, M., Laukka, E. J., . . . Bäckman, L. (2011). Onset and rate of cognitive change before dementia diagnosis: Findings from two Swedish population-based longitudinal studies. Journal of the International Neuropsychological Society, 17(1), 154-162. doi:10.1017/S1355617710001372 van den Hout, A., Muniz-Terrera, G., & Matthews, F. E. (2013). Change point models for cognitive tests using semi-parametric maximum likelihood. Computational Statistics and Data Analysis, 57(1), 684-698. doi:10.1016/j.csda.2012.07.024 White, S. R., Muniz-Terrera, G., & Matthews, F. E. (2018). Sample size and classification error for Bayesian change-point models with unlabelled sub-groups and incomplete follow-up. Statistical Methods in Medical Research, 27(5), 1476-1497. doi:10.1177/0962280216662298 Willis, S. L., Tennstedt, S., Marsiske, M., Ball, K. K., Elias, J., Koepke, K. M., . . . Wright, E. (2006). Long-term effects of cognitive training on everyday functional outcomes in older adults. Journal of the American Medical Association, 296(23), 2805-2814. doi:10.1001/jama.296.23.2805 Wilson, R. S., Boyle, P. A., Yu, L., Segawa, E., Sytsma, J., & Bennett, D. A. (2015). Conscientiousness, dementia related pathology, and trajectories of cognitive aging. Psychology and Aging, 30(1), 74-82. doi:10.1037/pag0000013

22

Jo

ur na

lP

re

-p

ro

of

Wilson, R. S., Leurgans, S. E., Boyle, P. A., & Bennett, D. A. (2011). Cognitive decline in prodromal Alzheimer disease and mild cognitive impairment. Archives of Neurology, 68(3), 351-356. doi:10.1001/archneurol.2011.31 Wilson, R. S., Segawa, E., Buchman, A. S., Boyle, P. A., Hizel, L. P., & Bennett, D. A. (2012). Terminal decline in motor function. Psychology and Aging, 27(4), 998-1007. doi:10.1037/a0028182 Wilson, R. S., Segawa, E., Hizel, L. P., Boyle, P. A., & Bennett, D. A. (2012). Terminal dedifferentiation of cognitive abilities. Neurology, 78(15), 1116-1122. doi:10.1212/WNL.0b013e31824f7ff2 Wu, W., Jia, F., Kinai, R., & Little, T. D. (2017). Optimal number and allocation of data collection points for linear spline growth curve modeling: A search for efficient designs. International Journal of Behavioral Development, 41(4), 550-558. doi:10.1177/0165025416644076 Yu, J., & Tatia, M. C. L. (2018). Profiles of cognitive impairments in an older age community sample: A latent class analysis. Neuropsychology, 32(1), 102-109. doi:10.1037/neu0000391 Yu, L., Boyle, P., Schneider, J. A., Segawa, E., Wilson, R. S., Leurgans, S., & Bennett, D. A. (2013). APOE ε4, Alzheimer's disease pathology, cerebrovascular disease, and cognitive change over the years prior to death. Psychology and Aging, 28(4), 1015-1023. doi:10.1037/a0031642 Zaninotto, P., Batty, G. D., Allerhand, M., & Deary, I. J. (2018). Cognitive function trajectories and their determinants in older people: 8 years of follow-up in the English Longitudinal Study of Ageing. Journal of Epidemiology & Community Health, 72(685-694). doi:10.1136/jech-2017-210116 Zissimopoulos, J., Crimmins, E., & St. Clair, P. (2014). The value of delaying Alzheimer's disease onset. Forum for Health Economics & Policy, 18(1), 25-39. doi:10.1515/fhep2014-0013