Multifactorial Modeling of Cognitive Trajectories Using an Advanced Regression Technique: Improving Our Understanding of Biomarkers and Modifiable Variables that Support Cognition

Current research into the brain, aging, and cognition contains important trends that provide a context for the article by Stark et al. [1]. One is the recognition that cognitive trajectories depend upon many factors that are often highly inter-related [2, 3]. Some of these factors, such as genetics [4], early life experiences [5, 6], and education [7, 8] are difficult to address by interventions in later life, although they are crucial for predictive power and conceptual understanding of cognitive change. However, a hopeful outlook is that many others are susceptible to clinical or lifestyle interventions. Thus, a second trend focuses on prospective early-stage intervention, rather than later remediation, as the best hope for maintaining healthy cognition into older age [9–11]. The article by Stark et al. [1] fits squarely into this trend. The authors model cognitive change among older adults diagnosed with mild cognitive impairment (MCI), using a large array of Alzheimer’s disease (AD) biomarkers and modifiable health variables. Their focus on MCI affords a valuable window into the dynamics of a prodromal stage of cognitive impairment, consistent with recent interest in interventions at this stage to slow or prevent progression to AD [12, 13].

From a methodological standpoint, more complex models require sophisticated techniques to adequately account for variable interactions and covariances, as well as nonlinear relations between variables and outcomes. Commonly used ordinary regression models are appropriate (and easily interpretable) when one has a relatively small number of variables and a priori hypotheses of how these are related to outcome. However, when modeling relations of a larger number of factors, there is increasing use of other approaches, including machine learning techniques (see, e.g., [14–17]), and in the case of the article by Stark et al. [1], partial least squares (PLS) techniques.

The current article is a companion to a previous publication by Stark et al. [18] that applies PLS in cross-sectional analyses using a similar array of factors. PLS techniques have been applied relatively recently in neuroimaging studies [19]. The current paper uses partial least squares regression (PLSR) for prediction of longitudinal change, while the earlier one uses partial least squares correlation (PLSC), finding the strongest correlations among demographic, health, brain, and cognitive variables cross-sectionally. Together, these papers provide a useful extension of knowledge about the relationships of multiple variables to baseline and longitudinal cognition, and a showcase of PLS techniques for analyzing questions of multiple, correlated factors associated with cognition and aging. The benefits of these findings are immediate, since both these papers reveal detailed profiles of association between biological and lifestyle variables and cognition or cognitive change. Because many of these variables are modifiable, such findings could help to inform public health policy, clinical interventions, and even personal lifestyle choices toward improved cognitive aging.

Whereas ordinary least-squares regression (OLS) is familiar, it may be helpful to briefly outline PLSR. OLS is straightforward to solve but can encounter difficulties due to strong (and often hidden) correlations among the predictor variables (i.e., multicollinearity)—a likely occurrence for models using a large number of variables. In that situation, some sort of data reduction is necessary, whether by eliminating variables using stepwise methods, or by extracting a smaller number of independent “principal components” from the array of predictors [20]. Let X be the matrix of predictor variables, and Y that of the outcome variables. Rather than directly regressing Y on X, regression in PLSR is conducted by judiciously selecting “latent” components L that simultaneously decompose X and predict Y [19, 20]. X and predicted Y are each expressed as a weighted sum (the weights are the “loadings” on components of L) of L, whose components “do all the work” of the regression. The loadings for Y also contain regression coefficients for associations with L. However, we are really interested in the observable rather than the latent variables. Thus, regression coefficients for each of the X observables (called B_PLS for “beta partial least squares”, analogous to ordinary β coefficients) must be computed from both sets of loadings. Finally, there is the “variable importance of projection” (VIP), a measure of each X predictor’s contribution to the outcome, analogous to the partial R² values in OLS. A variable’s VIP score is based on that variable’s loadings across the components of L times the amount of Y variance predicted by each component of L [21, 22].

In the current article [1], X consists of 29 factors from four domains including cardiometabolic risk, inflammation, neurotrophic/growth factors and AD pathology, while in separate analyses Y contains either two-year longitudinal episodic memory change or executive change. The results reveal different profiles of physiological and demographic variables for predicting episodic memory and executive function changes. In the array of nine AD-related biomarkers (APOE and cerebrospinal fluid (CSF) measures of amyloid, tau, and their ratios), seven were important predictors of memory change and eight predicted executive change, indicating strongly shared AD biomarker predictors of executive and memory decline in this MCI cohort. From there, the patterns diverged. For memory change, interleukin-6 receptor (an inflammatory variable), brain-derived neurotrophic factor, and vascular endothelial growth factor were important predictors. Interestingly, no cardiometabolic factors were important. Education was important for memory trajectories but not for executive. For executive change, cardiometabolic factors of systolic and diastolic blood pressure and high cholesterol, plus HB-EGF-like-GF (heparin binding epidermal-growth-factor-like growth factor) were significant predictors. Comparing these with the findings of the companion cross-sectional study [18] shows that AD-related markers and education were also important contributors to multiple measures of baseline cognition. Of note, cardiometabolic factors were not associated with any cognitive scores in that study.

In other recent research, cardiometabolic factors like blood pressure and cholesterol levels have been found to impact executive function via damage to white matter integrity [23–25] independently of gray matter degeneration [26]. Cardiometabolic factors (including blood pressure) are also associated with accelerated brain aging [27]. Interventions like diet and exercise to improve metabolic health may reduce executive decline and overall dementia risk [28]. Of note, the current paper [1] found that AD-related factors (i.e., APOE, CSF measures of amyloid and tau) were important predictors of both executive and memory trajectories. Although it is well known that these AD-related factors predict episodic memory decline (see, e.g., [29, 30]), it is less commonly reported that they also contribute to executive decline. However, this has been corroborated for amyloid PET (¹⁸F) tracer associations with decline in several cognitive domains, including executive, in a cognitively normal cohort with subjective cognitive decline [31]. The current paper examined CSF rather than PET markers. Nonetheless, combining the effect of amyloid PET in that cohort [31], with the current findings among MCI, may suggest an expanding role of AD abnormal protein markers in executive function loss as cognitive impairment progresses. Interestingly, the current findings of no cardiometabolic contributions to memory decline may be at odds with another recent analysis showing vascular dysregulation as the earliest factor in progression to AD [3]. However, the latter study used a large dataset involving all levels of cognitive syndrome.

This paper and its predecessor [18] present some challenges and limitations. The small sample size, consisting only of MCI participants, highlights the need for a larger replication in a cognitively heterogeneous data set. A strong theme in current research is the use of large data sets [32, 33] to identify markers for early detection of predicted future decline [16]. In a larger data set, the approach shown here could provide valuable delineations of cognitive domain-specific predictors that suggest interventions at all cognitive stages from healthy aging to dementia. The PLS approach is appropriate for large arrays of multicollinear variables [19], but its interpretation is less straightforward than in OLS, due to the one-remove of the observables from the latent variables. Thus, the relations of predictor and outcome observables are assessed from the B_PLS, and their relative explanations of outcome variance by VIP scores. Some of the variables are found to be “important” (VIP > 1 indicating a substantial contribution to overall model fit) but not “reliable” (B_PLS not significantly different than 0) [1]. These are subtle results that may require further elucidation, a larger dataset, or both.

In conclusion, the current paper uses PLSR to advance research trends toward more complex, multifactorial models of cognition and brain. The results delineate association profiles suggesting targeted interventions to slow cognitive decline in an already at-risk MCI population.