Discovering correlates of age-related decline in a healthy late-midlife male birth cohort

Univariate analyses

Cross-sectional-longitudinal and longitudinal correlations

All cross-sectional-longitudinal and longitudinal univariate correlations between brain IDPs and behavioural measures revealed no statistically significant relations when accounting for multiple testing (FDR > 0.05). Specifically, for longitudinal correlations, this was the case for correlations adjusted and unadjusted for the effect of average scores ((W-63+W-57)/2). We visualize results with Manhattan plots that show -log ₁₀ p-values for IDP-by-behavioural longitudinal correlations, arranged by behavioural measures on the x-axis, multiple testing thresholds across all pairwise associations are marked with a horizontal line, FWE top line (P_uncorrected = 6.01 x 10^-6) and False Discovery Rate (FDR) bottom line (P_uncorrected = 5.03 x 10^-5), Figure 1. Similarly, we visualize results with Manhattan plots that show -log₁₀ p-values for cognitive-by-all-other-behavioural cross-sectional-longitudinal correlations, arranged by cognitive variables on the x-axis; multiple testing thresholds across all pairwise associations are marked with a horizontal line, FWE top line (P_uncorrected = 4.80 x 10^-4) and FDR bottom line (P_uncorrected = 4.09 x 10^-4), Figure 2.

Figure 1. The significance of associations between IDP and behavioural variables, for longitudinal correlations. The Manhattan plot shows all results for 454 IDPs against each of the 114 behavioural (51,756 values) adjusted for confounders: age, motion, and head size. Significance is plotted as -log ₁₀ p-values, arranged by behavioural measures on the x-axis, multiple testing thresholds across all pairwise associations are marked with a horizontal line (FWE: 6.01 x 10^-6; FDR: 5.03 x 10^-5). IDPs are distinguished by plotting colour, determined by MRI modality and image processing tool applied to derive each measure. This created 6 imaging subdomains: 1) T1w percentage brain volume change (PBVC) modelled by SIENA 2) T1w global brain volume measures (normalized and unnormalized for head size) modelled by SIENAX (yellow), 3) T1w subcortical structures (shapes and volumes) modelled by FIRST (green), 4) T1w total grey matter volume within grey matter region-of-interests using partial volume estimates derived from FAST (red), 5) T2w-FLAIR total volume of white matter hyperintensities modelled by BIANCA (pink), 6) dMRI estimates of diffusivity measures contained within 48 standard-space WM tract region-of-interests modelled by TBSS (blue). Abbreviations: IQ-11, IQ-20, IQ-57, IQ-63 = general intelligence score ages ~11, ~20, ~57, and ~63; MOT = motor task; ME = mean error; ML = mean latency; PAL = paired associates learning; TE adjusted = total errors adjusted; TT Adjusted = total trials adjusted; PRM = pattern recognition memory; SD = standard deviation; CL = correct latency; RTI = reaction time task; MT = movement time; RT = reaction time; RVP = rapid visual processing task; MLB1-4 = mean latency block 1 to 4; SOC = Stockings of Cambridge; Mean Initial TT 5 Moves = mean initial total time 5 moves task; Mean Subse TT 5 Moves = mean subsequent thinking time 5 moves task; SRM = spatial recognition memory; TM = trail making task; SEP = social economic position; MDI = Major Depression Inventory; CBF = cerebral blood flow; PSQI = Pittsburgh Sleep Quality Index.

Figure 2. The significance of associations between each longitudinal/average cognitive measure and all (other) cross-sectional behavioural variables. The Manhattan plot shows all results for 64 cognitive variables against each of the 50 (other) behavioural variables (3200 values) adjusted for confounders: age, motion, and head size. Significance is plotted as -log ₁₀ p-values, arranged by cognitive variables on the x-axis, multiple testing thresholds across all pairwise associations are marked with a horizontal line, FWE top line (4.80 x 10^-4) and FDR bottom line (4.09 x 10^-4). All other behavioural variables are distinguished by plotting colour (Demographic = yellow, Health = red, Lifestyle = blue). Abbreviations: IQ-11, IQ-20, IQ-57, IQ-63 = general intelligence score at ages ~11, ~20, ~57, and ~63; MOT = motor task; ME = mean error; ML = mean latency; PAL = paired associates learning; TE adjusted = total errors adjusted; TT Adjusted = total trials adjusted; PRM = pattern recognition memory; SD = standard deviation; CL = correct latency; RTI = reaction time task; MT = movement time; RT = reaction time; RVP = rapid visual processing task; MLB1-4 = mean latency block 1 to 4; SOC = Stockings of Cambridge; Mean Initial TT 5 Moves = mean initial total time 5 moves task; Mean Subse TT 5 Moves = mean subsequent thinking time 5 moves task; SRM = spatial recognition memory; TM = trail making task).

Bland-altman plots

In addition to univariate correlations, we use Bland-Altman (BA) plots to assess the relation between longitudinal change in normalized IQ score from childhood (age ~11), youth (age ~20), and late midlife (ages ~57 and ~63) at different magnitudes of the measured (mean) IQ score. Specifically, BA plots presented in Supplementary Figure 3 do not exhibit any particular structure, as (e.g.) might be expected if high IQ subjects had relative greater change. Rather, the BA plots indicate that the direction and magnitude of change in IQ is unrelated to mean cognitive ability in our sample.

Multivariate associations

Whole-group multivariate associations

CCA identified a single statistically significant mode of population co-variation coupling longitudinal cross-subject variations in brain structure to an extensive range of behavioural measures (R_c = 0.9, permuted P_corrected = 0.001). Post-hoc correlational analyses indicated that decreases in cognitive performance (IQ-57 – IQ-20) and speed assessed tasks, higher rates of familial myocardial infarct, lower HDL cholesterol, less physical activity, and higher scores on the mental depression inventory are associated with larger decreases (from age ~57 to ~63) in whole brain GM and WM volume but increases in some WM and GM ROIs, in particular the GM cerebellum. Finally, we did not find evidence supporting the role of baseline scores as predictors of impending brain or behavioural change in late-midlife

For ease of interpretation and comparison with an earlier study, we invert the signs of all baseline (W-57) and follow-up (W-63) behavioural measures where lower values reflect higher cognitive performance or more favourable/healthy traits (e.g., speed assessed tasks, number of total errors, total cholesterol, BMI). Thus, in general, using Figure 3A, we interpret positive post-hoc correlations between each observed behavioural measure and the CCA-derived subject weights (i.e. canonical variate weights, U or V) as positive or “healthy” contributions to the CCA-mode, whilst all negative behavioural correlations are interpreted as negative or “unhealthy” contributions. However, as MRI-derived brain structural measures are themselves indirect measures of underlying brain neuroanatomy, we cannot be entirely certain what an observed brain measure or difference (i.e. change) score truly represents. Considering this uncertainty, assigning a “good” or “bad” direction to estimated longitudinal change scores in a brain biomarker is extremely risky and avoided in this study.

Figure 3. Top contributing variables to identified CCA-Mode using post-hoc correlational analyses. Individual behavioural (A) and IDP (B) measures most strongly associated with the CCA-mode of population covariation. The CCA-derived weights visualized indicate how much each measured variable contributes to the significant CCA-mode i.e., the measure of the strength of involvement of an observed variable to the CCA-mode, derived from post-hoc correlational analyses. Behavioural measures and IDPs are coloured according to their assigned subdomains. The vertical position of each variable is related to the scale of the association of that specific measure with the identified CCA-mode. Font size is indicative of variance explained by the CCA-mode. Here we do not report variables that attain a correlation value between 0.2 to -0.2. Abbreviations: Δ = longitudinal change (W-63 – W-57), M = average ((W-63 + W-57)/2), L = left, R = right, FA = fractional anisotropy, L1 = 1^st eigenvalue, L2 = 2^nd eigenvalue, L3, = 3^rd eigenvalue, MD = mean diffusivity, MO = tensor mode.

Post-hoc correlational analyses identified the strongest positively associated behavioural variable to the CCA-mode as (self-reported) familial history of diabetes (r² = 10.5%, r=0.33) and the strongest negatively linked variable as longitudinal change in IQ (IQ-53 – IQ-20; r² = 16.1%, r=0.40), Figure 3A. Other strong positive behavioural contributions to the CCA-mode include change in motor and reaction time task (RTI), youth IQ (IQ-20 and IQ-11), change in spatial recognition memory task (SRM percent correct), average score in processing speed (Trail Making A), average score in verbal paired associative learning and memory (15 word pairs retention), subject SEP and offspring. Other strong negative behavioural contributions to the CCA-mode include: change in IQ variables (IQ-63 – IQ-20, IQ-57 – IQ-11, IQ-63 – IQ-11), change in speed assessed tasks executive functioning/planning (SOC), change in attention with working memory load (RVP) task, change in pattern recognition memory (PRM) task, change in paired associates learning (total trials), and a number of lifestyle and health variables (e.g. physical activity, MDI score, familial history of myocardial infarct, and HDL cholesterol).

With regards to post-hoc correlations computed between IDPs and the CCA-mode, Figure 3B, we identified longitudinal change in GM volume of the cerebellum (right) as the strongest positively linked brain-imaging measure (r² = 30.8%; r =0.56), and longitudinal change in total WM volume (normalized for head size) as the strongest negatively linked (r² = 35.0%; r =-0.59). Other top contributing positive IDPs include change in GM volume of cerebellum and non-cerebellum regions-of-interest (ROIs), change in the diffusion properties of several microstructural WM ROIs, and change in the volume of subcortical structures, the nucleus accumbens (Nac) and caudate. Post-hoc correlational analyses also identified a number of strong negatively contributing IDPs to the underling structure of the identified CCA-mode. Of these, the most influential include: change in global brain volume (grey and white matter), change in GM volume of cerebellum ROIs (the juxtapositional lobule cortex, inferior and superior temporal gyrus), and a range of dMRI microstructural markers (medial lemniscus, cerebellar peduncle, internal and external capsule, crus fornicis and stria terminalis, cingulum cingulate gyrus, uncinate fasciculus).

While no one result can be taken in isolation, we pull out just a few variables to illustrate the directions of the effects: Higher rates of familial myocardial infarct, less physical activity, higher score on the mental depression inventory (MDI), decreases in cognitive performance (IQ-63 - IQ-11, IQ-57 - IQ-11, IQ-63 - IQ-20), and speed assessed tasks is associated with larger decreases (from age ~57 to age ~63) in whole brain GM and WM but increases in some WM and GM ROIs, in particular in the GM cerebellum.

We explored the multivariate results to establish that the estimated CCA-mode was not unduly influenced by the EGD. Specifically, a scatterplot of the IDP and behavioural canonical variates, with group membership indicated by plotting symbol, showed no evidence of clustering, Figure 4.

Figure 4. Scatter Plot of all Subject’s Relationship with the Significant CCA-Mode. The scatter plot shows the association between individual subject weights from the IDP canonical variate (V) versus individual subject weights from the behavioural canonical variate (U), with one point per subject. The high correlation observed here reflects the significant covariation between the behavioural and imaging longitudinal datasets. Group membership is indicated by plotting symbol (orange circle = group A i.e. improvers; blue triangle = group B i.e. decliners).

Strengths and limitations

A major strength of this study is the study-sample itself. As MDBC-1953 is a healthy, homogenous, single-year-of-birth male cohort, subjects are ethnically, culturally and geographically homogenous, and of general good health. This setup dramatically minimizes the unwanted effects of chronological age and the potentially troublesome contributions of disease, differential environmental factors, and population stratification to variations in health outcome. A further strength of this study pertains to its use of CCA to explore longitudinal associations [89]. Specifically, CCA boosts power by using the full dataset to extract latent factors that are based on the shared variance observed among sets of related measures. This approach allows the simultaneous prediction of multiple outcome variables, permits the isolation of distinct biological mechanisms, and largely attenuates the unexplained residual variance through its identification of multiple modes. Next, unlike many longitudinal studies that are biased by selective attrition (i.e. due to the “3M” – mobility, morbidity and mortality [46]), of the 193 subjects who attended W-57, 64% returned to provide follow-up data at W-63. Another strength of this study concerns the manner in which subjects were selected. That is, compared to conventional ageing studies that are biased towards higher educated, more intelligent subjects, we recruited participants on the basis of cognitive change from youth to late-midlife based on the Extreme Group Design (EGD) [66]. Specifically, by sampling subjects from the extremes of the change-in-IQ distribution, our approach maximizes the variability in participant characteristics (e.g. cognitive ability, occupational complexity, levels of motivation) and with it the applicability of our findings to the general population. Equally important, is the ability of EGD to maximise the variability in cognitive decline in order to detect biological correlations. Further strengths of this study concerns the age-range of participants. Specifically, there is a lack of evidence indicating that pathological change begins abruptly at old age. Instead, a growing body of research has converged in highlighting the importance of early-life and midlife measures in predicting later-life health outcome [31, 42, 58, 67–70]. In view of this, the available early-life data, in combination with the late-midlife measures allows us to assess the contribution of potential modifiers and the interdependence of age-related processes prior to confounding by overt or underlying later-life pathological conditions. Lastly, our study includes a comprehensive range of broad brush and specific cognitive tests, brain biomarkers, and age-related covariates reducing the amount confounding that is attributable to associations driven by other unmeasured factors. Furthermore, “specific” measures (e.g. cognitive tests measuring a particular skill, or a brain ROI) are hypothesized to form stronger links than general “broad brush” measures (e.g. total brain volume, general intelligence).

This study also reports a number of limitations. First, we acknowledge that a major limitation of the present study lies in its modest sample size, decreasing the studies power to detect modest-to-small effects. Second, although repeated measurements are what allow longitudinal studies to assess change over time, the use of identical tests at each assessment increases the risk of underestimating age-related changes. This is mainly attributable to repeat exposure to the testing material, environment, and operator which ultimately result in practice-related learning. Thus, it is possible that accrued familiarity to testing conditions and materials may explain the observed gains in some of the variables examined. Notably, however, practice-related learning effects are only applicable to the cognitive tests administered in the two late-midlife waves. Relatedly, practice effects may also be partly accountable for the lack of statistically significant cross-sectional-longitudinal correlations. That is, the practice-related gains may have attenuated what was already only modest declines in cognitive ability in subjects that are a generally healthy and with it eliminating the opportunity of observing potentially important associations. That being said, prior studies formally investigating the contribution of retest effects to observed gains have reported on average moderate-to-large retest effects, but small inter-individual variability [71]. Specifically, this indicates that associations between ageing-related changes and their correlates identify true covariates of age-related cognitive change, rather than covariates of practice-related gains. The number of measurement occasions available for investigation may also be a limiting factor in this study. Specifically, as our study consists of two occasions of longitudinal testing we were unable to account for nonlinear trajectories of brain and cognitive changes. Lastly, the homogeneity of subjects also means that the findings reported in this study should be extending to the general population with caution.

Participants: extreme group design (n=1,985)

The participants for this imaging sub-study were members of the longitudinal Danish Metropolitan Birth Cohort 1953 (MDBC-1953) [72]. For a detailed discussion regarding the subject selection criteria, recruitment, attrition and testing for this cohort see [72–74]. In summary, using youth and late midlife IQ scores, subjects were selected based on their estimated change in mental ability as part of an “extreme group design” (EGD) [75]. Specifically, the two well-validated tests, the Børge Priens Test (BP) [76] and Intelligenz-Struktur-Test 2000 R (IST) [77] were taken at ages ~20 (IQ-20) and ~57 (IQ-57) respectively. Since the cognitive change between these time-points was based on two different instruments, a change score was derived with a linear regression analysis of IQ-57 (IST-2000 R) on IQ-20 (BP) using a total of 1,985 subjects [74]. Both examinations comprise subtests that assess aspects of verbal intelligence (e.g. numerical series and verbal analogies), and thus are similarly structured and comparable. IQ-20 explained R²=50.4% of variance in IQ-57 (beta=0.71, p<0.0001), and we used each subject’s standardized residual about the regression line as a measure of their change in IQ across time. To avoid the effects of extreme test scores, subjects with absolute standardized residuals exceeding ±3 were omitted and the remaining members were classified into two groups pertaining to the degree of cognitive change observed from early-adulthood: group A = 66 improvers and group B = 57 decliners. This study has also been registered at clinicaltrials.gov (NCT03290040).

Participants: present study (n=123)

The majority of MDBC-1953 members have taken part in two early-life intelligence quotient (IQ) tests at ages ~11 (IQ-11) and ~20 (IQ-20). During this early-life period, information on early-life social and biological demographic factors was also acquired. Subsequently, in late-midlife, based on the degree of cognitive change, cohort members were selected (as described in section 1.1) to complete 2 waves of brain-imaging and behavioural assessments. The first wave (W-57, where 57 represents mean subject age at scanning, 57 years ±0.7 standard deviations (SD), took place during 2010-2013 and included a total of 193 subjects who had usable imaging and behavioural data. Data pertaining to W-57 have been previously investigated and reported [73, 78, 79]. The second wave, W-63 (mean subject age 62.5±0.9 years) began in 2015 and is scheduled for completion in 2020. To date, of the initial 193 subjects with brain-imaging and behavioural data from W-57, 192 subjects were invited back to participate in W-63. 136 of the initial W-57 subjects accepted their invitation and proceeded to the subject screening stage. Here, participant eligibility was determined and this resulted in the exclusion of 6 subjects’ due to conditions related to substance abuse comorbid with cognitive impairment, psychiatric or neurological disease, and contraindications to MRI. Of the subjects who fulfilled the eligibility criteria, a further 7 were excluded due to no show on the day of examination or non-completion of MRI session. The final number of subjects in each group was: group A n=66, group B n=57. The average observation interval between W-57 and W-63 was 4.82±0.9 years. Figure 6 shows a recruitment flow diagram for the present study sample used to investigate brain and behaviour longitudinal correlations. Although there was a small range of ages during data acquisition, in general we refer to the ages of participants as 11 (W-11), 20 (W-20), 57 (W-57), and 63 (W-63) years. This imaging study was approved by the local ethical committee (De Videnskabsetiske Komiteer for Region Hovedstaden) and registered by the Danish Data Protection Agency. All participants provided written informed consent.

Figure 6. Subject selection process for Wave 1/W-57 and Wave 2/W-63. To avoid effects of extreme test scores, subjects with standardized residuals ±3 were omitted defined as here as †. The final sample size for the current study includes n=123 subjects who completed wave 1 and wave 2. Group A = 66 improvers and Group B = 57 decliners.

Data

Neuropsychological assessment: repeated measurements

We include a detailed series of neuropsychological tests that were measured at both W-57 and W-63, Figure 7. All behavioural tests were acquired on the same day as the brain-MRI acquisition. In brief, global cognitive function was assessed with the mini-mental state examination (MMSE) and Addenbrooke’s cognitive examination (ACE). The Cambridge Neuropsychological Test Automated Battery (CANTAB) was administered to evaluate cognitive ability across the following cognitive domains: learning and memory (spatial and pattern recognition, and paired associates learning), executive function (planning), attention and reaction time [80]. Furthermore, we include both early-life measures of general cognitive ability acquired at W-11 (IQ-11) and W-20 (IQ-20) [81], as well as late-midlife measures of IQ acquired at W-57 (IQ-57) and W-63 (IQ-63). Table 1 presents the study sample characteristics for each cognitive examination used in the present analyses, separately for W-57 and W-63. To explore cross-sectional-longitudinal associations and longitudinal associations pertaining to brain and behaviour changes, we use cognitive scores acquired during W-57 and W-63 to estimate difference (i.e. change) (W-63 – W-57) and average ((W-63 + W-57)/2) scores. While it may seem more intuitive to compare change to a baseline, note that raw change is negatively correlated with baseline by construction. Thus, in the present analyses, each cognitive measure – with repeated measurements – is represented by its raw change and raw average counterparts and included as two independent measures of cognitive ability. Thus, in total we analyse 64 measures of cognitive performance of which 33 describe raw change, 27 describe raw average, and 4 describe IQ scores derived from W-11, W-20, W-57 and W-63.

Figure 7. Flow diagram showing the data collected at each time point for subjects used in this present sub-study. W-11, W-20, W-57, and W-63 = data acquired at ages ~11, ~20, ~57 and ~63 respectively.

Demographic, health and lifestyle assessment

We evaluate the effect of a range of reputed positive and negative measures on brain structure and cognitive performance. Assessments include both self-reported and objective measures such as, the Major Depression Inventory (MDI) [82], the Pittsburgh Sleep Quality Index (PSQI) [83], the Multidimensional Fatigue Inventory (MFI-20) [84], demographic factors, general health measures, history of non-communicable diseases (NCDs) and multiple health-related lifestyle behaviours. The majority of the potential age-related modifiers included were measured at W-63. Similar to neuropsychological tests with repeated measurements, demographic, health and lifestyle factors assessed more than once are included in subsequent analyses as raw change and raw average scores. These include: body mass index (BMI), total cholesterol (TC), high-density lipoprotein (HDL) cholesterol, low-density lipoprotein (LDL) cholesterol, and very low-density lipoprotein (VLDL) cholesterol. In summary, we report 8 = demographic, 34 = health, and 8 = lifestyle measures (total = 50), which together with the neuropsychological data is referred to as ‘behavioural’ measures. Finally, to assist the interpretation of results, behavioural measures were divided into four subdomains: cognitive, demographic (social and biological), health and lifestyle. See Tables 1–4 for a list of these variables and the study sample characteristics.

MRI data acquisition

All subjects underwent whole-brain MRI scanning using a 3.0 T Philips Intera Achieva (Philips Medical Systems, Best, the Netherlands), with a 32-channel phased-array head coil. In all participants the following images were acquired during resting conditions: 1. anatomical high-resolution 3D T1-weighted (T1w) images using a gradient echo sequence (TR/TE = 6.9/700 ms; flip angle = 9°; voxel size = 1.1 × 1.1 × 1.1 mm³), 2. T2-weighted (T2w) (TR/TE = 1300/12 ms; flip angle = 90°, voxel size 1.8 × 1.8 × 9.5 mm), 3. T2w FLAIR (T2w-FLAIR) images (Fluid Attenuated Inversion Recovery) using turbo spin echo sequence (TR/TE = 11000/125 ms; flip angle = 90⁰, 6 slices, voxel size = 0.45 × 0.45 × 4.5 mm), and 4. diffusion weighted images (dMRI) (TR/TE = 9729/55; matrix =112 × 110 × 60; voxel size = 2 × 2.04 × 2 mm³) utilizing a single spin-echo echo-planar imaging sequence. For each dMRI scan, 33 images were acquired: 1 image with no diffusion sensitization (b=0 image), and 32 diffusion-weighted images (b = 1000s/mm²). Finally, all images were visually inspected in their raw state for bias field corruption, excessive motion, and other potential artifacts.

Image analysis pipeline

We used the UKB image processing pipeline on our raw (non-processed) W-57 and W-63 brain-imaging data to enable future meta-analyses and replication studies [85]. Essentially, T1w structural data is used as the reference image to calculate cross-subject and cross-modality alignments required to process all other brain modalities.

In brief, we extracted 454 brain-imaging biomarkers (i.e., a broad set of biologically meaningful measures derived from multiple imaging modalities) that best capture the differential ageing processes and neuropathologies observed in a healthy ageing population. Subsequently, we categorized the extracted summary measures into 6 groups to reflect the MRI modality and image processing tool applied to derive each measure. These include: 1. T1w-SIENA percentage brain volume change (PBVC), 2. T1w-SIENAX (estimation of brain tissue volumes), 3. T1w-FIRST (segmentation of subcortical brain structures), 4. T1w total volume of grey matter (GM) in cerebellum and non-cerebellum regions-of-interest (ROI) [86, 87]¹ using FAST-derived GM partial volume estimates (PVE), 5. T2w-FLAIR-BIANCA (total white-matter hyperintensity volume), and 6. dMRI-TBSS (microstructural properties of specific white matter (WM) tracts). With regards to the volume of GM in cerebellum and non-cerebellum ROIs, we inverted the non-linear registration to standard space which was subsequently used to warp a cortical atlas of 139 ROIs into native T1 space. Next, within each ROI we then summed the total volume of GM using the FAST-derived GM PVE.

Tables 5, 6 list all image-derived phenotypes measured in this study (also referred to as IDPs), their function and study sample characteristics.

Statistical analysis

We used univariate correlations and multi-level latent variable modelling to investigate specific and general relations between multiple brain and behaviour measures. To extract estimates of longitudinal change between two successive measurement occasions, we computed “raw difference scores” (RDS) (i.e., cross-sectional follow-up score at W-63 subtracted from cross-sectional baseline score at W-57). Several reasons motivated our selection of this approach. First, application of the commonly used “residualized change model” (RCM) can lead to biased results if the study sample consists of pre-existing groups at baseline [88]. Conversely, the RDS approach has shown to arrive at the correct inference regardless of whether there are pretest (baseline) differences in action e.g., when the association of a covariate or confounding variable with baseline scores is not equal to zero [88]. Second, although the latent difference score (LDS) model is not vulnerable to the aforementioned biases and may have been a natural choice to investigate longitudinal relations, its undeniable value is most apparent when constituent scores are derived using a well-defined instrument. However, as we include a wide range of variables that were acquired using a mixture of measurement methods from multiple measurement occasions the application of the LDS model was on this occasion unsuitable.

To investigate 1) the relation between cross-sectional baseline (BL_W-57) and cross-sectional follow-up (FL_W-63) brain and behaviour scores with longitudinal change (i.e., Δ_W-63-W-57) referred to as “cross-sectional-longitudinal correlations”, and 2) coupled change between longitudinal brain and behavioural measures (i.e., Δ_W-63-W-57 and/or ((W-63 + W-57)/2)) adjusted and unadjusted for the effects of average scores ((W-63 + W-57)/2), referred to as “longitudinal correlations”, we used both univariate (Pearson correlations) and multivariate statistics (canonical correlation analysis - CCA) [89], both analyses adjusted for a number of common confound variables, head size, motion during MRI, and age.

Whole-group adjusted univariate associations

We used Pearson’s correlations to examine both cross-sectional-longitudinal correlations and longitudinal correlations (defined above) between each of the 454 (longitudinal) or 453 (cross-sectional) brain IDPs to each of the 114 (longitudinal and average) or 70 (cross-sectional) behavioural variables extracted from the MDBC-1953 database (full set of IDP x behavioural estimates: 1) 454 × 70 or 453 × 114 for cross-sectional-longitudinal correlations and 2) 454 × 114 for longitudinal correlations. Figure 8 provides a visualisation of all correlations computed between IDP and behavioural datasets for both univariate and multivariate analyses. Here, pink arrows indicate cross-sectional-longitudinal correlations and the blue arrow shows longitudinal correlations. Lastly, we also examined the relation between each of the 60 cognitive (longitudinal and average) measures to each of the (other) 50 (cross-sectional) behavioural variables (full set of cognitive variables × all (other) behavioural estimates: 64 × 50). In total, three variants of Manhattan plots are created to display the significance (-log10 P-values) of Pearson’s correlations for IDPs × behavioural estimates (1. cross-sectional-longitudinal correlations: 31,780 or 51,642 values; 2. longitudinal correlations: 51,756 values; and 3. cognition x all (other) behavioural measures (cross-sectional-longitudinal relations: 3200 values).

Figure 8. Summary of correlations computed between measures acquired at W-57 (baseline; BLW-57), W-63 (follow-up, FL_W-63), their differences i.e. change (Δ_W-63-W-57), and average ((Δ_W-57+W-63)/2). Measured brain-imaging and behavioural variables from W-57 and W-63 are represented by smaller-sized ovals (1a-1d). Measures of change estimated using the difference between W-63 and W-57 and their averages are represented by larger-sized ovals (2a-2c). Ovals 1a and 1b represent 70 cross-sectional behavioural items and ovals 1c and 1d represent 453 cross-sectional IDPs. Ovals consisting of longitudinal variables (i.e. change and/or average scores) include 454 IDPs (2a), 114 behavioural items (2b), and 60 cognitive items (2c). In this study, we explore “cross-sectional longitudinal correlations” (pink arrows), and “longitudinal correlations” (blue arrow) using univariate and multivariate analyses. All correlations were adjusted for nuisance confounders motion (during MRI), age, and head size.

To reduce the influence of potential outliers and increase the reliability of associations made, we applied rank-based inverse Gaussian transformation (quantile normalization) to enforce Gaussianity for each of the brain IDPs, behavioural, and confound variables. For univariate correlations, missing data was handled with a complete case approach individually for each pair of variables; for CCA, where missing data is particularly problematic, we then applied an iterative PCA algorithm (based on the soft shrinkage of eigenvalues) to impute missing data values until convergence [90]. Finally, five confound variables were created relating to effects that may trouble the interpretation of computed correlations: absolute motion during MRI, relative motion during MRI, head size, age (difference (W-63-W-57) and average ((W-63+W-57)/2). The confound variables were regressed out of all brain-imaging and behavioural variables prior to correlational analyses. To account for multiplicity, we assessed the strength of significance with two types of multiple testing correction controlling the familywise error rate (FWE) via Bonferroni and the false discovery rate (FDR) [91].

Extreme-group design validation test: univariate associations

In order to assess the impact of the EGD, we separately compute univariate associations between each IDP and behavioural measure for group A (“improvers”) and group B (“decliners”) subjects. Each sub-analysis should be free of any spurious associations driven by average group differences in cognitive level (i.e., an example of Simpson’s paradox [43], whereby suboptimal pooling across variables such as cognitive level can potentially generate misleading associations).

Whole-group adjusted multivariate associations

To explore the relation between multiple brain IDPs and behavioural measures simultaneously we applied CCA.

For the CCA, we adopted a similar approach as described previously [79, 85, 92]. In short, CCA was computed (canoncorr; MATLAB 2014a) following the model: U = AX and V = BY; where X represents the set of IDPs, Y is the set of behavioural measures, and A and B are optimized to maximize the correlation between each canonical variate pair, U and V [89]. The magnitude of the relationship between each variate pair is reflected by the canonical correlation coefficient (R_c), an indicator of how strongly the estimate of population covariation is reflected in both IDP and behavioural datasets. Intuitively, we can think of CCA as identifying two latent variables, U_i and V_i (i.e. canonical variates whose elements we refer to as individual subject weights)_, from a specific linear combination of weighted MRI-derived brain measures that are most strongly associated to a specific linear combination of weighted behavioural measures.

IDP and behavioural datasets for CCA analysis were prepared using the same procedure as for the univariate correlation analysis. This resulted in a brain-IDP matrix of size 123 x 454 (subjects × IDPs) and a behavioural matrix of size 123 × 114 (subjects x behavioural measures) when investigating longitudinal correlations, and a brain-IDP matrix of size 123 x 453 (subjects × IDPs) and a behavioural matrix of size 123 × 70 (subjects x behavioural measures) when investigating cross-sectional-longitudinal relations. Typically, these datasets are the inputs fed into the CCA algorithm. However, to reduce overfitting (i.e., tending towards a rank-deficient CCA solution), prior to CCA we separately reduced the dimensionality of each dataset using PCA. Specifically, after accounting for missing data as before, we compressed the size of each matrix along the respective phenotype dimension to the top 30 subject-eigenvectors which accounted for ~70% of the total variance in our datasets (66.9% for IDPs, 76.1% for behavioural measures). The final dimension of each matrix fed into CCA was therefore 123 x 30 (subjects x PCA-derived components), with an output of 30 CCA modes estimated.

Statistical significance of the modes estimated was determined using 10,000 permutations of rows of one matrix relative to another. CCA was then re-run after each permutation and the respective r-values for each permuted CCA mode was estimated. Each observed canonical correlation r is compared to the null permutation distribution of the largest canonical correlation creating familywise error p-values corrected for searching over all 30 canonical correlation dimensions.

Post-hoc correlations

To relate the CCA modes estimated back to the observed IDP and behavioural variables, we perform post-hoc correlations between each observed (quantile-normalised and deconfounded) variable with the canonical variate weights (U or V). This is analogous to the computation of factor loadings, and in CCA are formally referred to as canonical structure correlations. Generally, variables with larger post-hoc correlations indicate greater association with a CCA mode.