We found that a non-linear model, implemented with a Bayesian hierarchical analytic approach, generated robust fits to the observed cognitive trajectories of elderly subjects. Validating our approach, APOE ε4 alleles were associated with reduced age at midpoint of cognitive decline and psychosis was associated with increased rate of cognitive decline. We then implemented our model to test whether SNPs associated with an increased risk for late onset AD alter cognitive trajectory after accounting for the effects of APOE and demographic factors. We found that rs11136000 in CLU and rs3818361 in CR1 were associated with more rapid cognitive decline. rs541458 in PICALM was associated with an earlier age at midpoint of cognitive decline, although this latter association did not persist in an additive model designed to correct, in part, for multiple testing. For all SNPs except CLU SNP rs11136000 the allele conferring an adverse cognitive trajectory was the same as that associated with AD in prior GWA studies.
We utilized a non-linear model that allowed for censoring at the maximum and minimum values. This choice was based on a common property of cognitive tests, which often have defined maximum and minimum scores. As a result, prior to disease onset individuals may sustain maximal scores, while in end-stage disease sustained minimal scores may be present. Such observations cannot be fit adequately with a trajectory derived from a linear or quadratic model, although multiple linear fits (e.g. as applied in changepoint models), may be used to approximate subsets of points within a longitudinal cognitive trajectory (23
). Other psychometric properties of cognitive tests also contribute to non-linearity. Many tests are admixtures of easier, moderately difficult, and difficult questions, not necessarily in equal proportion. As a consequence, scores may change little during a given phase of cognitive decline, e.g. during early illness if there are few difficult questions. Alternatively, scores may show greater change during another phase, such as moderate disease, if there are proportionally more questions of moderate difficulty. Many global cognitive tests, including the 3MS, follow just such a pattern (24
). In contrast, the DSST requires repeating the same cognitive function, and is scored based on how many times it is successfully completed within a timed interval. However, the overall difficulty of the task results in non-linearity in moderate to severely impaired individuals, supporting the use of a non-linear model to fit this data (25
). Whether there may be a relative advantage to the use of cognitive measurements that demonstrate more consistent linear measurement properties across levels of disease severity for detection of SNP effects on cognitive decline would benefit from testing using additional measures that differ with regard to these properties.
We found rs11136000 in CLU
was associated with more rapid cognitive decline, however, the risk for more rapid decline was conferred by the allele opposite to that previously associated with AD (2
). Although rate of cognitive decline and presence of AD are not identical, it seems unlikely that a causal allele would confer different directions of risk for these two outcomes. Several authors have argued that significant allelic association in opposing directions is statistically unlikely (27
), and probably reflects true association via one of several underlying mechanisms (27
encodes the protein clusterin, which is expressed at increased levels in the brains of individuals with AD, can serve to prevent fibrillization of Aβ, and inhibit complement activation (31
). In individuals with MCI and AD, elevated plasma clusterin correlated with more rapid cognitive decline, though plasma clusterin concentrations were not associated with genetic variants in CLU
, including rs11136000 (32
We found that rs3818361 in CR1
was associated with more rapid cognitive decline. CR1
is a complement receptor expressed in cerebral cortex. There is emerging evidence that the complement cascade contributes to targeting synapses for elimination during development and in neurodegeneration via astrocyte-mediated opsonization with the complement component 3 fragment, C3b (33
supports clearance of opsonized targets due to its high affinity for C3b (34
). Recent evidence indicates that the reported associations of genetic variation in CR1
with AD may arise from linkage disequilibrium between these variants and a low copy repeat which codes for a CR1
isoform with an additional C3b binding site (35
). It is not currently known if CR1
contributes to synapse elimination in AD.
Finally, we found that rs541458 in PICALM
was associated with an earlier age at midpoint of cognitive decline, although it should be noted that this association did not persist in our additive model. PICALM
encodes the phosphatidylinositol-binding clathrin assembly (Picalm) protein, an essential factor in clathrin-mediated endocytosis (36
). Recent evidence indicates that Picalm is primarily expressed in vascular endothelial cells in human brain (37
), where it may affect the clearance of Aβ from brain. For example, rs541458 in PICALM
is significantly associated with cerebrospinal fluid levels of Aβ42 (38
). This interpretation would be congruent with a mechanism by which variants that result in overproduction or over-accumulation of Aβ most strongly impact age of cognitive decline.
The above associations of CLU, CR1
, and PICALM
were detected in models that accounted for demographic variables and the effect of APOE
ε4. This finding stands in contrast to a recent analysis of several cohorts, including the CHS, which found that rs11136000 in CLU
and rs3851179 in PICALM
did not add to the prediction of AD onset beyond demographic and APOE
). This may indicate there is increased power available in using a cognitive trajectory, rather than a dichotomous diagnosis, to identify SNP associations with longitudinal outcome in subjects at risk for AD. Of interest, we found that genetic variation in PICALM
was associated with lower age at midpoint of decline in models that included APOE
. This is somewhat surprising given recent evidence that APOE
genotypes are correlated, resulting in substantial reduction in the association of PICALM
SNPs with AD risk after accounting for APOE
). Unlike PICALM
associations with AD risk did not display confounding with APOE
), thus it is not surprising they demonstrated detectable effects after controlling for APOE
We used a Bayesian approach to fit cognitive trajectories. The principal advantage of Bayesian methods over classical (e.g. mixed model) analyses is that calculation of posterior distributions is typically straightforward even for complex models. However, Bayesian methods are often computer intensive, creating a potential limitation of our approach; it may not be practical for sequential screening of large numbers of SNPs. Another potential limitation in any model fitting is inadequate model convergence. In Bayesian hierarchical models, completely uninformative prior distributions may result in invalid (improper) posterior distributions. The standard solution to this is to incorporate a small amount of prior information to create “weakly informative” prior distributions. In clinical settings like the ones we modeled, this is simple and effective, because we can put reasonable limits on parameters, e.g., we know that for our subjects the age at midpoint of cognitive decline is between 30 and 130 years. The utility of these weak prior distributions can be seen in the fidelity of our trajectory fits to the observed data. Finally, an important modification to our Bayesian implementation was the use of a t-distribution, rather than a normal distribution, to model deviations of measurements from trajectory means. This approach substantially reduced the effects of occasional outlier values, a not uncommon occurrence in our observed data (Supplemental Fig 1
Other possible limitations to our findings should be considered. We selected for testing a limited number of SNPs based on replicated evidence of genome wide significant association in GWA studies. Other SNPs in these genes, which did not themselves reach genome wide significant association with AD risk, may nevertheless associate with trajectory of cognitive decline. The same may be true for genetic variation in other genes, including a number of SNPs since identified as demonstrating genome wide significant association in GWA studies of AD. Determining a trajectory requires a minimum number of observed measurements. We chose as inclusion criteria the presence of four measurements on the 3MS and DSST tests. This may have by necessity excluded some individuals with more rapid decline, who thus did not complete four tests. Similarly, the individuals who participated in the CHS Cognition Study and were thus available for this analysis were a non-random subset of all CHS participants, healthier and younger than the parent cohort. As such, our findings may not fully generalize to the elderly population.
In summary, we developed a Bayesian approach to addresses several goals for the analysis of cognitive trajectories in aging subjects, including the ability to: fit individual as well as group cognitive trajectories, make meaningful descriptive statements about the pattern of change and the variability in that pattern across subjects, develop credible regions for the resultant curves which include appropriate prediction limits, and evaluate the specific effects of covariates, including genetic covariates, by estimating their impact on the trajectory parameters. We validated this approach with two established predictors of different cognitive trajectory parameters, the presence of APOE ε4 alleles and the development of psychosis. We then used our approach to detect effects of recently identified AD risk alleles on cognitive trajectories. Replication of this approach using other data sets is warranted.