Cognitive lifestyle jointly predicts longitudinal cognitive decline and mortality risk

Data stem from the Paquid cohort, which is a longitudinal study of ageing with up to 20 years of follow-up [19]. Recruitment of 3,777 participants occurred across 75 civil parishes of the Gironde and Dordogne regions of south west France. Subjects were aged 65 years and above, residing at home at the study baseline in 1988. There have been up to nine subsequent waves of data collected on each individual at 1, 3, 5, 8, 10, 13, 15, 17, and 20 years after the baseline assessment. At the first follow-up, only subjects from Gironde were interviewed.

At each wave of Paquid, a multi-test cognitive battery was administered to the participants by a trained neuropsychologist. For this analysis we only consider scores from one of the tests, the Mini-Mental State Examination (MMSE) [20]. The MMSE is a test of global cognitive function that is brief to administer and has a scoring range of 0–30. The MMSE scores were treated as continuous data for the joint latent class mixed model analysis. For the multi-state model of cognitive change, MMSE categories were specified as follows: no impairment was defined as a score between 27 and 30, slight impairment for scores between 23 and 26, and moderate/severe impairment for scores below 23 [18]. An MMSE score between 23 and 26 has been shown to be as effective at predicting conversion to dementia as other more detailed clinical measures of mild cognitive impairment [21].

Three baseline measurements of cognitive lifestyle were included in this analysis: early-life education, mid-life occupation, and late-life social engagement. Education was split into three groups: no education or a non-validated primary school degree; a validated primary degree up to a non-validated secondary degree; and a validated secondary degree or higher. Mid-life occupation was dichotomised into intellectual (craftsmen and shopkeepers, policemen, nurses and white collar workers, and professional workers) versus non-intellectual type work (housewives, farm workers, farm managers, domestic service employees, and blue collar workers). Four binary response questions were combined to create a scale for late-life social engagement. They focussed on: membership of a group or association; visits from family and friends; membership of a golden age club; and membership of another club. A three category response was created after summing the scores from all four variables: low social engagement (sum score 0); medium social engagement (sum score 1); and high social engagement (sum score 2, 3, or 4). Although a more detailed list of social engagement questions was available for analysis, those chosen are analogous to the questions used in CFAS where such a measure was linked to cognitive decline [18].

Data were analysed using a joint latent class mixed model (pictured in Fig. 1). The MMSE was treated as a continuous variable and the changes over time were modelled jointly with death. The model distinguishes sub-populations (latent classes) that are characterised by different profiles of cognitive decline and mortality risk. The probability of latent class membership was explained according to sex, and the three cognitive lifestyle variables. Observed MMSE scores were assumed to be noisy, curvilinear measures of the true latent cognitive level [13]. Curvilinearity refers to the unequal sensitivity of the cognitive test to measure cognitive change. It means that a 1-point change does not represent the same cognitive loss from two different initial levels, and leads to floor/ceiling effects and a non Gaussian distribution of the score [22]. To normalize the observed MMSE scores and to link them to the true latent ability, a parameterized non-linear link function (specifically a Beta cumulative distribution function) [13] was applied. Evolution of the true latent ability was assessed using a latent-class-specific linear mixed model with a class-specific quadratic age trend to account for non-linear cognitive decline; a binary ‘first visit’ variable was included as a common estimate across the classes to account for a potential learning effect between waves one and two but not between waves thereafter [17]. This class common effect assumes that the learning effect is identical for all individuals. Class specific parameters increase the model complexity substantially but allow a more flexible fit. Where these effects were similar e.g., learning effects, these can be treated as class common effects, yielding a more parsimonious model. This can be formally tested for via a multivariate Wald test. Random-effects were included to incorporate individual variation in the intercept and both the linear and quadratic slopes of decline. The joint survival model with death as the time-to-event outcome was defined by a two parameter Weibull distribution with class-specific proportional hazards. Covariates were the same as those used for the class membership (sex and cognitive lifestyle variables) and were assumed to be class specific. However, given that some of the latent class profiles contained too few individuals with some characteristics (high education, for example), education and social engagement were re-coded as binary variables (lowest group versus the two highest groups for both variables) in order to estimate these class-specific parameters. After parameter estimation, the posterior probabilities to belong to each latent class were computed for each subject and they were then assigned to the class with the highest probability [15]. The number of latent classes was determined using the BIC selection criteria as in Proust-Lima et al. [15], a measure of entropy [23, 24], and by assessing the mean posterior probabilities of belonging to each latent class according to the final classification (minimum threshold of 0.65). Analyses were also repeated using different starting values to minimise the chance of the models converging to a local maximum. Data were analysed using a Fortran90 programme developed by Proust-Lima et al. [15], which can be found online (http://​etudes.​isped.​u-bordeaux2.​fr/​BIOSTATISTIQUE/​HETMIXSURV/​US-Biostats-HETMIXSURV.​html).

As a sensitivity analysis, an analogous multi-state model was built. Full details of the model and its assumptions have been previously published [8, 18]. Briefly, the model (pictured and described in detail in Fig. 2) contained three living states (no cognitive impairment; slight cognitive impairment; moderate/severe cognitive impairment) and death as an absorbing state. Transitions were modelled between adjacent states except for recovery from moderate/severe impairment which was too rare. The exact entry time into each cognitive state is unknown and the transition intensities vary by age, a time-dependent covariate, sex and the three cognitive lifestyle variables. Measurement error of the cognitive states was accounted for by a hidden Markov model that treats the observed MMSE states as potentially misclassified manifestations of the true underlying cognitive state. Back transitions from moderate/severe impairment were assumed to be misclassifications. Further sensitivity analyses were conducted to test for possible cohort effects by adding baseline age as a transition specific covariate and to lag the effect of social engagement by only considering cognitive data from the 5 year follow-up onwards. Data were analysed using R version 2.13.1 [25] and the R package ‘msm’ [26].

These findings were compared to those obtained by a multi-state model. Results are presented in Table 3. Compared to those with low education, subjects with high education had half the risk of moving to a slightly impaired state—HR 0.5 (95 % CI 0.3, 0.7); around a 30 times greater chance of cognitive recovery from slight impairment back to no impairment—HR 27.3 (95 % CI 9.6, 77.5); and one-and-a-half times the mortality risk from moderate/severe impairment—HR 1.5 (95 % CI 1.1, 2.1). Similar but attenuated associations were found for the medium educated group. The effects of occupation on the transitions were in the same direction as those for education but of a much smaller magnitude. There was also a small increase in the risk of moving from slight impairment to moderate/severe impairment for those with an intellectual (versus non-intellectual) occupation. Finally, medium and high levels of late-life social engagement were associated with a decreased mortality risk from all three cognitive states—HRs for high versus low social engagement were 0.6 (95 % CI 0.4, 0.8) for those with no impairment; 0.5 (95 % CI 0.3, 0.7) for those with slight impairment; and 0.8 (95 % CI 0.6, 0.9) for those with moderate/severe impairment.

Two additional sensitivity analyses examined potential cohort effects and lagged effects of social engagement. The former included baseline age as a covariate on each state transition. This had no effect on the associations for the cognitive lifestyle covariates (results not shown). Similarly, a model that considered cognitive decline and mortality 5 years after the baseline assessment found similar protective effects of social engagement on transitions to death (results not shown).

While the interpretation of the results for the multi-state model and the joint latent class mixed model are similar, relative strengths and weaknesses of the approaches can still be discussed. The main benefits of the joint latent class mixed model are three-fold. Firstly is its ability to use all available information from quantitative response variables, which avoids the need to generate cut-points and to define states. Moreover, extension of the latent class model can allow the combination of information from multiple tests to create a general cognitive factor that evolves over time [15]. Secondly the model accounts for population heterogeneity by identifying latent classes and display underlying trajectories of cognitive decline. However, individuals are not allowed by the model to change latent class. Thirdly, the joint latent class model is particularly robust to missing data. It explicitly deals with death, and missingness due to dementia dropout is handled via the latent cognitive trajectories. An advantage of using either method for longitudinal analyses of MMSE scores is that they overcome curvilinearity via cognitive state definitions or a nonlinear transformation of the MMSE scores. Both methods are also able to model death. Despite commonly being used in longitudinal models of cognitive ageing [8, 11, 12], a potential limitation is our use of the MMSE. It is typically used as a screening tool for dementia prediction, which provides rationale for its use in the multi-state model. Furthermore, while it is insensitive to change at the ceiling and floor of the distribution [13], our mixed modelling approach was able to account for this.

Limitations of the joint latent class mixed model analysis include a less intuitive interpretation of the results compared to the multi-state model, which yields a single set of HRs for each covariate. A unique feature of the multi-state model was the explicit modelling of cognitive recovery from slight impairment back to no impairment. An alternative approach to the joint latent class model could be a two-stage approach where a latent class mixed model would be estimated first using only repeated measures of MMSE to identify the subpopulations and then a survival model would be estimated in each posterior class. However, the joint model is a better option whenever possible because it accounts for truncation by death when estimating the trajectories and because variances of the regression parameters in the survival model are better estimated by taking into account the uncertainty of the estimates of the latent class mixed models.

Both multi-state models and joint latent class mixed models have flexible properties that enable a realistic modelling of longitudinal cognitive decline although subtle differences exist in terms of interpreting output. For future analyses the most appropriate model will depend on the hypothesis to be tested, the cognitive test under study and the study design. If the objective is to study cognitive recovery or life expectancies, and if clinically meaningful cognitive states can be defined then the multi-state model is ideal. On the other hand, a joint latent class mixed model, which uses all of the information provided by quantitative scores, is ideal when change in the dependent variable is likely to be small, when cognitive states are difficult to define, or when multiple cognitive outcomes are being assessed simultaneously.