Longitudinal Trajectories of Quality of Life Among People With Mild-to-Moderate Dementia: A Latent Growth Model Approach With IDEAL Cohort Study Data

Abstract Objectives We aimed to examine change over time in self-rated quality of life (QoL) in people with mild-to-moderate dementia and identify subgroups with distinct QoL trajectories. Methods We used data from people with mild-to-moderate dementia followed up at 12 and 24 months in the Improving the experience of Dementia and Enhancing Active Life (IDEAL) cohort study (baseline n = 1,537). A latent growth model approach examined mean change over time in QoL, assessed with the QoL-AD scale, and investigated associations of baseline demographic, cognitive, and psychological covariates with the intercept and slope of QoL. We employed growth mixture modeling to identify multiple growth trajectories. Results Overall mean QoL scores were stable and no associations with change over time were observed. Four classes of QoL trajectories were identified: 2 with higher baseline QoL scores, labeled Stable (74.9%) and Declining (7.6%), and 2 with lower baseline QoL scores, labeled Stable Lower (13.7%) and Improving (3.8%). The Declining class had higher baseline levels of depression and loneliness, and lower levels of self-esteem and optimism, than the Stable class. The Stable Lower class was characterized by disadvantage related to social structure, poor physical health, functional disability, and low psychological well-being. The Improving class was similar to the Stable Lower class but had lower cognitive test scores. Discussion Understanding individual trajectories can contribute to personalized care planning. Efforts to prevent decline in perceived QoL should primarily target psychological well-being. Efforts to improve QoL for those with poorer QoL should additionally address functional impairment, isolation, and disadvantage related to social structure.

With regard to the measure of awareness, the small number of participants who scored zero on screening but were administered the rest of the RADIX in error were treated as missing.

Latent Growth Curve Model
To determine how quality of life and indices of 'living well' change over time for people with dementia, latent growth curve growth modelling (LGCM) was conducted in Mplus Version 8.2 (Muthén & Muthén, 1998-2017 using the first three waves of IDEAL data (T1-T3). A LGCM consists of a measurement model which is then extended to a second order growth model allowing estimation of the mean intercept (baseline) and the mean slope (change over time) in the variable of interest, with random effects to account for variation across individuals (Wickrama et al., 2016).
The measurement model for quality of life as indicated by scores on the QoL-AD scale is described in the main paper. Here we describe the model for 'living well'. We built the 'living well' latent factor from three measures, QoL-AD, Satisfaction with Life Scale (SwLS), and the WHO-5 Well-Being Index (WHO-5), at each time-point by longitudinal confirmatory factor analysis (LCFA). QoL-AD was selected as the marker variable, with loading fixed to 1 at each time point and the intercept fixed to zero to allow for model identification. The scale for 'living well' was expressed on the same scale as QoL-AD and the variance of each latent factor and covariance among latent factors were defined by QoL-AD (Brown 2006). The associations between SwLS and WHO-5 were estimated relative to their association with QoL-AD. Variances were estimated for each subdomain indicator and autocorrelated errors specified and retained in the model to avoid misspecification (Little, 2013). For a model to be considered good, a Comparative Fit index (CFI) and Tucker-Lewis index (TLI) greater than 0.90 and a root mean square error of approximation (RMSEA) less than 0.08 (Hu & Bentler, 1999) are required. As shown in Supplementary Table S1, the unconstrained measurement model (configural model) was a good fit to the data indicating that each factor was defined by the same variables and that the same general pattern of factor loadings held across time (Millsap & Cham, 2012;Millsap & Olivera-Aguilar, 2012). In order for meaningful comparisons to be made in a LCFA, the assumption of longitudinal measurement variance should be met (Byrne & Watkins, 2003;Chen, 2007). Three levels of measurement invariance were tested imposing additional restrictions at each step: metric invariance (constrained factor loadings across measurement occasions), scalar invariance (constrained factor loadings across measurement occasions and intercepts across time to be equal), and strict invariance (constrained factor loadings across measurement occasions, and intercepts and residual variances across time to be equal). Each level of measurement invariance was applied and model fit indices examined to ensure that the model fit did not weaken when each level of constraint was applied. Studies have suggested that CFI, RMSEA and SRMR are the most important indicators when it comes to testing measurement invariance, with strict cut offs of <0.01 change in CFI, <0.015 change in RMSEA, and <0.030 change in SRMR (Chen, 2007;Cheung & Rensvold, 2002). ΔX 2 was also examined but as it is sensitive to sample size it was not relied upon (Chen, 2007;Kline, 2011;Schermelleh-Engel et al., 2003). As shown in Supplementary Table S1, each more constricted model had minimal impact on fit indices when compared with the previous model, indicating that metric, scalar and strict measurement invariance held. Further analyses were conducted with the strict invariance model.
The 'living well' factors defined in the LCFA model were used as indicators of the second-order growth curve where the intercept and slope factors of 'living well' were estimated, each with their associated mean and variance. The model diagram is shown in Supplementary Figure S1A. The equivalent measurement model for quality of life using only QoL-AD measurements at T1-T3 as indicators of the second-order growth curve is shown in Figure 1A in the main paper. The intercept loadings were fixed to 1 for each latent intercept, and 0, 1 and 2 for time based on the yearly measurement occasions. Due to only having 3 time points a linear trend was assumed.

Missing data
Where there are missing values on outcome measures, Mplus uses the full information maximum likelihood (FIML) estimator (Enders & Bandalos, 2001), which allows computation of parameter estimates on the basis of all available data without imputing or dropping data when missing under the assumption that data are missing at random (MAR).
To test this assumption, we conducted growth curve analyses for QoL-AD, SwLS and WHO-5 and compared the estimates with a Diggle-Kenward selection model that incorporates dropout (Diggle & Kenward, 1994;Muthen et al., 2011) (Supplementary Table S2); we judged the occurrence of missing data to be ignorable. To specifically test whether death was an informative missing process, we adopted a joint model approach within the JM package in R, which allows simultaneous modelling of longitudinal and time to event data (Rouanet et al., 2019) using mixed models and a Cox proportional hazards regression model. There was minimal impact on the estimates compared to the model without death (Supplementary Table   S3). Multiple imputation of missing data on covariates was generated from Markov Chain Monte Carlo (MCMC) simulations in Mplus (Asparouhov & Muthen, 2010). Estimates from 25 imputed datasets were combined using Rubin's rules (Rubin, 1996).

Latent class growth analysis and growth mixture modelling
So far, our approach has assumed that growth trajectories of all individuals can be adequately described using a single estimate of growth parameters. We employed latent class growth analysis (LCGA) and growth mixture modelling (GMM) to examine whether multiple growth trajectories of quality of life and 'living well' exist in the IDEAL cohort population (Jung & Wickrama, 2008;Muthen, 2004;Muthen & Shedden, 1999). Different assumptions were tested. The LCGA fixes variances of the global growth factors to zero across classes (assuming trajectories within a class are homogeneous). The GMM-CI constrains the variances of the global growth factors across classes to be equal (homogeneous classes), and the GMM-CV freely estimates all variances of the global growth factors across classes. A frequent problem with these models is non-convergence and local solutions (Hipp & Bauer, 2006), with the more complex models, particularly those with free variances, more likely to experience convergence difficulties (Grimm & Ram, 2009). To support convergence, residual variances were free across time but constrained across classes. Between 1 and 5 class solutions were tested for each assumption, with 1000 random starts and 20 iterations for each model in order to avoid local solutions. Following successful convergence, the optimal number of distinct trajectories were determined using BIC, sample size adjusted BIC (ssBIC), the Lo-Mendell-Rubin likelihood ratio test (LMR-LRT) and the bootstrapped likelihood ratio test (BLRT) which provide between model comparisons (k vs k-1), and entropy (Jung & Wickrama, 2008;Nylund et al., 2007;Tein et al., 2013). Entropy is a standardized index of model-based classification accuracy based on the average posterior probability, with higher values indicating clearer class separation (Muthen, 2004). Substantive criteria were based on a class size greater than 1% and theoretical and practical interpretability of the classes. Upon finding an optimal solution, the model was repeated with double the number of starts and iterations to ensure a global solution.
Due to its person-centred approach, GMMs allow for examination of predictors of class membership (Wickrama et al., 2016). The categorical latent class is related to the covariates by way of multinomial logistic regression which assigns each individual fractionally to all classes using posterior probabilities. Predictors of class were examined using the '3-step' approach in Mplus (R3STEP) in order to protect the latent class structure from influences of the covariates (Asparouhov & Muthen, 2013;Vermunt, 2010).

Latent Trajectory Model selection
Three models were tested as described above: LCGA, GMM-CI and GMM-CV.  Supplementary Table S1. Testing factorial measurement invariance for the 'living well' latent factor. The configural model has no constraints. The metric model has constrained factor loadings across each measurement occasion. The scalar model has constrained factor loadings across each measurement occasion and intercepts across time are set to be equal. The strict model has constrained factor loadings across measurement occasions, and intercepts and variances across time are set to be equal. ΔCFI, ΔRMSEA and ΔSRMR were determined to assess model fit. ΔX 2 was examined but not relied upon.

Supplementary Tables and Figures
Note. Bayesian Information Criterion, BIC; degrees of freedom, df; comparative fit index, CFI; Tucker-Lewis index, TLI; root mean square error of approximation, RMSEA; standardized root mean squared residual, SRMR.           Note. Each column represents classification probabilities (averages of the individual probabilities in each class) for the 4-class solution of the estimated GMM-CI, and each row represents the classification probabilities for the most likely class. If classes were perfectly separated, the diagonal components would be 1, and the off diagonals would be 0.

Model
Supplementary Table S8. Testing increasing numbers of classes in LCGA, GMM-CI and GMM-CV models for 'living well'. In the LCGA, variances and covariances are set to zero.
In a GMM-CI, variances and covariances are freed between classes but not within classes (variances fixed across classes). In a GMM-CV all parameters are freed.