Growth Curve Approaches to Longitudinal Data in Gerontology Research Discussion Karen Bandeen-Roche Department of Biostatistics & COAH Johns Hopkins University GSA Annual Meeting November 16, 2001 Thanks for the invite! Thanks for getting me stuff on time! Been looking forward to this.

Important Issues Jones: Memory Maintenance Hall: Natural history of dementia onset Lighthouse: Impact of sensory loss Newsom: Widows’ depression persistence One thing I loved about this session: uniformly important issues addressed. Contrast versus toy examples.

Alternative analytic approaches? Marginal model Do populations learn at different rates, on average? Numeric data  no distinction in fixed effect Autoregressive / transition model Does initial performance predict learning rate? Does initial depression score predict future scores? Change point, versus spline, versus curve? Treatment of time-varying covariates? Marginal model—GEE—my department. * Explain difference in interpretation * Fixed effect = average slope * Rich—better advantage of “random” parts of the model. * Charlie: explicit focus on random part of model (heterogeneity in changepoints). Would have been interested in bivariate random effect description (individuals’ changepoint precedences) Models that predict current response directly from previous response Examples Re depression: Jason’s approach much superior, important. Rich: seems that relation of underlying start to trajectory, and of initial performance to later performance, might be important. Also, no covariance between factors? Mention Andreas Change point, thresholds, curvilinear relationships– all very relevant to research on aging Charlie’s approach really important—profile likelihood, Bayesian far superior to ad-hoc approaches Would ask: reasonable to imagine a changepoint rather than a curve? Effects on inference? Rich: loved your log time trend. Just mention treatment of time-varying covariates. * Effects on measurement about trend vs. “move’ to different trajectory. GGMM * Jason: question re precedence: depression affecting perceived health rather than other way around?

A Fine Point Are Multilevel and Latent Growth Equivalent? It depends on the software used The distinction: treatment of predictor variables Multilevel, M-plus: ADL trajectories in populations with different sensory status LISREL: Covariation between ADL trajectories and sensory status, and among sensory variables Deep-seated statistical debate SEM latent growth: predictor measurement model Multilevel etc: That is, conditions on predictors, as if determined a priori. LISREL : “joint distribution” –key = correctly describe correlations among the predictors as well as among the outcomes and between the predictors and the outcomes. Debate – won’t get into; Mark or Ya-ping: worry that failure of the interaction model really reflects failure in describing the covariate side of the model, rather than quality of interactions in predicting ADL. Interested in why LISREL for this application. *Maybe about to answer my own question: approach admits measurement error in predictors—health, depression, etc. Nice feature.

MODEL CHECKING One Nudge Charlie—Sensitivity analysis Mark / Ya-Ping: goodness of fit Picture to demonstrate data adherence.

Heart of the Matter What Has Been Gained ? The truth? Avoidance of spurious findings? Subtlety? Nothing? Obfuscation? Congratulations to today’s speakers! Intro: several good conversations with my epidemiologist and physician colleagues about the role of stats. Simple is best—though would buy into growth curve. Statisticians have responsibility to ask ourselves: role of type of methods where we can be important—more for us or more for them? Hierarchy: (Read) While I’d love to see where the speakers would place themselves on this spectrum, I think that growth curve analysis was the right way to think about the questions being addressed today. Congratulate them for showing their power to enlighten important questions and for teaching us so much in this session.