Contents

## Why LDA What I Hope Youll Get Out of This The basic longitudinal methods Diggle, Heagerty, Liang & Zeger, 2001 Population-average models Subject-specific models

Tomalin, Terry, Contributor has reference to this Academic Journal, PHwiki organized this Journal A Practical Guide to the Selection, Analysis, in addition to Interpretation of Longitudinal Models Qian-Li Xue, PhD Departments of Medicine, Biostatistics, & Epidemiology in addition to Center on Aging in addition to Health Johns Hopkins University December 6, 2010 Why LDA Top four reasons Changes in disability prevalence over time 4. To in as long as m policy Functional trajectories in addition to their etiologies 3. To study natural histories Cognitive status transitions 2. To make prognoses, incorporating history Intervention A or risk adoption B changes outcomes 1. To progress from association toward cause Value of LDA Neuropsychological effects of amateur boxing

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Value of LDA Neuropsychological effects of amateur boxing Unlinking model: B in addition to een-Roche et al., 1999 What I Hope Youll Get Out of This The basic longitudinal modeling methods How to decide which model to use How to interpret the models Heads up on the primary challenges Heads up on causality considerations An Example Emotional vitality in addition to mobility (Penninx et al., 2000) Study: Womens Health & Aging I (n=1002; Guralnik et al., 1995) Question: Does emotional vitality affect mobility trajectory Emotional vitality (X: 1 if vital; 0 ow) High mastery, being happy, few depressive/anxious symptoms 35% vital Mobility (Y) Usual walking speed (max 2 trials) Time (T) Study rounds 0-6

The basic longitudinal methods Diggle, Heagerty, Liang & Zeger, 2001 Top four reasons Population average (marginal models; GEE) 4. To in as long as m policy Subject-specific (r in addition to om effects; growth curves) 3. To study natural histories Transitions (autoregressive & Markov models) 2. To make prognoses, incorporating history Time-varying covariates (with complexities) 1. To progress from association toward cause Population average v. Subject-Specific PA: Compare populations over time (Fixed) time effect = slope of the averages SS: Compare women to selves over time (Fixed) time effect = average of the slopes Subtle point: These are equal with continuous outcomes Y (linear regression); NOT otherwise provided that within-person correlation is explicitly accounted as long as t t y y Population-average models Keywords Marginal models GEE (Generalized Estimating Equations) Liang & Zeger, 1986 Panel analysis Sound bites Focus usually on averages (their trajectories) Serial correlation often a nuisance Robust

Population-average models Description of average trajectories Modeltime-invariant covariates (x): rate of change in average walk speed of non-vital persons Difference in rate of change in average walk speed between vital & non-vital persons Key points Greek = fixed; Roman = variable ANCOVA model Coding: main effects as long as treatment, time; interaction Population-Average Models Pictures Data displays Side-by-side box plots (by time, treatment) Connect-the-means plots (over time, by treatment) Y versus t smoothed scatterplot, per x average speed time Vital (x=1) non-vital (x=0) 0 0 0 + 1 slope= 2 slope= 2 + 3 Population-average models Treatment of serial correlation error: amount that speed of woman i differs from population average at time 7 Key points Errors are correlated within persons Most software: you choose the correlation structure Exchangeable all measures equally strongly correlated Autoregressive, b in addition to ed measures closer in time more strongly correlated Unstructured as it sounds (here: 7 choose 2 = 21 s) Independence all correlations assumed = 0

Population-Average Models: Fitting Software SAS: GENMOD (GEE); MIXED, repeated (MLE) SPSS: Advanced model package Stata: xtgee (GEE); xtreg (MLE) GEE versus MLE (maximum likelihood est.) Both: accurate coefficient estimates whether or not correlation structure choice is correct GEE: st in addition to ard errors also accurate, regardless MLE: More powerful if choice is correct Subject-specific models Keywords Mixed effects, growth curves, multi-level Mixed model; hierarchical (linear) model GEE Laird & Ware, 1982; Raudenbush & Bryk, 1986 R in addition to om coefficient model Sound bites Focus usually on individual trajectories Heterogeneity: variability of trajectories Assumptions are made, in addition to may matter Subject-specific models Average & individual trajectories Modeltime-invariant covariates: amount baseline speed as long as person i exceeds or falls short of the average amount speed trajectory as long as person i differs from average Key points: The additional coefficients are r in addition to om Modeling assumes a distribution: usually normal Distribution variance characterizes heterogeneity Heterogeneity results in within-person correlation One may define correlation structure as long as eijs too

Subject-Specific Models Pictures b0i = r in addition to om intercept b2i = r in addition to om slope (could define more) heterogeneity spread in intercepts, slopes Sentinel data display: spaghetti plot (Ferrucci et al., 1996) time vital non-vital . 0 0 + 1 2 + 3 + b0i slope: – b2i Subject-specific models: Fitting Software SAS: MIXED, r in addition to om; GLIMMIX (macro); NLMIXED SPSS: Advanced model package Stata: xt sequence Other: HLM, MLWIN, Splus, R, winbugs Data Example

Usual Walking Speed in WHAS Panel Plot vital Non-vital Usual Walking Speed in WHAS Spaghetti Plots Emotionally vital Emotionally non-vital Does vitality affect walking speed wrong

Usual Walking Speed in WHAS Heterogeneity Residual SD: 0.167 Represents variability of a womans speeds about her own regression line (i.e. individual trajectory) Intercept SD: 0.276 95% of baseline walk speed estimated between 0.03 in addition to 1.13 m/sec Test-retest estimate = .076/(.076+.028)=.73 Slope SD: 0.031 95% of slopes estimated between -0.07 in addition to 0.05 m/sec per year Intercept, slope correlation: .23 better trajectories as long as better starters Unstructured correlations: .6 – >.99 Highest late in the study Vitality & Walking Speed in WHAS Summary Beneficial association with emotional vitality Begin better by ~.1; 95% CI ~ [.06,.14] Moderate evidence: Decline rate ~ halved Remarkable stability evidenced Modest average decline Heterogeneity: moderate to modest Stability increased with duration in study To advance toward causation: much needed Control as long as confounders Change on change Population average v. Subject-Specific How to choose Science Advantages of subject-specific models Characterization of heterogeneityestimates May well embody mechanisms Advantages of marginal models More robust St in addition to ard errors valid if correlation model wrong (GEE) Fixed effect estimates distribution-insensitive Computationally faster, more transportable (GEE) An MLE advantage: Missing data treatment

Analysis of Longitudinal Data: Model Comparison Population Average: GEE Subject Specific: REM Between-Subject Heterogeneity – + Model Assumptions + – H in addition to ling Missing Data – + Irregular Time Intervals – + Cluster Size + – Computation + – Why LDA Top four reasons Changes in disability prevalence over time 4. To in as long as m public policy Functional trajectories in addition to their etiologies 3. To study natural histories Cognitive status transitions 2. To make prognoses, incorporating history Intervention A or risk adoption B changes outcomes 1. To progress from association toward cause Some LDA & causality punch lines Thats progress from association toward cause Temporality = one necessary component of causality The others: association, isolation von Suppes, 1970; Bollen, 1989; Rubin, 1974 Not all LDAs are created equal Top of the hierarchy: Change-on-change Change in response (Y) versus change in predictor (X) Key = use of individuals as their own controls

LDA Challenge 1 Feedback, endogeneity Decline in speed may erode emotional vitality or, the vital may try harder at the measured walk test An issue with time-varying or invariant xs Solution 1: Sophisticated modeling Cross-lag, Structural, Marginal Structural Geweke, 1982; Bollen, 1989; Robins, 1986 Solution 2: Transition modeling LDA Challenge 2 Dropout, Missing Data The issue: Those missing may differ systematically from those observed Sicker Less emotionally vital Functionally declining Findings accuracy, precision may suffer Missing data, in addition to Missing data Rubin, 1976; Little & Rubin 1989 A st in addition to ard hierarchy: Missing completely at r in addition to om (MCAR) Missing at R in addition to om (MAR) Measured variables, only, may influence missingness including past Ys Not Missing at R in addition to om (NMAR) Depends on outcomes after dropout: really tough The distinctions matter because the type of missing data mechanism determines the analytic sophistication that is needed

Take home points If youre out to save Millions at a Time© Population average (marginal) model Choice 1: GEE (corr-robust) vs. MLE (MAR-robust) Choice 2: Association structure to fit Mean trajectory estimates not sensitive If one at a time, or seeking to target Subject-specific (r in addition to om effect) model Benefit if model correct: heterogeneity characterization, MAR-robust, MLE: precise Temporality necessary, not sufficient, re causality Transitions; time-varying covariates

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