Trajectories of Health: Methods and Insights from Structural - - PowerPoint PPT Presentation

Trajectories of Health: Methods and Insights from Structural Equation Modeling

Important contributions from: Douglas Gunzler, PhD, Megan Holmes, PhD, Joseph Sudano, PhD & Susan Yoon, PhD Adam T. Perzynski, PhD Assistant Professor of Medicine and Sociology

OUTLINE

Part 1: An example using data on older adults Part 2: An example using data on kids

DISCLAIMER

• Longitudinal latent variable

models can be very complicated

• There are many different

flavors of models.

• Jargon and Acronyms are

bountiful

(and occasionally used inconsistently)

LONGITUDINAL PATTERNS OF DEPRESSIVE SYMPTOMS IN THE HEALTH AND RETIREMENT STUDY

PART 1

AIM

• Explore the use of Latent Class Growth

Analysis to model changes in depressive symptoms over time in the Health and Retirement Study.

OVERVIEW

• Most studies of older adults compare the

change in mean scores between two waves.

• A small number of studies have modeled

change as a single growth trajectory

CHANGE IN MEANS BETWEEN WAVES

• Often we simply calculate the mean

depressive symptoms at Wave 1 (baseline).

• Subract it from the mean at Wave 2

(followup).

WHAT IS A TRAJECTORY?

• Regrettably, the term “trajectory” has taken
• n multiple meanings across disciplines

and research studies.

• A broad, inclusive definition of trajectory

modeling is the analysis of patterns of change or stability.

• Confusion is possible (if not likely)

EXAMPLE OF A SINGLE (LINEAR) GROWTH TRAJECTORY

SEM REPRESENTATION OF A SINGLE GROWTH TRAJECTORY

Intercept Slope W1 W2 W… W7

CONTINUOUS LATENT GROWTH CURVE ANALYSIS

• LGA / LGCA
• Studies in older adults (ie George and

Lynch 2003) typically find that the slope of the latent growth curve for depressive symptoms is small and positive, and that the slope of the curve is steepest in the

• ldest cohorts.

EXAMPLE FROM GEORGE AND LYNCH (2003)

EXAMPLE OF AN LGA FINDING

LGA ESTIMATES A SINGLE AGGREGATE TRAJECTORY

• Assumes that the average population starting

point (intercept for the growth curve) and average amount of change (slope) are a sufficient depiction

• f variation over time in depressive symptoms.
• If discrete subtypes of depressive symptom

trajectories exist, but are ignored (as in single latent growth curve and autoregressive models) the magnitude of associations could be grossly misestimated.

WHAT IS LATENT CLASS GROWTH ANALYSIS?

• Latent Class Growth Analysis (LCGA),

also referred to as growth mixture modeling, belongs to a family of statistical techniques referred to as general latent variable modeling or GLVM.

WHY WOULD WE EVER THINK WE SHOULD USE LCGA?

• Studying the mean change or using a single trajectory for everyone

assumes uniform heterogeneity in the population.

• Researchers use familiar methods and typically assume that the

underlying (latent or real) distribution of variables is continuous.

• We have theoretical reasons to suspect that underlying distributions

could be categorical.

• Life course theorists (Dannefer) specifically caution that intracohort

differentiation is unlikely to be homogeneous.

WHY WOULD WE USE LCGA?

• We think individuals and cohorts diverge
• ver time
• Cumulative change differentiates

individuals and cohorts.

PRIOR LCGA MODELS OF DEPRESSION OR DEPRESSIVE SYMPTOMS

• LCGA models and closely related Longitudinal Latent

Class Analysis (LLCA) have been used to estimate models of depressive symptoms in prior studies of

– maternity (Campbell et al 2009; Mora et al 2009) – childhood and adolescence (Meadows et al 2006) – adolescence through young adulthood (Olino et al 2009) – response to antidepressants among adults (Muthen et al, 2007; Hunter et al 2009) – patients who have had a cardiovascular event (Kaptein et al 2006).

METHODS

• 5,195 age-eligible respondents from the 1992 Health and

Retirement Study cohort, who completed interviews in all seven waves through 2004.

• Depressive symptoms in HRS are measured using a dichotomous,

8-item version of the CES-D. Analysis begins with Wave 2 data due to a change in response categories from Wave 1.

• Using MPlus, we compared the fit of LCGA models of two to eight

classes while also accounting for the HRS complex sampling design.

• We then tested the effect of a small number of covariates. This is

very similar to a multinomial logistic regression.

DEMOGRAPHIC CHARACTERISTICS

• Gender

– 60.3% female

• Race/ethnicity

– 76.4% non-Hispanic White – 14.4% Black – 7.4% Hispanic – 1.8% other racial/ethnic groups

• Age

– Median=55

• Education

– Mean=12.4 years (SD=3.0).

RULE FOR DETERMINING THE NUMBER OF LATENT CLASSES

• “How many trajectories are there?”
• Measures of model fit including:

– Lo-Mendell-Rubin Test (LMR test) – log-likelihood (LL) – Bayesian Information Criteria (BIC) (Vuong, 1989; Muthen, 2004; Muthen, & Muthen, 2005; Nylund et al, 2007).

• Here we will use the LMR Test
• Where k is the number of latent classes, this test gives a p-

value for the k-1 versus the k-class model when running the k- class model (Vuong, 1989; Muthen, B. 2005).

• The first time p > .05, k-1 is the preferred number of classes.

I = Intercept S = Slope W1 W2 W… W7 C = Categoric al Latent Classifica tion

RESULTS

• How many classes are there?
• What do the classes look like?
• How is this different from looking at means or single

trajectory?

• Are any demographic variables associated with being in a

particular class?

HOW MANY CLASSES ARE THERE?

K LL BIC Adjusted BIC LMR Test LMR p Entropy 2

• 56367.49

112983.09 112890.94 10525.69 0.000 0.955 3

• 55146.65

110618.41 110497.66 2410.38 0.000 0.922 4

• 54652.99

109708.09 109558.74 974.66 0.015 0.925 5

• 54357.08

109193.27 109015.32 519.88 0.149 0.901 6

• 54090.08

108736.27 108529.72 397.39 0.354 0.912 7

• 54079.98

108793.06 108557.91 97.55 0.392 0.920 8

• 53895.87

108501.85 108238.10 307.84 0.314 0.732 Table 1. Depressive Symptoms LCGA Model Fit Comparison, N = 5,195

HOW MANY CLASSES ARE THERE?

K LL BIC Adjusted BIC LMR Test LMR p Entropy 2

• 56367.49

112983.09 112890.94 10525.69 0.000 0.955 3

• 55146.65

110618.41 110497.66 2410.38 0.000 0.922 4

• 54652.99

109708.09 109558.74 974.66 0.015 0.925 5

• 54357.08

109193.27 109015.32 519.88 0.149 0.901 6

• 54090.08

108736.27 108529.72 397.39 0.354 0.912 7

• 54079.98

108793.06 108557.91 97.55 0.392 0.920 8

• 53895.87

108501.85 108238.10 307.84 0.314 0.732 Table 1. Depressive Symptoms LCGA Model Fit Comparison, N = 5,195

WHAT DO THE CLASSES LOOK LIKE?

1 2 3 4 5 6 1994 1996 1998 2000 2002 2004 Mean # of Depressive Symptoms HRS Study Wave

Figure 1: Four Latent Classes of Depressive Symptoms over 12 Years of the HRS

Many Persistent Symptoms = 5.4% Decreasing Symptoms = 9.6% Increasing Symptoms = 11.5% Almost No Symptoms = 73.5%

N = 5195

DOES ANYTHING INFLUENCE THE CHANCES OF BEING IN A PARTICULAR CLASS?

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Latent Class Probability Years of Education

Figure 2. Relationship between Years of Education and Depressive Symptoms Trajectory/Latent Class Membership

Many Symptoms Decreasing Symptoms Increasing Symptoms Almost No Symptoms

N = 5195

WHAT PREDICTS TRAJECTORIES?

• Females, African Americans and those

with fewer years of education have a higher probability of being in the Many Symptoms trajectory.

N = 5195 OR b p OR b p OR b p Age 0.94

• 0.057

0.010 0.96

• 0.043

0.014 1.02 0.016 0.422 Female 2.19 0.785 0.000 1.53 0.428 0.001 1.41 0.346 0.002 Black 1.89 0.635 0.000 1.90 0.641 0.000 1.54 0.429 0.001 Hispanic 1.12 0.113 0.655 1.59 0.461 0.018 1.19 0.178 0.461 Low Education 1.32 0.274 0.000 0.84

• 0.173

0.000 0.90

• 0.105

0.000

• Table. Effects of Demographics on the Likelikhood of a Depressive Symptoms Trajectory
• vs. Almost No Symptoms (reference category)

Many Symptoms Decreasing Increasing

PART 2

Cohort sequential methods for understanding development among maltreated children

BACKGROUND

• Researchers seeking to understand child development
• ver time face important challenges when using

longitudinal data.

• Some designs make it impractical to enroll only same

aged individuals (e.g. developmental studies of children)

• Children from different ages at the same measurement

intervals

• Study waves and child developmental stages become

confounded with time

COHORT SEQUENTIAL METHOD

• The cohort sequential design has been used previously in

multiple studies of child well being (for example Cole et al, 2001 among others).

• Prior cohort sequential models of child development are

confined to single latent growth curve models

APPLYING THE COHORT SEQUENTIAL FRAMEWORK TO GROWTH MIXTURE MODELS

DEVELOPMENT

INFANCY BIRTH – 2 PRESCHOOL 3 – 5 EARLY SCHOOL 6 – 10 EARLY ADOLESCENCE 11 – 14

WEEK 1

WEEK 2

WAVE BY WAVE ANALYSIS LOOKS LIKE THIS

THE COHORT SEQUENTIAL MODEL REPRESENTS AGE AS TIME TO UNDERSTAND DEVELOPMENT

METHODS

National Survey of Child and Adolescent Well- Being (NSCAW)

• Nationally representative sample
• Reported to Child Protective Services
• Birth to 5 years old at Time 1
• Residing with a biological caregiver
• SEM analyses conducted using MPLUS
• N= 1,678 Children

DATA COLLECTION

Wave 1 (Time 1) Wave 2 Wave 3 (Time 2) Wave 4 (Time 3) Wave 5 (Time 4) Start and end date 11/15/99- 04/30/01 10/01/00- 03/31/02 04/01/01- 09/30/02 08/01/02- 02/28/04 09/05/05- 11/15/07 Months after baseline measure 6-10 12-16 30-34 53-94 Respondent Child Current Caregiver Caseworker Teacher X X X X X X X X X X X X X X X X X X

SAMPLE DEMOGRAPHICS

Child Characteristics M (SD) % Age at baseline 1.69 Male 52.6 Race/Ethnicity White, Non-Hispanic 43.6 Black, Non-Hispanic 30.4 Hispanic 18.8 Other 6.4 Caregiver Characteristics M (SD) % Education Less than high school 38.4 High school graduate 60.7 Poverty 76.3

MEASURE

PROSOCIAL SKILLS

• Pro-social skills include positive behaviors including sharing, cooperating,

empathy, and taking turns.

• Measured with the Social Skills Rating System (SSRS). This is a caregiver

reported measure.

• Reliability was >.90

Comparison across age cohorts is a further complication. We chose a ranking approach.

• Produced quantiles (e.g., deciles) of the distribution of each variable

– Advantage: capturers important variation in the distribution with out the drawback of a binary variable

ANALYSES

Cohort Sequential Latent Growth Mixture Model

1 2 3 4 5 6 7 8 9 10 T1 T2 T3 T4 T1 T2 T3 T4 T1 T2 T3 T4 T1 T2 T3 T4 T1 T2 T3 T4 T1 T2 T3 T4

REMEMBER: WAVE BY WAVE ANALYSIS LOOKS LIKE THIS

RESULTS

PROSOCIAL SKILLS GMM

RESULTS

PROSOCIAL SKILLS CS-GMM

INFANCY BIRTH – 2 PRESCHOOL 3 – 5 EARLY SCHOOL 6 – 10

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 1 2 3 4 5 6 7 8 9 10 Deciles of Academic Performance Age in Years

High and Stable Over Time (Resilient) (Group 1) Increasing Over Time (Resilient) (Group 2) Low and Stable Over Time (Group 3) Decreasing Over Time (Group 4) Decrease/Recovery/Decrease (Group 5)

RESULTS

ACADEMIC COMPETENCE

Resilient Resilient

19.9% 17.1% 21.4% 20.1% 21.5%

RESULTS

 Entropy is a measure of classification quality.  In the prosocial skills results the entropy was .822 for the four trajectory CS-GMM model as opposed to just 0.606 for the wave-by-wave GMM four trajectory model .  In other analyses, a similar improvement was found for academic competence (.790 vs .629)  This suggests an enhanced ability to characterize developmental pathways.

SEM IS AWESOME!

 Typically requires large sample sizes  Enables correction for and examination of measurement error  Extraordinarily flexible  Opportunity for sophisticated handling of change

• ver time (e.g. modeling of developmental

pathways)

DIVERSE & DISTINCT OUTCOMES

Academic Competence Neglect Physical Abuse Internalizing Symptoms Sexual Abuse Neglect Early Substance Use Physical Abuse

Variation

Diverse groupings of developmental pathways can be explicitly modelled as opposed to ignored or assumed away. Longitudinal studies should carefully consider the consequences of modeling decisions. Even some highly sophisticated techniques (univariate latent growth models and growth mixture models) can conceal important variation of interest to researchers and policy makers.

Thank you!

Adam T. Perzynski, PhD Assistant Professor of Medicine Adam.Perzynski@case.edu