2017 Raine Biostatistics SIG trajectories AnneSmith 19april · 2017-08-29 · 19/05/2017 2 Click to edit Master text styles Second level Third level Fourth level ‘TrajectoryFifth

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Raine Study

Max Bulsara and Angela JacquesBiostatistics SIG meeting, Raine Study House, 19th April 2017

Raine Study trajectory analysis

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Health behaviour trajectories: Latent Class Trajectory Analysis

A/Prof Anne SmithSchool of Physiotherapy and Exercise Science

Curtin university

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Fifth level‘Trajectory models’=‘Growth Curve Models’model between‐person

differences in within‐person change over time

Change over timetime trends, time paths, time‐course, life‐

course, growth curves, trajectories

Trajectory Analysis



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Choice of methods guided by:

• question of interest, not the study design

• understanding of the field and underlying mechanisms

Life‐course epidemiology utilising cohort studies

International Journal of Epidemiology special issue. 2016. 45(4), particularly Hardy & Tilling. Commentary: The use and misuse of life course models p1003‐1005.



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Curran et al. 2010. Twelve frequently asked questions

about growth curve modelling. J Cogn Dev 11(2): 121‐136.

• Multilevel (mixed, hierarchical, random effects) Models

• Structural Equation Models

• ‘Latent Class’ Trajectory Models

Terminology is Confusing!!!

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Latent Class Analysis

‘aims to identify subgroups of people who share common characteristics in such a way that people within the subgroups have a similar scoring pattern on the measured variables, while the difference in scoring patterns between the subgroups are as distinctly different as possible.’

Kongsted A, Nielsen AM. An introduction to Latent Class Analysis in health research. J Physiother.(2016), http://dx.doi.org/10.1016/j.jphys.2016.05.018



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Latent Class Analysis as a grouping procedure

• Part of family of ‘unsupervised’ classification procedures

• Advantages over ‘distance-based’ cluster analysis procedures:

o Probability-based using maximum likelihood based estimation procedures

o Measures of model fit allow better judgement for choosing number of classes

o Handles variables of mixed type o Handles missing data o Provides classification probabilities

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Latent Class Trajectory Analysis groups people by common patterns over time• Latent Class Analysis (Repeated Measures LCA)

o Indicator variables are the observations of the variable over time

• Latent Class Growth Analysiso Indicator variables are the trajectory growth parameters. o No variance in growth parameters within classes.

• Latent Class Growth Mixture Modelso Indicator variables are the trajectory growth parameters.o Variance in growth parameters within classes.

For a review and comparison of different methods, see J. Twisk, T. Hoekstra / Journal of Clinical Epidemiology 65 (2012).

• Useful when:o when there are very different patterns over timeo when there are complex patterns of change over timeo to make ‘summary’ variables of trajectories to use as

explanatory or outcome variables



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Latent Class Analysis (Repeated Measures LCA)

• Classifies people by pattern of observations over time, ignoring the longitudinal nature of the data.

• No growth parameters are fitted, change can be modelled in flexible form.

• Useful for lots of up and down changes, concerns about correct model for functional form of the variable, or have separate measures of a construct.

Latent Class Trajectory Analysis

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Coenen P, Smith A, Paananen M, O'Sullivan P, Beales D, Straker L. 2017. Trajectories of low-back pain from adolescence to young adulthood. Arthritis Care & Research 69(3):403-412



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Latent Class Growth Analysis (LCGA)• Developed by Nagin and Tremblay and originally implemented in the

SAS procedure Traj (Nagin D. Analyzing developmental trajectories: a semi‐parametric group based approach. Psychol Methods 1999;6:18e34.)

• Aims to identify k different latent classes with qualitatively distinct trajectories

• Applies latent class analysis to the individual growth parameters NOT the observed repeated measure outcomes.

• Trajectories can be modelled as polynomial functions of time, allowing each parameter to vary in each group so groups can have quite distinct trajectory shapes.

• In ‘Traj’ can model normal, censored normal, zero‐inflated Poisson and binary logit models. Capacity for incorporating effect of time‐stable and time‐varying covariates, subsequent outcomes, joint trajectory models.

• The variance of the growth parameters are fixed to 0 within classes, i.e. there is no additional variation in the estimated trajectory within class, just random error.


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Smith AJ, O’Sullivan P, Straker L, Beales D and de Klerk N. T. (2011) Trajectories of childhood body mass index are associated with adolescent sagittal standing posture. International journal of Pediatric Obesity Vol.6(2-2) p.e97-106



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Latent Class Growth Mixture Models (LCGMM)• Developed by Muthen et al. and originally implemented in Mplus

software program. (Muthen B, Shedden K. Finite mixture modeling with mixture outcomes using the EM algorithm. Biometrics 1999;55:463e9.)

• Extension to Latent Class Growth Analysis (LCGA) in which individuals within a class are allowed to differ in growth trajectory.

• Twisk and Hoekstra. Classifying developmental trajectories over time should be done with great caution: a comparison between methods. Journal of Clinical Epidemiology 65 (2012). performed comparisons on both real and simulated data.

o LCGA is simpler and in many cases gives comparable trajectories.

o Large number of random effects estimated in LCGMM can lead to convergence problems.

o LCGMM tends to have an optimal solution with fewer number of classes due to allowance of variation within classes.


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Wang et al. Developmental trajectories of sleep problems from childhood to adolescence both predict and are predicted by emotional and behavioral problems. (Manuscript in preparation).

6 items from the Child Behaviour Checklist added to give continuous score of sleep problems at 5,9,10 and 14 years of ageLCGMM used to estimate two distinct trajectory classes.

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5 9 10 14

Normal Sleepers (89.4%)

Troubled Sleepers (10.6%)



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• Useful and flexible family of techniques for life‐course analysis BUT should be applied with caution

• Detecting subgroups in the sample may not be the same as detecting underlying ‘true’ population subgroups (non‐normality, sample fluctuations)

• Not always the only or best method for the research question

• Always consider level of uncertainty in class assignment and how this influences further analyses

Conclusions

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Acknowledgements

• The Raine Study participants and their families

• The Raine Study management and staff

• Core funding institutions

• NH&MRC long term funding



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Extra, unused slides

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Trajectories can be usedo To describe the life‐course of a factor

o As an exposure variable influencing a future outcome

o As an outcome

o As confounders or moderators of associations between other X‐Y measures

o Parallel processes; relating trajectories of one variable to trajectories of another



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McVeigh, Smith, Howie & Straker. Trajectories of television watching from childhood to early adulthood and their association with body composition and mental health outcomes in young adults. PlosOne. | DOI:10.1371/journal.pone.0152879 April 20, 2016.

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• Latent class analysis was used to estimate trajectories of TV watching using an ordinal logit model, which was most appropriate for the ordinal nature of the indicator variables, TV watching at 5, 8, 10, 14, 17 and 20 years.

• A series of models with 1 to 6 classes were estimated

• sex used as an active covariate.

• To avoid local rather than global latent class solutions, each model used 200 random starts and 100 iterations per set of start values.

• As there are no definitive decision criteria for the optimal number of classes, the judgement as to the optimum solution was based upon a combination of statistical criteria, parsimony and interpretability [31]. The following were considered:

i) the minimum values of the goodness of fit measures Bayes Information criteria (BIC), Akaike’sinformation criteria (AIC) and the Consistent AIC (CAIC) as indicators of the optimal number of classes,

ii) consideration of the identification of the model in terms of the proportion of random starts converging on the same solution,

iii) bootstrapped p‐value for the log‐likelihood difference between models where differences in BIC and AIC were similar,

iv) the degree to which the trajectory classes identified captured distinct and potentially meaningful patterns in the data, and

v) the quality of the model in terms of posterior probability diagnostics, namely the entropy R2 value, average posterior probability for each trajectory class, odds of correct classification and classification error.

• Participants were assigned to the trajectory class for which they had the highest posterior probability of membership.

• Subsequent analyses weighted according to probability of membership for assigned TV watching class.



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Multilevel (mixed, hierarchical, random effects) models

o Fixed effect: mean of the trajectory parameter of all individuals (starting point, rate of change etc)

o Random effects: the variance around that mean parameter (so each individual has different starting point, rate of change).

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Wei

ght(Kg)

1 2 3 4 5time

IndividualsPrediction for Individuals for Gastic Band Marginal Prediction for Individuals for Gastic Band

Slope coefficient =

Inte

rcep

t=

Yij = β0 + b0i + β1time + b1timei + eij

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Structural Equation Models

o ‘measurement’ model ‐ ‘observed’ indicator repeated measures load onto ‘latent’ unobserved trajectory parameters. These latent variables can be trajectories.

o ‘structural’ model relates variables (trajectory parameters can be related to other variables of interest)

bmi010

1 2.4

bmi020

2 4.2

bmi050

3 5.8

bmi030

4 4.8

bmi070

5 3.8

bmi060

6 8.2

bmi080

7 2.9

bmi090

8 3.3

Intercept28

26Slope

.19

.35

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.073

Documents

2017 Raine Biostatistics SIG trajectories AnneSmith 19april · 2017-08-29 · 19/05/2017 2 Click to edit Master text styles Second level Third level Fourth level ‘TrajectoryFifth