Investigating differential changes using Mixture Latent Change Scores

Investigating differential changes
using Mixture Latent Change
Scores (MLCS) modeling
SESSION 2.5: Advanced Longitudinal Modeling Techniques
Emil Coman1, Judith Fifield1, Jack McArdle2, Monique Davis-Smith3
1Ethel
Donahue TRIPP Center, U. of Connecticut Health Center, 2 University of Southern California, 3 Medical Center of Central Georgia
The 1st author thanks David Kenny for introducing him to the causal modeling
world through the path analysis backdoor, for his constant mentoring and extensive
generous discussions and advice, and to SEMNET mentors who so generously
shared their time and expertise and taught Latent Variable modeling to many
students of applied statistics across the globe for many years.
Modern Modeling Methods Conference, Storrs, CT, May 20-21, 2014
Origin of structural models – Sewall Wright
“Accounting for correlations” using the Method of Path Coefficients
"Senior Animal Husbandman in Animal Genetics, Bureau of Animal
Industry, United States Department of Agriculture“
Wright, S. (1921). Correlation and causation. Part I Method of path coefficients. Journal of agricultural research, 20(7), 557-585. [CITED BY 2119, GOOGLE.SCOLAR.COM ]
MMM 2014 LCS Mixture
2
Some works on analyzing changes I should have read
Kenny, D. A. (1975). A quasi-experimental approach to assessing treatment effects in the nonequivalent control group design. Psychological Bulletin, 82(3), 345.
CITED BY 206, GOOGLE.SCOLAR.COM ]
MMM 2014 LCS Mixture
3
Some works on analyzing changes I should have read
Kenny, D. A., & Cohen, S. H. (1980). A reexamination of selection and growth processes in the nonequivalent control group design. Sociological methodology, 290-313.
CITED BY 15, GOOGLE.SCOLAR.COM ]
MMM 2014 LCS Mixture
4
Comparative Effectiveness of Treatments
Main old issue: how to best compare changes.
TX
Comparative
Effectiveness
Outcome
The common questions in CE are:
1. Are the 2 treatments benefiting patients
equally?
2. Is one much better than the other?
- statistically vs. clinically vs. patient-wise
MMM 2014 LCS Mixture
5
Models of change
MMM 2014 LCS Mixture
6
AR1 model
σ2Y1= est.
Y1
αY2 = est.
Y2
β
µY1 = est.
αe @ 0
error
σ2e= est.
Notes: All un-labeled regression coefficients are equal to 1 (unity).
MMM 2014 LCS Mixture
7
Models of change
MMM 2014 LCS Mixture
8
LCS: model
MMM 2014 LCS Mixture
9
LCS: Latent Change Score model
σ2e= 0
Set=1
FG1
FG2
Set=1
Change depends
Set=1
on initial state
1-to-2 FG Latent
Change
Inter-individual differences in intra-individual changes can
depend on prior state, but also on other factors, like a
constant change cumulative effect, similar to LGM slope.
Notes: All un-labeled regression coefficients are equal to 1 (unity).
MMM 2014 LCS Mixture
10
LCS: Latent Change Score model
αe@0 e
Y2
σ2Y1= est.
αY2@0
Y2
Y1
µY1 = est.
σ2e@0
γ = β-1
LCS(1->2)
αLCS = est.
σ2LCS= est.
Notes: All un-labeled regression coefficients are equal to 1 (unity). URL for a brief visual history.
MMM 2014 LCS Mixture
11
LGM: Latent Growth Model
Intercept
Y1
Y2
Y3
@0
@1
@2
Slope
Notes: All un-labeled regression coefficients are equal to 1 (unity).
MMM 2014 LCS Mixture
12
LCS: Latent Change Score model
Y1
Y3
Y2
est.
LCS21
est.
LCS32
Notes: All un-labeled regression coefficients are equal to 1 (unity).
MMM 2014 LCS Mixture
13
LCS model replicating LGM
0,0
Initial
*,*
level
0,0
0,0
@0
@0
Y1
0,=
@0
*
Y3
Y2
0,=
@0
@0
LCS21
Constant
Change
LCS32
*,*
Notes: All un-labeled regression coefficients are equal to 1 (unity); 1st digit is mean, second
variance, if alone, covariance; hexagons are intercepts.
MMM 2014 LCS Mixture
14
Mixture modeling
(MM) – Jeff Harring
MM is old. Karl Pearson
showed in 1894 that if data
are the result of a mixture
of probability distributions
(like two normal
distributions with different
means and variances), the
resulting distribution will
appear as one asymmetric
and bimodal, when in fact it
represents two homogenous
normal distributions, or two
subpopulations.
Harring, J. R. (December 4, 5 & 6, 2013). Introduction to Finite Mixture Models. Details: http://www.cilvr.umd.edu/Workshops/CILVRworkshoppageFMM2013.html College Park,
Maryland.
Pearson, K. (1894). Contributions to the mathematical theory of evolution. Philosophical Transactions of the Royal Society of London. A, 185, 71-110.
MMM 2014 LCS Mixture
15
Mixture modeling (MM) – Jeff Harring
The general mixture specification assumes a composite (mixed)
distribution as the sum of K classes pdf’s (probability density
functions) distributions, each with class-specific parameters θk, and
weights or mixing proportions φi, which specify in fact the class
proportions.
The likelihood for one patient’s observations is then obtained as the
probability of his/her data as a function of the parameters, and then a
global likelihood function L is calculated as the product of individual
patients’ likelihoods.
Using Maximum Likelihood (ML) or Bayesian estimation, one can then
obtain the parameter values that maximize the loglikelihood L.
MM software use in practice is an Expectation-Maximization (EM)
algorithm, which acts as an optimizer (not estimator) by generating
starting values for the parameters θk and then, given posterior
probabilities for φik, obtains new estimates for φik and θk, and
continues in such steps until the change in the likelihood from
successive iterations is sufficiently small. (Harring, 2013).
Harring, J. R. (December 4, 5 & 6, 2013). Introduction to Finite Mixture Models. Details: http://www.cilvr.umd.edu/Workshops/CILVRworkshoppageFMM2013.html. College Park,
Maryland.
MMM 2014 LCS Mixture
16
Study background
• A church and faith-based diabetes prevention
intervention among African Americans and Blacks
(AA&B), that implemented two versions of the
DPP (Diabetes Prevention Program).
• CBDPT-2 is a two-site (Macon GA and Hartford
CT), church-randomized, controlled trial of N=570
prediabetics recruited from 42 African American
and Black churches.
• The preliminary CBDPT-2 data to date contains
repeated measures collected over 4 waves, on FG
and BMI, as well as data on physical activity,
religious orientation, readiness to change, and
the EQ-5D health status index
Diabetes Prevention Program Research, G., 10-year follow-up of diabetes incidence and weight loss in the Diabetes Prevention Program Outcomes Study. The Lancet, 2009. 374(9702): p. 16771686.
Boltri, J.M., et al., Diabetes prevention in a faith-based setting: results of translational research. Journal of Public Health Management and Practice, 2008. 14(1): p. 29-32.
MMM 2014 LCS Mixture
17
Sample GMM syntax Mplus
GMM :
CLASSES = whohow (3);
ANALYSIS: TYPE = MIXTURE;
MODEL:
%OVERALL% i s | FG_B@0 FG_6@1 FG_12@2 FG_24@4;
%whohow#2%
i ; s ;
i with s; !can add also s on interv ;
MMM 2014 LCS Mixture
18
Sample LCS syntax Mplus
MODEL: !LCS model
LFG1 by FG_B; LFG2 by FG_6 ; !setup true scores with placeholder
LFG3 by FG_12 ; LFG4 by FG_12@0 ;!
LFG5 by FG_24 ;
FG_B-FG_24 (MeasErr); ! equal measurement errors
LFG2 on LFG1@1; LFG3 on LFG2@1;
LFG4 on LFG3@1; LFG5 on LFG4@1;
dLX21 by LFG2@1; dLX32 by LFG3@1; !define LCS by the 2nd variable
dLX43 by LFG4@1; dLX54 by LFG5@1;
[LFG1-LFG5@0 ] ; !intercepts of latents set = 0
[dLX21-dLX54@0 ]; ! residual LCSs set =0
LFG1-LFG5@0; ! residual latents set =0
initial BY LFG1@1; !initial level linked to 1st latent only
ctchange BY dLX21-dLX54@1; !constant change pointing to all LCS
[initial] (MInit); [ctchange](AvCtCh); initial (VInit);
ctchange (VCtCh) ;initial WITH ctchange (CvInCtCh);
dLX21 on LFG1 (DLXonX); ! proportional changes
dLX32 on LFG2 (DLXonX);
dLX43 on LFG3 (DLXonX);
dLX54 on LFG4 (DLXonX);
DLX32
WITH DLX21 @0; !Unwated correlations
DLX43
WITH DLX21 @0; etc.
MMM 2014 LCS Mixture
19
LCS benefits
LCS models are better equipped to explore dynamic inter-connected
processes of mutual changes, e.g.:
ILC0
LIX
LIY
γYX
βX
ΔLILC10
ILC1
γYX
βX
ILC2
ΔLILC21
ξYX
ξXY
γXY
ΔLIUS10
γXY
βY
βY
IUS0
ΔLIUS21
IUS1
IUS2
Notes: X=ILC, Y=IUS; only three waves are shown for simplicity; parameters represent: β - the
proportional growth (dotted arrows); γ – coupling (interrupted double lines); ξ - changes-to-changes
(double line arrows); the constant change slope factors feed into all their respective repeated measures
(not shown for clarity); all unlabeled paths are set to unity.
Coman, E., Lin, C. A., Suggs, L. S., Iordache, E., McArdle, J. J., & Barbour, R. Altering dynamic pathways to reduce substance use among youth: changes achieved by dynamic coupling. Addiction
Research & Theory. doi: 10.3109/16066359.2014.892932
20
MMM 2014 LCS Mixture
GMM vs. LCSM 3 class solutions
GMM
LCSM
c1LCSM c2LCSM c3LCSM
c1GMM 482
390
66
26
c2GMM
35
22
10
3
c3GMM
3
0
412
1
77
2
31
520
The 520 patients were classified like
 GMM classes (left gray shaded column)
482c1GMM, 35c2GMM, and 3c3GMM .
 LCSM finds 3 classes of patients (bottom green row)
412c1LCSM, 77c2LCSM and 31c3LCSM
MMM 2014 LCS Mixture
21
GMM brief results
Comparative Effectiveness of M (More) vs. L (Less)
DPP in Fasting Glucose changes for 2 classes - GMM
Lc1 GMM3
Mc1 GMM3
Lc2 GMM3
Mc2 GMM3
Single lines - Less DPP, double lines More DPP;
interrupted lines Class 1 GMM, continuous lines
Class 2 GMM means .
Mc2 vs. Lc2
100.0
Mc1 vs. Lc1
Note: the third class had no cases with all four wave FC valid values.
70.0
Mc1 vs. Lc1: p = .048 (favors L; linear time-by-condition interaction effect)
Mc2 vs. Lc2: p = .128, Quadratic p=.095.
MMM 2014 LCS Mixture
22
LCSM brief results
Comparative Effectiveness of M (More) vs. L (Less) DPP
in Fasting Glucose changes for 3 classes - LCSM
Mc1 vs. Lc1
Mc2 vs. Lc2
Lc1 LCSM3
Lc2 LCSM3
Lc3 LCSM3
Mc1 LCSM3
Mc2 LCSM3
Mc3 LCSM3
100.0
70.0
Mc3 vs. Lc3
Single lines - Less DPP, double lines More DPP (larger marker);
similar patterns: means of LCSM classes 1 , 2 and 3 .
Mc1 vs. Lc1: p = .900; Mc2 vs. Lc2: p = .033 (favors L; Quadratic time-bycondition p=.002); Mc3 vs. Lc3: p = .969 (Quadratic p = .013; Cubic p = .025).
MMM 2014 LCS Mixture
23
LCS Mixture modeling
1. The Latent Change Score Mixture (LCSM) modeling promises more
nuance and fine-tuning of classes of patients who are bound to
develop differently, but following similar complex dynamic
patterns of change. LCS mixture models allow for endless
extensions and opportunities.
2. Practitioners and researchers can use early change information
to predict class membership, and hence re-assign patients to
more beneficial treatments.
3. The meaningfulness of classes needs explorations; reasons for
adherence may be a factor.
1. Unique combinations of known moderators of effects are likely
predicting classes.
2. Patient input in assigning meaning is key.
MMM 2014 LCS Mixture
24
DONE!
Thanks
[email protected]
MMM 2014 LCS Mixture
25

Download Report