. . . . . . . . Introduction . . . . hlme . . . . . . lcmm . . . . . Jointlcmm . . Conclusion LCMM: a R package for the estimation of latent class mixed models for Gaussian, ordinal, curvilinear longitudinal data and/or time-to-event data C´ ecile Proust-Lima Department of Biostatistics, INSERM U897, Bordeaux Segalen University in collaboration with Amadou Diakit´ e and Benoit Liquet Department of Biostatistics, INSERM U897, Bordeaux Segalen University Rencontres R - Bordeaux - July 2nd, 2012
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. . . . . .
. .Introduction
. . . .hlme
. . . . . .lcmm
. . . . .Jointlcmm
. .Conclusion
LCMM: a R package for the estimation oflatent class mixed models
for Gaussian, ordinal, curvilinearlongitudinal data and/or time-to-event data
Cecile Proust-LimaDepartment of Biostatistics, INSERM U897, Bordeaux Segalen University
in collaboration withAmadou Diakite and Benoit Liquet
Department of Biostatistics, INSERM U897, Bordeaux Segalen University
Rencontres R - Bordeaux - July 2nd, 2012
. . . . . .
. .Introduction
. . . .hlme
. . . . . .lcmm
. . . . .Jointlcmm
. .Conclusion
Context
Linear mixed model (LMM) routinely used in longitudinal studies todescribe change over time of longitudinal outcomes according tocovariates
Assumptions :
(i) continuous longitudinal outcome
(ii) Gaussian random-effects and errors
(iii) linearity of the relationships with the outcome
(iv) homogeneous population
(v) missing at random data
Widely implemented : lme, lmer in R ; proc mixed in SAS
. . . . . .
. .Introduction
. . . .hlme
. . . . . .lcmm
. . . . .Jointlcmm
. .Conclusion
Objective of lcmm
To provide a package that extends the linear mixed model estimation to :
- heterogeneous populations (relax (iv))
→ hlme for latent class linear mixed models (i.e. Gaussian continuous
outcome)
- other types of longitudinal outcomes : ordinal, (bounded)quantitative non-Gaussian outcomes (relax (i), (ii), (iii), (iv))
→ lcmm for general latent class mixed models with outcomes ofdifferent nature
- joint analysis of a time-to-event (relax (iv), (v))
→ Jointlcmm for joint latent class models with a longitudinaloutcome and a right-censored (left-truncated) time-to-event
. . . . . .
. .Introduction
. . . .hlme
. . . . . .lcmm
. . . . .Jointlcmm
. .Conclusion
Heterogeneous profiles of trajectory
Ex : Trajectories of verbal fluency in the elderly
0
5
10
15
20
25
30
35
40
0 2 4 6 8 10 12 14
Isaa
cs S
et T
est
time since entry in the cohort
. . . . . .
. .Introduction
. . . .hlme
. . . . . .lcmm
. . . . .Jointlcmm
. .Conclusion
Heterogeneous profiles of trajectory
Ex : Trajectories of verbal fluency in the elderly
0
5
10
15
20
25
30
35
40
0 2 4 6 8 10 12 14
Isaa
cs S
et T
est
time since entry in the cohort
. . . . . .
. .Introduction
. . . .hlme
. . . . . .lcmm
. . . . .Jointlcmm
. .Conclusion
Latent class linear mixed model : the model
N subjects (i, i = 1, ..., N) & G latent classes (g, g = 1, ..., G)
Discrete latent variable ci for the latent group structure :ci = g if subject i belongs to class g
πig = P (ci = g|X1i) =eξ0g+X1i
′ξ1g∑Gl=1 e
ξ0l+X1i′ξ1l
Repeated measures of the longitudinal marker Yij (j = 1, ..., ni) :
Yij |ci=g = Z ′ijuig +X ′
2ijβ +X ′3ijγg + ϵij
Zij , X2ij , X3ij : 3 different vectors of covariates without overlapuig ∼ N
(µg, ω
2gB
)& ϵij ∼ N
(0, σ2
)
. . . . . .
. .Introduction
. . . .hlme
. . . . . .lcmm
. . . . .Jointlcmm
. .Conclusion
Latent class linear mixed model : the implementation
hlme(fixed= Y ∼ Time+X1+Time:X1, random=∼ Time,
subject=’ID’, mixture=∼ Time, classmb=∼ X2+X3, ng=2,
data=data hlme, B=Binit)
Program details :
- Program written in Fortran90 and interfaced in R
- Marquardt algorithm for a fixed number of latent classes (strict
→ similar technique and output with covariate effects and/or latent classes
. . . . . .
. .Introduction
. . . .hlme
. . . . . .lcmm
. . . . .Jointlcmm
. .Conclusion
Predictions in the MMSE scale
65 70 75 80 85 90 95
1520
2530
MM
SE
65 70 75 80 85 90 95
1520
2530
MM
SE
65 70 75 80 85 90 95
1520
2530
MM
SE
65 70 75 80 85 90 95
1520
2530
MM
SE
65 70 75 80 85 90 95
1520
2530
MM
SE
65 70 75 80 85 90 95
1520
2530
MM
SE
thresholds
thresholds95%CIlinear95%CI
using predictY function with Bayesian approximation of the predictions
distribution
→ similar technique and output with covariate effects and/or latent classes
. . . . . .
. .Introduction
. . . .hlme
. . . . . .lcmm
. . . . .Jointlcmm
. .Conclusion
Heterogeneous profiles of trajectory in link with a clinicalevent
Ex : PSA trajectories after radiation therapy in Prostate Cancer
-1
-0.5
0
0.5
1
1.5
2
2.5
3
0 1 2 3 4 5 6 7 8 9
log(
PS
A+
0.1)
time since end of RT
no recurrence of Prostate cancer vs. recurrence of Prostate cancer
. . . . . .
. .Introduction
. . . .hlme
. . . . . .lcmm
. . . . .Jointlcmm
. .Conclusion
Joint latent class model : the principle
Latentclass
C
ObservedLatent
Longitudinal
Y marker
Subject i (i=1...,N)Class g (g=1,...,G)Occasion j (j=1...,ni)
Event T*
- Latent classes of subjects :
→ latent class membership :
πig = P (ci = g|X1i) =eξ0g+X1i
T ξ1g∑Gl=1 e
ξ0l+X1iT ξ1l
- Given class g,
→ specific marker evolution(mixed model)
→ specific risk of event(prop. hazard model)
. . . . . .
. .Introduction
. . . .hlme
. . . . . .lcmm
. . . . .Jointlcmm
. .Conclusion
Joint latent class model : the implementation
Jointlcmm(Y ∼ Time+X1+X1:time, random=∼ Time,
subject=’ID’, mixture=∼ Time, classmb=∼ X2+X3, ng=2,
survival=Surv(Tevt,Event) ∼ X1 + mixture(X4),
hazard=’Weibull-Specific’)
Program details :
- Same methodology as hlme and lcmm
- PHM with different possible hazards families (splines, piecewise, weibull) andspecification (common, specific, proportional over classes) + delayed entry
- Class-specific & class-common effects in the 3 submodels
- Information criteria + score test for conditional independence
- Predictive accuracy measures
. . . . . .
. .Introduction
. . . .hlme
. . . . . .lcmm
. . . . .Jointlcmm
. .Conclusion
Predicted trajectories & survival functions from JLCM(Proust-Lima, 2012)