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Application of Latent Curve Models in Medical Research – A Review
beneficial to implement a neighbourhood-based walking programme
Figure 4: Multilevel Latent Curve Model for
of low to moderate intensity in order to promote QoL among senior Quality of Life in Older Adults
residents at a community level.
Mixture Latent Curve Models
QoL
baseline QoL3-month
QoL
6-month
Heterogeneity is commonly encountered in longitudinal analysis of
medical research. For heterogeneous data there exist some latent
Variance
classes under which the interested characteristics might present Variance
Mean
completely different change patterns.
Mean
Between-level
Quality-of-life Quality-of-life (neighbourhood)
(between-neighbourhood) (between-neighbourhood)
A mixture of LCMs can be used to characterise the heterogeneity and
intercept slope
to reveal specific change patterns for each distinctive latent class.
Compared with the basic LCM, the additional tasks in applying mixture
LCMs are to identify the number of latent classes, detect the
membership of each individual observation and predict the probability
of each individual falling in a specific class. To formulate the probability
of an individual belonging to the latent class, the following multinomial QoL
Within-level
baseline QoL3-month
QoL
6-month
(individual)
logistic regression model was introduced. For k=1,2 … K,
Variance
Variance
exp(a
0k
+ a
1k
x
i1
+a
2k
x
i2
+ ... + a
pk
x
ip
) Quality-of-life Quality-of-life
P(Ci = k| xi1, xi2, ... xip) =
(8) (between-neighbourhood) (between-neighbourhood)
k
intercept slope
exp(a
0j
+ a
1j
x
i1
+a
2j
x
i2
+ ... + a
pj
x
ip
)
j=1
where K is the number of latent classes, Ci is the class membership
Age Gender Ethnicity Education
Household
income
for individual i, x
i1
, x
i2
, …, x
ip
, are co-variates that may potentially
influence the chance of individual i belonging to latent class k and a
0k
, Source: Fisher and Li, 2004.
a
1k
, ... , a
pk
are corresponding regression co-efficients that reflect the
importance of potential co-variates.
Figure 5: Five-group Classification of Drug Use
Trajectories Based on Mixture Latent Curve Model
Hser et al.
10
applied this model to examine long-term trajectories of
drug use for primary heroin, cocaine and methamphetamine users.
25
The data included 629 primary heroin users, 694 cocaine users and
474 methamphetamine users. The main outcome measure was the
20
number of days using the primary drug per month.
15
As shown in Figure 5, the analysis of mixture LCMs revealed five
distinct groups with different drug use trajectories over a 10-year
Days of use
10
follow-up: consistently high use, increasing use, decreasing use,
moderate use and low use. In addition, primary drug type was 5
significantly associated with different trajectory patterns.
0
Heroin users were most likely to be in the consistently high use
12345678910
Year
group and cocaine and methamphetamine users were most likely to
Decreasing use High use Increasing use
be in the moderate use group. The study also revealed that users in
Moderate use Low use
the high use group had earlier onset of drug use and crime, longer
incarceration durations and fewer employed periods than those in
Source: Hser et al., 2008.
other groups. Compared with other existing studies of drug
addiction, the use of mixture LCMs in this analysis emphasised the presence of positive, negative and neutral events) of the patients
heterogeneity of drug use patterns and the importance of were collected for up to 35 consecutive days.
understanding and addressing the full spectrum of drug use
patterns over time. The analysis of mixture LCMs suggested a two-class model for
the MI patients: an ‘optimist’ class, with stable positive affect
Another application of mixture LCMs is the analysis of depression and declining perceived negative events, and a ‘pessimist’
in persons with myocardial infarction (MI). Elliott et al.
4
analysed class, with declining positive affect and continuing perceived
affect and event data from subjects post-MI in order to understand negative events. Depressed subjects had a 92% chance of
how mood and reactivity to negative events over time relate to belonging to the ‘pessimist’ class compared with 62% among
diagnostic-level depression. In this study, 35 patients who had non-depressed subjects. This finding uncovered some hitherto
experienced an MI within the past year and were in treatment were unobserved structure in the positive affect and negative event data
investigated. The affect scores and event indicators (indicating in this sample.
EUROPEAN NEUROLOGICAL REVIEW 55
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