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© 2010 BY THE JOURNAL OF DRUG ISSUES
JOURNAL OF DRUG ISSUES 0022-0426/10/04 755–782
__________
Jeffrey T. Ward is an Assistant Professor in the Department of Criminal Justice at the University of
Texas at San Antonio and a Harry Frank Guggenheim Dissertation Fellow. His research interests include
quantitative methodology, sanction effects, violence & gangs, developmental & life-course criminology,
and space, place, and crime. John Stogner is an Alumni Fellow at the University of Florida and an
Assistant Professor in the Political Science Department at Georgia Southern University. His research
interests include the relationship between health and delinquency, drug use and drug policy, general
strain theory, biosocial theories, and quantitative methodology. Chris L. Gibson is an Assistant
Professor in the Department of Sociology and Criminology & Law at the University of Florida and a
W.E.B. Du Bois Fellow for the National Institute of Justice. Using mainly applied quantitative methods,
his research centers on neighborhoods and quality of life, biosocial and life-course criminology, and
violence and victimization. Dr. Ronald L. Akers is a Professor of Criminology and Sociology at the
University of Florida. He has conducted extensive research and published widely on criminological
theory, alcohol and drug behavior, sociology of law, juvenile delinquency, crime, corrections, and
deviant behavior. He is recipient of the Edwin H. Sutherland Award and a Fellow of the American
Society of Criminology. He has been inducted onto the Roll of Honor of the Southern Sociological
Society, and an endowed Professorship in Criminology and Deviance has been established in his name
in the Department of Sociology at the University of Kentucky.
A NEW TRICK FOR AN OLD DOG: APPLYING
DEVELOPMENTAL TRAJECTORIES TO INFORM DRUG
USE PROGRESSION
JEFFREY T. WARD, JOHN STOGNER, CHRIS L. GIBSON, RONALD L. AKERS
The frequent criticisms of the “gateway hypothesis” have led scholars to note
the importance of considering the role of intra-individual change for drug
use progression. While studies employing drug use trajectories have added
considerably to our understanding of drug use comorbidity, the extent to which
trajectories inform drug use progression remains largely unknown despite the fact
that there are several theoretical reasons to suspect that intra-individual change
is important to the gateway phenomenon. The current study employs latent class
growth models using a sample from the Boys Town study of adolescent drug and
drinking behavior. The results demonstrate that knowing how gateway drug use
changes over time provides important information above and beyond knowing
frequency of gateway use for predicting harder drug use trajectories. Implications
of the empirical fi ndings and directions for future research are discussed.
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INTRODUCTION
One of the most contentious debates in the fi eld of drug use and abuse is whether
the use of one substance precedes and functions as a “gateway” to use of another
harder drug. The gateway hypothesis posits that the typical sequence of substance use
begins with alcohol or tobacco, moves into use of marijuana, and ends with harder
drug use such as cocaine and heroin (Kandel, 1975; 2002; Kandel & Yamaguchi,
1999, Peele & Brodsky, 1997). While the gateway sequence has been supported
across a variety of domestic and international samples (Kandel, Yamaguchi, &
Chen, 1992), it remains controversial for various reasons (Golub & Johnson, 1998).
First, some researchers have challenged the order of the gateway sequence
(Kandel, 2002), pointing out that not every individual who engages in drug use
follows the same sequencing pattern (Andrews, Hops, Ary, Lichtenstein, & Tildesley,
1991; Blaze-Temple, & Lo, 1992). For instance, not only can entire stages of drug
use be skipped (Golub & Johnson, 1994) but drug use can often occur in the opposite
direction of the expected gateway sequence (Blaze-Temple & Lo, 1992; Golub &
Johnson, 1994; Mackesy-Amiti, Fendrich, & Goldstein, 1997; Young et al., 1995).
Second, determining which substances should be categorized as gateway drugs is
problematic and is frequently disputed (Kandel, 2002). Though many consider licit
substances to be gateway drugs (Kandel et al., 1992; Kandel, 2002), marijuana is
also frequently labeled a gateway drug to use of heroin, barbiturates, or other harder
drugs (DeSimone, 1998; Golub & Johnson, 1994). Inconsistencies surrounding the
sequencing of drug use have led some to question the focus of drug use progression
research; for instance, Kandel (2002) asks “should one not refer to ‘gateway use’
of a drug rather than to a ‘gateway drug’?” (p. 8). This shifts the emphasis of drug
use progression research from strict sequencing to use patterns of a substance,
drawing specifi c attention to the ramifi cations gateway use trajectories have for use
trajectories of subsequent substances.
Despite the large number of dimensions that are employed to describe use of a
drug (e.g., see Wohlwill, 1973), sequencing, age of onset, and frequency of use have
received most of the empirical attention in drug use progression research (Fergusson
& Horwood, 2000; Labouvie & White, 2002). Initiation of alcohol use at an early
age has been linked to a number of problems later in adolescence, including use
of illicit drugs (Grant & Dawson, 1997; Pederson & Skrondal, 1998; Robins &
Pryzbeck, 1985). Studies have found that frequency of use of gateway substances has
a signifi cant effect on harder drug use (Duncan, Duncan, & Hops, 1998; Fergusson
& Horwood, 2000; Fergusson, Horwood, & Swain-Campbell, 2002). While this
research is informative, it is based primarily on inter-individual variations, and
knowledge about drug use progression can be improved by incorporating intra-
individual change in use over time (Labouvie & White, 2002).
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Recent research has begun to recognize the importance of examining intra-
individual change in drug use over time, but has largely been limited to describing
trajectories of a single drug (e.g., see Windle & Wiesner, 2004). The few studies
examining trajectories of multiple substances have focused on comorbidity of drug
use (i.e., how use trajectories of two drugs unfold contemporaneously) (e.g., see
Flory, Lynam, Milich, Leukefeld, & Clayton, 2004; Jackson, Sher, & Schulenberg,
2008). Respectively, these approaches neglect to account for the relationship between
drug use trajectories and completely omit drug use sequencing.
The current study estimates group-based trajectories of alcohol and marijuana
use over two different three year periods to determine the extent to which intra-
individual change in alcohol use aids in predicting intra-individual change in
subsequent marijuana use. Exploring the heterotypic continuity of drug use within a
trajectory framework (see Nagin, 2005) results in the ability to determine which types
of gateway use patterns of alcohol over time are most strongly linked to the most
problematic, subsequent marijuana trajectories. This application of a relatively new
statistical technique to an old and lingering problem represents a key advancement
in gateway research and a modifi cation of the standard gateway perspective.
ADVANTAGES OF UTILIZING TRAJECTORIES FOR DRUG USE PROGRESSION
Early studies examining the gateway drug hypothesis failed to account for
the rates of change in gateway drug use and instead focused largely on drug use
prevalence and temporal ordering (Andrews et al., 1991; Kandel et al., 1992).
For example, studies examining marijuana use employed cross-sectional or two-
wave longitudinal research designs (von Sydow, Lieb, Pfi ster, Hofl er, & Wittchen,
2002) that were unable to model rates of change. While these empirical studies
helped establish the typical sequence of drug use, they stopped short of more fully
explaining how substance use unfolds over time and what the implications may be
for the relationship between substance use trajectories. Recent advances in statistical
modeling procedures (i.e., latent class growth analysis) (see Nagin, 2005) have led
to a number of studies that have begun to examine drug use behavior over time.
Nevertheless, trajectory analysis has not yet been employed to examine drug use
progression, although there are reasons, which we develop more fully below, to
believe doing so may further our understanding of the heterotypic continuity of
drug use.
Studies employing trajectory analysis have examined trajectories of alcohol use
(Chassin, Pitts, & Prost, 2002; Colder, Campbell, Ruel, Richardson, & Flay, 2002;
Hill, White, Chung, Hawkins, & Catalano, 2000; Jackson & Sher, 2005; Oesterle
et al., 2004; Schulenberg, O’Malley, Bachman, Wadsworth, & Johnston, 1996;
Schulenberg, Wadsworth, O’Malley, Bachman, & Johnston, 1996; Tucker, Orlando,
& Ellickson, 2003; Windle, Mun, & Windle, 2005), tobacco use (Abroms, Simons-
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Morton, Haynie, & Chen, 2005; Chassin, Presson, Pitts, & Sherman, 2000; Colder et
al., 2001; Orlando, Tucker, Ellickson, & Klein, 2005; Soldz & Cui, 2002; Stanton,
Flay, Colder, & Mehta, 2004; Tucker, Ellickson, Orlando, & Klein, 2006; White,
Pandina, & Chen, 2002; Wills, Resko, Ainette, & Mendoza, 2004), or marijuana
use (Brown, Flory, Lynam, Leukefeld, & Clayton, 2004; Ellickson, Martino, &
Collins, 2004; Kandel & Chen, 2000; Schulenberg et al., 2005; Windle & Wiesner,
2004), independent from trajectories of other substances. These studies are important
because they help to explain trajectories of a single substance but they neglect the
possibility that different drug use trajectories can infl uence one another.
More recent work has examined the comorbidity of drug use behaviors including:
alcohol and tobacco use (Jackson, Sher, & Schulenberg, 2005), alcohol and
marijuana use (Flory et al., 2004; Patton et al., 2007), alcohol with both marijuana
and gambling (Wanner, Vitaro, Ladouceur, Brendgen, & Tremblay, 2006), and
alcohol with tobacco and marijuana (Hawkins, Hill, Guo, & Battin-Pearson, 2002;
Jackson et al., 2008). Importantly, these studies have furthered knowledge about
how use of two or more substances unfolds contemporaneously. Hence, we now
know that some substance use trajectories are associated with one another. We also
know, despite the inconsistencies, that there is a typical sequence of drug use that
holds in a variety of contexts (Kandel et al., 1992). However, research examining
the comorbidity of drug use has neglected the issue of sequencing, which is the
cornerstone of the gateway hypothesis and a generally relevant component for drug
use progression research. Therefore, this body of research is unable to use one’s
developmental history with a gateway substance to aid in the prediction of use
patterns of a subsequent and often harder substance.
Unlike studies examining comorbidity of drug use trajectories, trajectory analysis
examining the heterotypic continuity of drug use explicitly takes into account
drug use sequencing as well as the associations between trajectories of drug use.
Examining trajectories separated in time allows for a greater understanding of how
use trajectories of one substance may infl uence use trajectories of a subsequent
substance.
1
While the current study has the potential to extend the exploration of the
gateway hypothesis, its practical utility lies in improving our ability to identify those
at risk for transitioning to problematic marijuana trajectories given their membership
in a specifi c alcohol use trajectory. While our data do not allow us to explicitly test
hypotheses concerning factors driving the potential relationship between drug use
trajectories, we now offer several theoretical reasons why we may expect trajectories
of substance use to be related in a heterotypic continuity fashion.
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FACTORS ASSOCIATED WITH CHANGING TRAJECTORIES OF DRUG USE
An individual’s gateway substance use trajectory will follow one of two distinct
forms: either an individual will be somewhat stable or will undergo noticeable change
over time in his or her substance use. Individuals in these groups are in many ways
fundamentally different from one another and these differences may be important
above and beyond the importance of age of onset or frequency of substance use. An
individual that is stable is consistent in their substance use despite maturation and
other life events. While some stable users ingest heavily, these individuals maintain
their respective use at a consistent level with no indication that use will increase.
Those with changing trajectories, whether increasing, decreasing, or oscillating, are
by defi nition altering their substance use over time.
2
While all adolescent drug use
is problematic, those who are on an increasing trajectory of a gateway substance,
even if their initial level of use is low, should be a major concern as the factors
that infl uence them to be on an increasing trajectory may also make them more
susceptible to experiencing an increasing trajectory of other substances later in life.
Numerous explanations have been proposed for the drug sequencing patterns
associated with gateway theories (see Choo, Roh, & Robinson, 2008) and some
may also be helpful in the explanations of patterns of drug use and the effect of one
trajectory on another. These rationales have been divided into the pharmacological,
socio-cultural, and predisposition schools (for a review, see Goode, 2008). The
pharmacological school attempts to attribute the gateway phenomenon to the
properties of gateway drugs themselves by arguing that the drugs’ intrinsic effects
and the development of tolerance lead individuals to experiment with and become
dependent upon harder drugs (Jones & Jones, 1977; Nahas, 1990). Consistent with
notions of social learning theory (Akers, 1973; Burgess & Akers, 1966), the socio-
cultural school holds that one’s activities and peers are what lead one to transition
from gateway drugs to harder drugs. The predisposition school directly contradicts
the claims of the other and maintains that the observed gateway phenomenon is
spurious; the association results from differential propensities toward drug use. The
availability, ease of acquiring, and cost of different drugs are key to this argument
as those with a personality that predisposes them to use are likely to fi rst use those
drugs most easily available to them (Levinthal, 2008; Tarter, Vanyukov, Kirisci,
Reyonlds, & Clark, 2006).
One reason that some individuals are on increasing trajectories of gateway
substance use while others are stable may be linked to euphoria seeking and the
development of tolerance. This reasoning, characteristic of the pharmacological
school, suggests that increasing use indicates decreased satisfaction with a drug,
which may eventually necessitate the progression to use of drugs with stronger
psychoactive effects. Alcohol use provides an excellent example. Those who drink
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alcohol develop a tolerance which requires them to intake higher quantities of the
substance to experience many of those effects which the user perceives as positive.
The development of tolerance is, however, extremely variable (Fleming, Mihic, &
Harris, 2006). Those with more rapidly increasing tolerances may fi nd it increasingly
diffi cult to afford to consistently reach a state of intoxication. In contrast, those who
use relatively consistent amounts of alcohol over time are likely to be more satisfi ed
with their drug use. A trajectory may therefore indicate something important about
individual differences in tolerance processes. Progressing to another substance
may ultimately result if high quantities of the gateway substance do not result in
the desired effects. Since marijuana users may also develop a tolerance to some of
its effects (Abood & Martin, 1992), it is possible that this tolerance process will
manifest itself similarly in subsequent, harder drugs. This suggests the importance
of examining linkages among gateway trajectories of alcohol use and trajectories
of subsequent marijuana use.
A second potential reason that increasing use of a gateway substance is expected
to have an infl uence on harder drug use is that gateway trajectories may be the result
of underlying shifts in peer affi liations. This socio-cultural approach offers a plausible
explanation as to why individuals change their use of one drug. According to social
learning theory, individuals learn defi nitions favorable to and the mechanics of
deviant acts from those with whom they associate (Burgess & Akers, 1966). Stable
use patterns over time, whether heavy, light, or none, could possibly refl ect more
stable peer networks, whereas accelerating use patterns over time may potentially
refl ect important changes in peer networks. More specifi cally, those varying their
use are likely to be moving into new networks or within a network that is changing.
Therefore, it is possible that many of those on an increasing alcohol trajectory are
associating with more deviant peers over time and their evolving associations, if
they continue following the same pattern, will expose them to new substances.
Peer networks have been shown to have a major infl uence on a youth’s level of
deviance (Haynie, 2002), so it logically follows that those whose use and networks
are changing are especially at an increased risk of progressing to heavier drugs.
We have outlined two reasons why associations between alcohol and marijuana
use trajectories may be important, but a fi rst-order question is whether the association
between trajectories exists in the fi rst place. Without evidence suggesting that drug
use progression research can indeed be enhanced by examining intra-individual
change in substance use over time, it is premature to test the underlying theoretical
mechanisms. In other words, there is reason to suspect that drug use trajectories
should be linked in a heterotypic continuous fashion but there is no evidence to
suggest that this is indeed the case. This current study on drug use progression
seeks to fi ll a gap in the literature by applying trajectory analysis to determine how
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group membership in a given alcohol use trajectory predicts group membership in
a subsequent marijuana use trajectory.
DATA AND METHODOLOGY
DATA AND SAMPLE
To begin to explore the relevance of gateway substance use patterns for drug use
progression within a latent class growth analysis framework, this study employs
data from the Boys Town study on adolescent drug use (see Akers, Krohn, Lanza-
Kaduce, & Radosevich, 1979). More specifi cally, largely unexplored retrospective
survey questions about drug use behavior are used to construct alcohol and marijuana
trajectory groups. Retrospective data has been used in prior drug use research
and can be a cost-effective data collection method (see Freedman et al., 1988).
Moreover, retrospective behavioral self-report data can be a valid and reliable source
of information, even for heavy users of narcotics (Anglin, Hser, & Chou, 1993).
The original sample comprised of 3,065 male and female students from 22 schools
in seven Midwestern communities was reduced for the present analysis following
the procedures outlined below. First, individuals had to be in either grade 11 or 12
at the time of the survey. This procedure ensured enough time points to estimate
both alcohol and marijuana use trajectories while keeping the sample size as large as
possible. There were 1,175 students in grades 11 and 12. Second, individuals had to
have valid data for use of alcohol in grades 7 through 9, use of marijuana in grades
9 through 11, and key demographic factors such as age, race, and gender. Missing
data was not a serious problem as only 5% of the sample was excluded. Specifi cally,
there were 1,116 individuals in grades 11 and 12 with valid data. Finally, since we
are interested in assessing the relevance of change in drug use over time for drug
use progression, we follow the lead of Duncan and colleagues (1998) and exclude
individuals that had used marijuana prior to the measurement period of interest
(i.e., those that used prior to grade 9). This is a necessary procedure imposed on the
data to enable the study of drug use progression with developmental trajectories.
3
The fi nal sample size for the current trajectory analysis is N=915. Importantly, key
characteristics of the fi nal analysis sample closely resembled those of the original
sample.
For instance, approximately, 58% of the analysis sample (56% of the original
sample) is female and about 4% of the analysis sample (4% of the original sample)
is non-white.
MEASURES
Respondents were asked to report both their alcohol and marijuana use in prior
grades using Likert-type scale with response options that included: 0=None; 1=A
Little; 2=Some; 3=A Lot. Alcohol use trajectories are estimated for grades 7 through
9, whereas marijuana use trajectories are estimated for grades 9 through 11. Thus,
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for each of the two trajectory models there are three time points which specify
the frequency of drug use during a particular grade. Consistent with the typical
sequence in drug use progression research (Kandel, 2002; Kandel & Yamaguchi,
1999), alcohol use trajectory group membership is being used to predict marijuana
use trajectory group membership.
MODEL ESTIMATION PROCEDURES
While an extensive review of model estimation procedures for group-based
trajectories can be found elsewhere (see Nagin, 2005), a brief discussion of model
estimation procedures seems warranted. Mplus v3.1 (Muthén & Muthén, 1998–2004)
was employed to estimate the latent class growth analysis (LCGA) and can easily
handle categorical variables such as those utilized in this study. With the LCGA
model for ordered categorical data specifi ed, the establishment of the correct number
and functional form of the trajectory groups is of primary concern. Given there
are only three time points to estimate the alcohol and marijuana trajectory groups,
directional changes in use cannot be modeled and, as a result, the appropriate
functional form is linear.
The appropriate number of groups is chosen based on the Bayesian Information
Criteria (BIC), which is a statistic that can be used to determine the number of groups
in both nested and unnested models (D’Unger, Land, McCall, & Nagin, 1998; Nagin,
1999). BIC scores are calculated with the following equation:
BIC = log (L) + log (n) * k.
L denotes the maximum likelihood, n denotes the sample size, and k denotes
the number of parameters. BIC scores favor parsimonious models by exacting a
penalty for adding parameters (Jones, Nagin, & Roeder, 2001; Nagin, 2005). Mplus
BIC scores have positive values and the choice of the best model is given by the
smallest BIC score.
4
Supplementing BIC criteria for model selections are Entropy
and the Vuong-Lo-Mendell-Rubin likelihood ratio tests. Entropy values closer to 1
indicate better separation of latent classes or trajectory groups (Celeux & Soromenho,
1996). The Vuong-Lo-Mendell-Rubin LRT compares k versus k-1 classes, where
a non-signifi cant p-value associated with the LRT test is evidence in favor of the
more parsimonious model (i.e., k-1 classes).
CROSS-CLASSIFICATION ANALYSIS
For the current study, we employ cross-classifi cation analysis which is appropriate
when analyzing behaviors that are expected to be comorbid (i.e., behaviors that
evolve over time together) or heterotypic continuous (i.e., one behavioral trajectory
infl uences another at some later point in time) (Nagin, 2005). While the comorbidity
of drug use has previously been explored in prior trajectory research, the current study
is focused on heterotypic continuity given its emphasis on how trajectories aid in
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understanding drug use progression. Cross-classifi cation analysis yields reasonably
similar results to dual-trajectory analysis when the posterior probabilities of group
assignment are high (Nagin, 2005), which is the case in the current analysis.
5
The
procedure involves estimating trajectories in isolation and obtaining conditional
probabilities via cross-tabulation. That is, the statistic given from cross-classifi cation
analysis is the probability of being a member in a specifi c marijuana use trajectory
group given one’s membership in a specifi c alcohol use trajectory group. Thus,
one cannot only see what is most likely to occur but what is likely to occur more
generally; this increases the ability to predict drug use progression and, consequently,
is an important methodological technique for drug use progression research.
ANALYTIC STRATEGY
To assess the relevance of knowing one’s gateway substance use trajectory
for understanding one’s subsequent harder substance use trajectory, the analysis
proceeds in a series of steps. First, a latent class growth analysis for categorical
outcomes was employed to estimate a series of trajectory models for alcohol use
and marijuana use. Using relevant model selection criteria, we identify the best
fi tting trajectory models for both alcohol and marijuana use and then examine
the posterior probabilities of group assignment as a way of assessing the relative
precision of the best fi tting alcohol and marijuana use trajectory models (see
Nagin, 2005). Second, we describe relevant features of the alcohol and marijuana
trajectory models separately, including the number of latent classes, the proportion
of individuals belonging to each latent class, and the stability or change associated
with each trajectory. Finally, we examine the heterotypic continuity of drug use by
calculating the probability of being a member of a given marijuana use trajectory
group in grades 9 to 11, conditional on membership in a particular alcohol use
trajectory group in grades 7 to 9. In other words, the key empirical question for drug
use progression policy that is addressed is whether knowing one’s early alcohol use
trajectory aids in predicting one’s subsequent marijuana use trajectory. While the
focus on the current research is on assessing heterotypic continuity of drug use in
a trajectory framework, one should not lose sight of the fact that most individuals
that progress to marijuana use do become poly-drug users in grades 9 to 11—as
opposed to substituting marijuana use for alcohol use.
RESULTS
MODEL SELECTION
Table 1 presents the results of the LCGA for both alcohol and marijuana use. For
alcohol, the results of the model comparison statistics favor a fi ve class solution.
More specifi cally, the BIC score is lowest and the entropy value is highest for the
fi ve class model. Additionally, the LRT test favors a fi ve class model over a four
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TABLE 1. LCGA MODEL SELECTION CRITERIA FOR ALCOHOL USE AND
MARIJUANA USE TRAJECTORIES
TABLE 2. MEAN POSTERIOR PROBABILITIES FOR TRAJECTORY
GROUP ASSIGNMENTS: ALCOHOL
TABLE 3. MEAN POSTERIOR PROBABILITIES FOR TRAJECTORY
GROUP ASSIGNMENTS: MARIJUANA
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class model. For marijuana, the results of the LCGA are less clear given that the
model comparison statistics do not all favor a single solution. The entropy of the two
class model is highest whereas the BIC for the four class model is lowest, lending
initial support for the two and four class models, respectively. However, the BIC
value for the four class model is not substantively lower than it is for the three class
model, whereas the BIC value for the three class model is substantively lower than
it is for the two class model (see Nagin, 2005). While the BIC provides support for
the four class model, there is a signifi cant probability the three class model is the
correct model (37%) and essentially no chance the two class model is the correct
model. Additionally, the three class model is preferred over the two class model
according to the LRT, but the four class model is not preferred over the three class
model. Therefore, the three class model is determined to be the best fi tting trajectory
model for marijuana use.
Tables 2 and 3 contain the mean posterior probabilities of group assignment
for the best fi tting alcohol and marijuana use trajectory models, respectively. The
mean posterior probabilities of group assignment were all substantially greater
than the standard cutoff of 0.7 (Nagin, 2005). This indicates that the best fi tting
fi ve class alcohol use trajectory model and three class marijuana use trajectory
model are adequately precise in their group assignments. Importantly, since the
posterior probabilities are relatively large, cross-classifi cation analysis will closely
approximate dual trajectory analysis (see Nagin, 2005).
TRAJECTORY GROUPS
ALCOHOL
Five distinct developmental trajectories emerged for alcohol use (see Figure 1).
The fi ve latent classes can be categorized into two basic types that capture whether
change in alcohol use was observed over the study period. Three trajectories were
stable across time while two trajectories exhibited change across time. With respect
to individual use patterns that were stable over time, non-users comprise 38%
percent of the sample (n=348) and are classifi ed as individuals that had essentially
no alcohol consumption during grades 7 to 9. Light users, with an average frequency
of approximately 1 (a little) across all three grades, also had stable use patterns and
made up approximately 12% of the total sample (n=111). Finally, chronic users
comprising less than 3% of the sample (n=24) had a relatively stable use pattern with
an average use just above 2 (some). With respect to individuals that had use patterns
that were accelerating across time, low accelerators were the more common of the
two types, making up about 33% of the sample (n=303). These individuals started
out with no alcohol use in grade 7, but ended with use approximately equal to 1
(a little) by grade 9, which is similar to the frequency of use among the light users
group. High accelerators comprised about 14% of the sample (n=129) and moved
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from below 1 (less than a little use) by grade 7 to approximately 2 (some use) by
grade 9, which is similar to the frequency of use among the chronic users group.
MARIJUANA
Unlike the alcohol use trajectories, only three distinct developmental trajectory
groups emerged for marijuana use (see Figure 2). The majority of the sample (n=536)
are classifi ed as non-users of marijuana with essentially no use across grades 9 to 11.
While there are no stable users of marijuana (e.g., light users or chronic users), there
are two distinct accelerating marijuana use trajectories that emerge from the data.
First, low accelerators maintain a consistent growth in marijuana use from 0 (none)
to just over 1 (a little). Second, high accelerators begin marijuana use in grade 9 at
a level equal to about 1 (a little) and increase their use to approximately 2 (some)
by grade 10. This group further increases their marijuana use slightly, reaching their
highest use level in grade 11. These low and high accelerating trajectory groups
made up about 25% (n=233) and 16% (n=146) of the sample, respectively.
HETEROTYPIC CONTINUITY OF DRUG USE
While describing the models individually gives insight into the separate patterns
of alcohol and marijuana use over time for this sample, it does not divulge the
FIGURE 1. LATENT TRAJECTORY CLASSES OF ALCOHOL USE (N=915)
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relationship between membership in alcohol and marijuana use trajectory groups.
While there are several ways to represent the results of a dual-trajectory analysis (see
Nagin, 2005), the probability of being in a particular subsequent trajectory group
conditional on being in a given earlier trajectory group is most appropriate given
the current focus on the heterotypic continuity of drug use. Figure 3 displays the
probability of being in a particular marijuana use trajectory conditional on being in
a given alcohol use trajectory group. In other words, the values reported in Figure 3
are the probability of being a non-user, low accelerator, or high accelerator marijuana
user given one’s status as a non-user, low accelerator, light user, high accelerator,
or chronic user of alcohol. The overall model for the cross-classifi cation analysis
was statistically signifi cant (χ
2
(8, N=915)=149.21, p<0.001). More importantly,
the arrows in Figure 3 signify whether the adjusted residuals of a specifi c cell are
signifi cantly larger (↑) or smaller (↓) than would be expected due to chance alone
(i.e., the observed value of a specifi c cell is signifi cantly greater or lesser than the
expected value).
PROGRESSION FOR STABLE ALCOHOL USERS AND NON-USERS
We fi rst focus our attention on individuals that reported little or no change in
alcohol use across time (e.g., non-users, light users, chronic users). Non-users
FIGURE 2. LATENT TRAJECTORY CLASSES OF MARIJUANA USE (N=915)
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of alcohol have about a 76% chance of being in the non-user marijuana group, a
20% chance of being in the low accelerator marijuana group and a 4% chance of
being in the high accelerator marijuana use group. All three of these conditional
probabilities are statistically signifi cant; that is, non-users of alcohol are signifi cantly
more likely to be non-users of marijuana and signifi cantly less likely to be low or
high accelerating marijuana users. Thus, avoiding early involvement in alcohol
consumption in this adolescent population is a strong, but not complete, preventive
for later involvement in marijuana use. Compared to non-users of alcohol, light
users of alcohol have greater probabilities of being both low and high accelerator
marijuana users, but have a lesser probability of being a non-user of marijuana.
However, none of the observed conditional probabilities for the light users of alcohol
group are statistically different from what is expected by chance alone. Thus, those
with light, steady alcohol use over grades 7 to 9 are no more or less likely to be a
member of any particular marijuana use trajectory group in grades 9 to 11. This is
in direct contrast to non-users of alcohol who had statistically signifi cant favorable
marijuana use outcomes with respect to all trajectories (i.e., greater chance of being
FIGURE 3. PROBABILITY OF MARIJUANA USE TRAJECTORY GROUP MEMBERSHIP CONDITIONAL
ON ALCOHOL USE TRAJECTORY GROUP MEMBERSHIP (N=915)
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on a non-user marijuana trajectory and lesser chance of being on a low or high
accelerating marijuana user trajectory).
For chronic users of alcohol, the situation is considerably bleaker. For example,
there is a 38% chance of becoming a high accelerator user of marijuana, which is
approximately ten times the proportion of non-users of alcohol and nearly three times
the proportion of light users of alcohol. Importantly, chronic users of alcohol are
statistically more likely to be high accelerator marijuana users. Compared to both
non-users and light users of alcohol, chronic alcohol users have a lower probability
of being a non-user of marijuana. The conditional probability of being on a non-
user of marijuana trajectory on a chronic alcohol user trajectory does not, however,
reach statistically signifi cance. Among individuals with little change in alcohol use
over time, those that use more alcohol in grades 7 through 9 have a greater chance
of becoming a high accelerator user of marijuana and a lesser chance of becoming
a non-user of marijuana in grades 9 through 11. In other words, when comparing
non-users, light users, and chronic users of alcohol, we conclude that trajectories for
marijuana use tend to be more probable when there is higher sustained alcohol use
over time. This, however, does not yet answer the question of whether accelerating
alcohol use trajectories, which capture important changes in alcohol use over time,
add to the general understanding of drug use progression and, specifi cally, to how
subsequent marijuana use unfolds over time.
PROGRESSION FOR ACCELERATING ALCOHOL USERS
Comparing the conditional probabilities of low accelerators to the light users,
which had approximately an equivalent level of use during the fi nal grade, we see
that low accelerators of alcohol have a slightly greater probability of both being a
high accelerator and low accelerator of marijuana as well as a lower probability of
being a non-user of marijuana. In fact, while none of the conditional probabilities for
light users of alcohol were statistically signifi cant, low accelerator users of alcohol
are signifi cantly more likely than chance to be low accelerator users of marijuana
and less likely than chance to be non-users of marijuana.
The relevance of accelerating alcohol use for drug use progression is considerably
more pronounced when comparing high accelerators to the chronic users of alcohol,
the latter of which reported the heaviest use of alcohol in each of the three years.
High accelerator alcohol users have a 43% chance of becoming high accelerator
marijuana users as opposed to a 38% chance among chronic users of alcohol. More
noteworthy is the fact that high accelerator users of alcohol have a 26% chance of
becoming low accelerator marijuana users (compared to 13% for chronic users of
alcohol) and only a 30% chance of becoming a non-user of marijuana (compared
to 50% of chronic users of alcohol). Moreover, while chronic users of alcohol are
signifi cantly more likely than chance to become high accelerator users of marijuana,
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individuals that are high accelerator users of alcohol are not only more likely than
chance to become high accelerator users of marijuana but are also less likely than
chance to become non-users of marijuana.
When viewed in this light, sustained frequency of alcohol use over time appears
to be somewhat less important in infl uencing trajectories of marijuana use than
accelerating use of alcohol over time. A behavioral pattern of increasing alcohol
consumption in this time period, then, is a clearer sign of risk for becoming a
marijuana user than the fact of drinking itself. This appears to the be the case despite
the fact that low and high accelerators actually have lower cumulative alcohol use
rates during grades 7 through 9, and appear largely similar in grade 9 with respect to
frequency of alcohol use, than light users and chronic users, respectively (see Figure
1). This, however, is not to say that frequency of alcohol use is not important and
acceleration of alcohol use is instrumentally independent of other factors. Indeed,
marijuana use trajectories for chronic users of alcohol appear more problematic
than those for low accelerator users of alcohol. Thus, exploring changes in alcohol
use over time, as we have done here, has the potential to add unique and important
insights and questions to the study of drug use progression that complement, rather
than contradict, existing knowledge about gateway substance use.
DISCUSSION AND CONCLUSIONS
Prior research has seldom examined trajectories of two or more substances
simultaneously to understand how drug use contemporaneously unfolds over time
(Jackson et al., 2008) and no study to our knowledge has investigated the possibility
that trajectories of gateway substances may have important utility for predicting
subsequent trajectories of harder substances. While exploring comorbidity of drug
use is important in helping to identify risk factors that may explain poly-drug use
behavior, using trajectories to explore heterotypic continuity of drug use may also
be important in our understanding of drug use progression. This study has attempted
to address the heterotypic continuity of drug use by employing latent class growth
analysis to determine the extent to which knowing one’s alcohol use trajectory can
be useful in predicting subsequent marijuana use trajectories. In general, the results
demonstrate that knowing how alcohol use changes over time provides important
information above and beyond knowing frequency of alcohol use for predicting
marijuana use trajectories.
In the fi rst principal stage of the analysis, we identifi ed alcohol and marijuana
use trajectory groups separately. Five alcohol use trajectory groups emerged from
the data, three of which had relatively stable rates of alcohol use over time (i.e.,
non-users, light users, chronic users) and two of which had accelerating rates of
alcohol use over time (i.e., low accelerators, high accelerators) (see Figure 1). Only
three marijuana use trajectory groups emerged from the data, one of which was a
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non-user trajectory group and the other two were low and high accelerating trajectory
groups (see Figure 2). The most common trajectory group for both substances was
the non-user trajectory group. Still, about 62% of individuals were classifi ed into
one of four different trajectory groups that used alcohol across grades 7 through
9 and approximately 42% of individuals were classifi ed into one of two different
trajectory groups that used marijuana across grades 9 through 11. Thus, alcohol
and marijuana use in general was relatively common in the sample but important
differences between subgroups of individuals, with respect to the relative frequency
of use and changes in use over time, became evident when employing latent class
growth analysis.
Following the identifi cation of alcohol and marijuana use trajectories, we
examined the heterotypic continuity of drug use by calculating the probabilities
of marijuana trajectory group membership conditional on alcohol trajectory group
membership. When examining only trajectories of individuals with relatively
stable alcohol use over time, it was found that greater alcohol use led to more
problematic marijuana use trajectories. This fi nding is not all that surprising given
the consistency of empirical research that demonstrates that as frequency of use
of a gateway substance increases, the likelihood of using a harder substance also
increases (Duncan et al., 1998; Fergusson & Horwood, 2000). When comparing the
trajectories of individuals who were accelerating in their use of alcohol over time
to the stable alcohol use trajectory most similar in frequency of use during the fi nal
year (i.e., low accelerators vs. light users, high accelerators vs. chronic users), it
was found that individuals with accelerating use of alcohol had more problematic
marijuana trajectories despite having lower cumulative alcohol use across grades 7
through 9. However, when comparing, for example, chronic users of alcohol to low
accelerator users of alcohol, the former group had a larger proportion of individuals
classifi ed as high accelerator users of marijuana. Taking these fi ndings together,
greater frequency of alcohol use combined with accelerating alcohol use seems to
lead to the most problematic marijuana use trajectories. Thus, exploring heterotypic
continuity of drug use with trajectories yields important information about drug use
progression that is lost with comorbidity trajectory analysis or panel longitudinal
approaches to assessing the gateway sequence.
Recall that the low and high accelerator alcohol trajectory groups ended with
similar frequency of use in grade 9 as the light users and chronic users, respectively
(see Figure 1). In other words, if one ignored alcohol use in grades 7 and 8 and took
a snapshot of the trajectory groups in grade 9, the high accelerators would appear
similar to the chronic users and the low accelerators would appear similar to the light
users. It is possible that low and high accelerator alcohol users have substantially
higher amounts of alcohol use than their comparison stable trajectory groups (i.e.,
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chronic users, light users) in grades 10 and 11 and this is responsible for the fi nding
that accelerating use is particularly important in progressing to problematic marijuana
use trajectories. If this were indeed found to be the case, then it may be evidence
for comorbidity of drug use during grades 10 and 11 and it would directly call into
question the utility of examining the heterotypic continuity of drug use trajectories
and the results of the current study. To address this possibility, we determined whether
there were statistically signifi cant differences in alcohol use in grades 10 and 11
across the trajectory groups. Although low and high accelerator users of alcohol,
on average, reported slightly greater frequency of alcohol use than light users and
chronic users of alcohol, respectively, these mean differences were not statistically
signifi cant.
6
While comorbidity of drug use should continue to be explored to
better understand how poly-drug use unfolds over time, these results suggest the
importance of studying how heterotypic continuity may aid our understanding of
drug use progression, especially in early adolescence.
Earlier we raised the possibility that stable drug use may indicate consistent
social use, whereas accelerating drug use could refl ect increasing tolerance levels
and progressively decreasing levels of satisfaction without increased use. This
ultimately might be one mechanism leading accelerating alcohol users to progress to
marijuana use at greater rates. While we do not have the data to test this possibility,
we do fi nd it interesting that the low accelerator users of alcohol have the greatest
proportion of individuals becoming low accelerator users of marijuana (31%).
Moreover, high accelerator users of alcohol similarly have the greatest proportion
of individuals becoming high accelerator users of marijuana (43%). This would
seem to support the idea that there may be different subpopulations with relatively
homogenous rates of tolerance. These subgroup differences may indeed manifest
themselves similarly across different drugs, which could potentially explain the
aforementioned drug use progressions. While this is an interesting idea, future
research is needed to determine whether these observations can be explained by
differences among individuals with respect to the rates at which drug tolerance
occurs. Piquero (2008) notes that quantitative latent class trajectory analysis can
be used to identify a distinct number of trajectory groups that can be isolated for
further qualitative study. Given the possibility that stable and accelerating alcohol
use may refl ect different motivations to progress to marijuana use, we encourage
future researchers to identify unique trajectory groups and determine the similarities
and dissimilarities in the causes of drug use progression.
We also entertained the possibility that accelerating alcohol use could refl ect
important changes in peer groups. Here, comorbidity analysis of latent class
trajectories of drug use and peer groups may be particularly useful. If accelerating
drug use refl ects changing peer networks, we would expect these behaviors to unfold
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contemporaneously. While an abundance of research suggests that peer associations
are infl uential in the decision to use drugs, we know of no study to-date that has
assessed changes in peer networks and accelerating drug use in a dual trajectory
framework. Doing so may help to reveal the mechanisms for the observed drug use
progression patterns found in this study.
Regardless of the reasons for the empirical findings, there are important
implications for policy. If acceleration of alcohol use over time is important in
understanding the likelihood of transitioning to more problematic marijuana use
trajectories as was found in this study, identifying who is most “at-risk” would
require not only identifying more frequent users but also tracking changes in drug
use over time. Thus, the identifi cation of changing alcohol use behavior by parents
or teachers is crucial and should help to focus interventions onto those most likely
to transition into more problematic marijuana use trajectories.
There are a number of important qualifi ers that lead us to accept the conclusions
only with caution. While retrospective data can be a cost-effective approach to data
collection and a relatively reliable source of drug use history, the retrospective data
collection method is subject to a number of problems. First, individuals may not be
able to accurately recall their drug use history. We believe this to not be a serious
threat to the internal validity of the empirical fi ndings because there were only four
ordinal response options helping to create discernible response categories. Moreover,
the retrospective questions asked about drug use in specifi c grades, which may aid
in memory recall. Second, the retrospective data collection method limits our ability
to assess the extent to which the empirical fi ndings hold when taking into account
potential factors that may explain the association between alcohol and marijuana use
trajectories. This limitation in the current study arises due to the fact that potential
control variables are measured only for the past year. Thus, these variables are
measured after drug use histories have already unfolded and are consequently of
little utility in assessing whether the empirical fi ndings are spurious.
Control variables are important to account for in drug use progression research;
for example, Morral and colleagues (2002) argue that the use of a gateway substance
has no infl uence on harder substance use because individuals are differentially
predisposed to drug use. While we are unable to control for a large number of factors
that may explain the association between alcohol and marijuana use trajectories
found in the current study, we were able to assess the robustness of the empirical
fi ndings when accounting for basic demographic factors that are similar regardless
of the time of measurement. We estimated a multinomial logistic regression model
(not shown) using alcohol use trajectories to predict marijuana use trajectories while
simultaneously controlling for age, sex, and race (non-White). Using non-users of
alcohol and marijuana as the respective reference categories, the results mirror the
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bivariate fi ndings reported in Figure 3. Nevertheless, future research is needed to
determine whether the association between alcohol and marijuana use is the result
of a causal mechanism as explicated in the gateway drug hypothesis or simply a
refl ection of a predisposition to drug use.
There are also important limitations of our sample that warrant mention. While
being a highly comprehensive and competently executed study on adolescent
substance use and abuse for its time, the Boys Town data is now fairly dated.
Additionally, the Boys Town sample consists of adolescents in Midwestern America
and lacks suffi cient representation of minority racial groups, raising issues of
generalizability across regions and races. Additional research is needed to determine
whether the empirical fi ndings here generalize across time, region, and/or race.
Notwithstanding the limitations of the current analysis, it appears that examining
heterotypic continuity of drug use using drug use trajectories is a fruitful endeavor
and one that is, at least, worth additional empirical attention. Existing support for
the gateway hypothesis as it is currently formulated is limited, which points to the
possibilities that the hypothesis may need to be refi ned and the infl uence of intra-
individual change in behavior may need to be more strongly considered (Labouvie
& White, 2002). This study has taken an initial step in that direction by explicitly
modeling how intra-individual change in drug use of one substance may infl uence
intra-individual change in a harder substance, but important questions remain.
Perhaps a fi rst-order issue is whether the empirical fi ndings hold with other samples
and in other contexts. If so, is the utility of examining heterotypic continuity of drug
use within a dual-trajectory framework confi ned to the specifi c drugs of alcohol and
marijuana? Or is it confi ned to examining drug use progression during adolescence?
We discussed at some length reasons for why intra-individual change may matter in
drug use progression. Do these hypotheses explain the effect? Employing trajectories
to explore these and other issues pertaining to the heterotypic continuity of drug use
may provide important insights into both the causes and solutions to the problem
of drug use progression.
NOTES
1. Care, however, should be taken in inferring causality since, similar to all gateway
drug research, biological, sociological, and psychological factors could account
for the association between alcohol and marijuana use trajectories.
2. There is an important conceptual distinction between quantity of use and
frequency of use. Empirically, however, frequency and quantity of use are
two highly correlated constructs (e.g., see Akers, Krohn, Lanza-Kaduce, &
Radosevich, 1979). Thus, there is reason to believe that trajectories of frequency
of use and quantity of use should largely covary. However, our data do not permit
the isolation of these conceptually distinct concepts and future research should
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seek to empirically determine the extent to which the heterotypic continuity of
drug use trajectories applies to both quantity and frequency of use.
3. After carefully considering what knowledge could be gained through various
procedures, we elected to exclude pre-ninth grade marijuana users from
the analysis sample. If we were to estimate both alcohol and marijuana use
trajectories from grades 7 to 11 for the entire sample we would gain information
about the comorbidity of drug use over time (which is an important topic but
has already been assessed in prior research) and not on the relevance of drug
use trajectories for drug use progression (which is an important policy question
and the principal contribution of our research). In sum, our research cannot
speak to all drug users since a certain proportion on individuals do not follow
the gateway sequence, but does yield critical insights into whether trajectories
of drug use can aid in our understanding and prediction of drug use progression
for adolescents that may be using a gateway drug, namely alcohol.
4. Mplus BIC scores = log (L) + log (n) * k. Nagin’s (2005) BIC scores differ by
a factor of negative 2; thus, BIC = -2 log (L) + log (n) * k.
5. Dual trajectory analysis is an extension of group-based trajectory modeling
where the trajectories for two different behaviors are fi rst estimated in isolation,
adhering to the aforementioned model selection criteria and then are estimated
together to examine the empirical relationship between the trajectories.
6. Given the ordinal nature of the dependent variable (see measures section),
we employed a Kruskal-Wallis test to assess overall signifi cant differences in
alcohol use in grades 10 and 11. Given there were signifi cant differences, we then
employed the Mann-Whitney test with Holm’s sequential Bonferroni correction
to test for signifi cant differences between the relevant pairs of trajectory groups.
The conclusions are substantively similar to those given by a standard one-way
ANOVA; therefore, we report the results from relevant post hoc comparisons of
the one-way ANOVA results for ease of interpretation. Low accelerators have
a grade 10 mean of 1.528 and users of alcohol have a mean of 1.459 (p>0.05).
Similarly, in grade 11, low accelerators have mean of 1.779, whereas users have
a mean of 1.694 (p>0.05). High accelerators have a grade 10 alcohol use mean
equal to 2.124 and chronic users have a mean equal to 1.875 (p>0.05). With
respect to grade 11, high accelerators have a mean of 2.163 and chronic users
have a mean of 1.875 (p>0.05).
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