Reassessing The Marijuana Gateway Effect

[Jacob Bell]

Andrew R. Morral, Daniel F. McCaffrey & Susan M. Paddock
Drug Policy Research Center, RAND, Arlington, VA, USA

ABSTRACT
Aims
Strong associations between marijuana use and initiation of hard drugs
are cited in support of the claim that marijuana use
per se
increases youths' risk
of initiating hard drugs (the 'marijuana gateway' effect). This report examines
whether these associations could instead be explained as the result of a common
factor–drug use propensity–influencing the probability of both marijuana
and other drug use.
Design
A model of adolescent drug use initiation in the United States is constructed
using parameter estimates derived from US household surveys of drug
use conducted between 1982 and 1994. Model assumptions include:
(1) individuals have a non-specific random propensity to use drugs that is normally
distributed in the population; (2) this propensity is correlated with the risk
of having an opportunity to use drugs and with the probability of using them
given an opportunity, and (3) neither use nor opportunity to use marijuana is
associated with hard drug initiation after conditioning on drug use propensity.
Findings
Each of the phenomena used to support claims of a 'marijuana gateway
effect' are reproduced by the model, even though marijuana use has no
causal influence over hard drug initiation in the model.
Conclusions
Marijuana gateway effects may exist. However, our results demonstrate
that the phenomena used to motivate belief in such an effect are consistent
with an alternative simple, plausible common-factor model. No gateway
effect is required to explain them. The common-factor model has implications
for evaluating marijuana control policies that differ significantly from those
supported by the gateway model.
KEYWORDS
Adolescents, drug use, marijuana gateway effect,
mathematical model

INTRODUCTION
Alcohol, tobacco and marijuana are widely regarded as
'gateway' drugs. Although the gateway concept admits a
number of definitions, one in particular predominates in
drug policy discussions: use of gateway drugs causes
youths to have an increased risk of progressing to other,
more serious drugs. For instance, in debates on marijuana
decriminalization or the medicinal use of marijuana,
policy makers frequently suggest that use of
marijuana increases youths' risk of initiating more
dangerous drugs such as cocaine and heroin (US
Congressional Record 1998, 1999). Although marijuana is the least prevalent of the three principal gateway
drugs, it is currently the focus of extensive policy reassessment
in the United States, Canada, Western Europe and
Australia. Using a simulation model, we demonstrate that
the primary evidence supporting the marijuana gateway
effect can be explained completely by the order in which
youths first have the opportunity to use marijuana and
other drugs, and by assuming a non-specific liability to
use drugs, without any assumption that use of marijuana
contributes to the risk of initiating use of hard drugs. We
argue that although marijuana gateway effects may truly
exist, available evidence does not favor the marijuana
gateway effect over the alternative hypothesis that marijuana and hard drug initiation are correlated because
both are influenced by individuals' heterogenous liabilities
to try drugs.
The popular concern that marijuana use increases the
risk of progressing to other, more serious drugs is a longstanding
one, and has influenced US drug policy since at
least the 1950s (Goode 1970; Whitebread & Bonnie
1972; National Research Council 1982). Some social scientists
have also suggested that marijuana gateway
effects probably account for several phenomena observed
in adolescent drug use initiation patterns (e.g. Goode
1970; O'Donnell & Clayton 1982; Yamaguchi & Kandel
1984b). Three such phenomena represent the primary
evidence for a marijuana gateway effect. The first concerns
the
relative risk
of hard drug initiation for
adolescent marijuana users vs. non-users. In general,
marijuana users in many countries appear to have a significantly
elevated risk for drug use progression (Adler &
Kandel 1981; Kandel 1975; Blaze-Temple & Lo 1992;
Stenbacka, Allebeck & Romelsjö 1993; Beenstock &
Rahav 2002). Indeed, one US study found their risk to be
85 times those of non-users of marijuana (Center on
Addiction and Substance Abuse 1994). Another form of
relative risk that is occasionally cited in support of the
gateway effect is that younger marijuana initiates have a
higher risk of initiating hard drug use than older marijuana
initiates (O'Donnell & Clayton 1982; Yamaguchi &
Kandel 1984b; Kandel & Yamaguchi 1993; Center on
Addiction and Substance Abuse 1994). This relative risk
differs from the first only insofar as it finds that risk of
hard drug initiation is conditioned on a characteristic of
the user (age), rather than on marijuana use alone.
Therefore, it does not provide strong evidence supporting
a gateway effect.
The second observation routinely cited in support of
the marijuana gateway effect concerns the remarkably
invariant
ordering
in adolescents' initiation of different
drug classes. Adolescents rarely initiate hard drug
use before marijuana (Ellickson
et al.
1992; Kandel,
Yamaguchi & Chen 1992; O'Donnell & Clayton 1982;
Yamaguchi & Kandel 1984a). For instance, in a longitudinal
sample of 1265 New Zealand youths between the
ages of 15 and 21, Fergusson & Horwood (2000) found
only three cases reporting use of hard drugs before marijuana.
This figure is dramatically lower than the roughly
124 such cases that would be expected from annual
incidence rates if use of marijuana and hard drugs were
independent.
The third phenomenon used to support claims of a
marijuana gateway effect concerns the strong relationship
between the frequency of marijuana consumption
and the risk of hard drug initiation: as the frequency of
marijuana use increases, so too does the risk of initiating
hard drug use Fergusson & Horwood 2000). Fergusson & Horwood
(2000), for instance, developed a proportional hazards
model suggesting that youths reporting 50 or more uses
of cannabis in the past year had hazards of progression
to hard drugs that were more than 140 times greater
than those for youths reporting no use of cannabis. Findings
like this suggest an even stronger form of the marijuana
gateway effect defined earlier: not only does
marijuana use increase youths' risk of hard drug initiation,
but every instance of marijuana use adds to that
risk. For convenience, we refer to this phenomenon as
marijuana's apparent
dose—response effect
on hard drug
initiation.
The three phenomena of relative risk, ordering in drug
use initiation and dose—response are not sufficient to
prove that use of marijuana, rather than some associated
factor, increases the risk of hard drug initiation (Joy
et al.
1999). Indeed, a frequently cited alternative explanation
is that a common factor, which we might refer to generically
as a propensity for drug use, could influence use of
both marijuana and hard drugs, thereby causing initiation
of these drugs to be correlated (Goode 1972; Huba
et
al.
1981; Donovan & Jessor 1985; Hays
et al.
1987; Mac-
Coun 1998). For instance, if high drug use propensities
elevate individuals' risk for use of both marijuana and
hard drugs, this could explain why marijuana users have
a higher relative risk of hard drug initiation in comparison
with non-users.
This 'common-factor' model does not immediately
account for the ordering and dose—response phenomena.
To make sense of these observations, proponents of the
common-factor approach suggest that ordering in drug
use initiation results from the order in which opportunities
to use marijuana and hard drugs are presented to
young people (Goode 1972; Jessor & Jessor 1980). Those
with the highest propensities to use drugs are likely to use
the first one offered to them, and that happens to be marijuana
in most cases. Moreover, if a high drug use propensity
is associated with greater frequencies of drug use, the
common-factor theory can also account for the dose—
response phenomenon: marijuana use frequency is associated
with risk of hard drug initiation because both are
controlled by drug use propensity.
The common-factor model is appealing in part
because it takes account of what is a substantial scientific
literature demonstrating the existence of genetic, familial
and environmental characteristics associated with a generalized
risk of using both marijuana and hard drugs. For
instance, several studies examining drug use among
monozygotic and dizygotic twins in the USA demonstrate
genetic and family environment contributions to the likelihood
of any drug use (van den Bree
et al.
1998) and any
drug use initiation (Tsuang
et al
. 1998; Kendler
et al
.
1999, 2000). Similarly, community drug use or drug
availability may contribute to individuals' risk of using
drugs (Lillie-Blanton, Anthony & Schuster 1993).
Although the common-factor model is plausible, previous
research has not demonstrated that propensities to
use drugs and environmental factors such as drug use
opportunities could, in fact, account for the strong
relative risk, ordering and dose—response phenomena
observed among adolescents. Indeed, two lines of
research provide some evidence that the common-factor
model cannot account for drug use initiation without
assuming a marijuana gateway effect. Firstly, several
studies examine the association between marijuana use
and the risk of hard drug initiation after controlling for a
large number of risk factors, such as delinquency and
peer drug use (Yamaguchi & Kandel 1984b; Fergusson &
Horwood 2000). By the logic of this approach, any residual
marijuana effect on hard drug initiation that remains
after controlling for these candidate common factors
lends credence to the suggestion that marijuana use
per
se
increases the risk of hard drug initiation. However, if
the selected covariates are less good proxies for the propensity
to use drugs than is marijuana use itself, these
findings are perfectly consistent with a strict commonfactor
model. Because this approach does not observe all
or even most individual risk factors, it provides little persuasive
evidence against a common-factor explanation.
We will illustrate this point with data derived from the
model described later on in this paper.
A second approach to contrasting the gateway and
common-factor models of drug use initiation uses instrumental
variables in an effort to account for both observed
and unobserved person-level risk of initiation. Two of
these studies (DeSimone 1998; Pacula 1998) suggest
that common factors alone cannot explain observed gateway
phenomena. The third (Beenstock & Rahav 2002)
provides qualified evidence that observed marijuana
gateway phenomena are not attributable to a gateway
effect, but instead derive from individuals' predispositions
to use both marijuana and hard drugs. However, none of
these studies take into account the observation that
opportunities to use marijuana precede those for hard
drugs, and may themselves be associated with propensity
to use drugs through, for instance, drug-seeking behavior.
This is a critical omission, since proponents of the
common-factor model have consistently cited the ordering
in drug use opportunities as an essential part of the
explanation of ordering in drug use initiation. Indeed, in
a series of analyses on US and Panamanian data,
Anthony, Van Etten and colleagues have shown that gender,
race and neighborhood differences observed in rates
of drug use initiation are attributable, to a large extent, to
differences in the rates at which groups are exposed to
drug use opportunities (Crum, Lillie-Blanton & Anthony
1996; Van Etten, Neumark & Anthony 1997, 1999
Delva
et al
. 1999; Van Etten & Anthony 1999). Thus,
econometric models have not tested the common-factor
model adequately.
In this report we describe a Monte Carlo model of drug
use initiation with parameters selected to match the drug
use experiences of the population of US residents under
the age of 22. The model describes the joint distribution of
four events: the ages of first opportunity to use marijuana
and hard drugs, and the ages of first use of marijuana and
hard drugs. Each of these events depends on a common
factor–drug use propensity–but conditional on this
factor, the ages of first opportunity to use and first use of
marijuana are independent of opportunity to use and use
of hard drugs. Thus, the model is designed to exclude any
causal gateway effect. Random draws from the modeled
joint distribution are used to examine the relative risk,
ordering and dose—response phenomena that might be
expected by chance in the US if model assumptions are
accurate.
METHODS
Procedure
We build a common-factor model of adolescent drug use
initiation using parameter estimates derived from a representative
sample of youths in the US population. With
this model, we observe the rates at which phenomena of
relative risk, ordering and dose—response can occur when
no causal gateway effects are present. We compare these
rates to those observed in the sample of US youths to demonstrate
that a common-factor model designed to match
US rates of drug use initiation and drug use opportunities
without a gateway effect can still reproduce all of the
gateway phenomena observed in the population. In the
remainder of this section we describe the model specification
and the statistical methods used to estimate the values
for the model parameters and the gateway effects
observed among youths in the US.
Model specification
Drug use propensity
Each case is assigned an arbitrary propensity to use
drugs,
q
, which we conceptualize as the resultant shared
risk of reporting use of both marijuana and hard drugs
after accounting for all person-level risk factors that
remain more or less constant during adolescence. Examples
of such invariant predispositions to report drug use
could include genetic and family environmental history
factors (Kendler
et al
. 1999; Tsuang
et al
. 1998; van den
Bree
et al.
1998; Kendler
et al
. 2000) and community
drug use or drug availability (Lillie-Blanton, Anthony &
Schuster 1993). We assume that propensity is correlated
not just with the probability of drug use, but also with the
probability of having the opportunity to use drugs at any
particular age. This assumption is supported by several
considerations. Firstly, we define propensity as resulting,
in part, from environmental risk factors. Local drug use
norms and the availability of drugs are examples of
environmental influences likely to affect both individuals'
risk of drug use and their risk of having an opportunity to
use drugs (Lillie-Blanton
et al
. 1993). Drug use propensity
is also likely to be correlated with age of first opportunity
to use drugs because individuals with greater
propensities are more likely to seek out drug use opportunities,
or recognize them when they present themselves.
Finally, empirical studies document a strong
association between the risk of drug offers (and, by extension,
opportunities) and a range of characteristics likely
to correlate with drug use propensity, such as smoking,
alcohol use and parental substance use (Stenbacka
et al.
1993). Each of these considerations suggests propensity
will be correlated with drug use opportunities as well as
drug use.
Although epidemiological studies provide evidence
supporting the existence of a drug use propensity
(Tsuang
et al
. 1998; van den Bree
et al.
1998; Kendler
et al
. 1999, 2000), no information exists about its distribution
in the population of adolescents. Thus, in the
model we draw drug use propensities,
q
, at random from
a standard normal distribution.
Drug use opportunities
We assume that for any individual, the age of first opportunity
to use marijuana,
Y
M
, and the age of first opportunity
to use hard drugs,
Y
H
, are drawn at random from
distributions describing the risk of first marijuana or hard
drug use opportunity at each age. These risk distributions
are functions of the individual's drug use propensity:
higher propensities shift the risk curves so that exposure
to a drug use opportunity is more likely at earlier ages.
Thus, between the ages 0 and 22, we define the cumulative
distribution of age of first opportunity to use marijuana
as 1
-
S
YM
(
t
,
q
), where
S
YM
(
t
,
q
) is the survival
function describing the probability that age of first opportunity
to use marijuana exceeds
t
, conditional upon
q
.
Similarly, the distribution of age of first opportunity to use
hard drugs is given by 1
-
S
YH
(
t
,
q
). We use a frailty model
to construct these conditional survival functions. Frailty
models are a standard approach to describing joint survival
functions when risks for each modeled event are
presumed to correlate due to heterogeneity across individuals
in the population (Hosmer & Lemeshow 1999;
Therneau & Grambsch 2000):
The function
f
transforms
q
to the corresponding
value from the Gamma distribution with mean of 1 and
variance
b
1
.
Under this parameterization the frailty
model produces a correlation between age of first use
opportunities
Y
M
and
Y
H
that increases as
b
1
grows. We
estimate
b
1
and the functions
S
*
YM
(t)
and
S
*
YH
(
t)
from US
data on adolescent drug use opportunities, as described
below. The estimated functions are defined so that marginal
survival functions for the model (expected values
over
q
of
S
YM
(
t
,
q
) and
S
YH
(
t
,
q
)) equal marginal survival
functions fit to our sample of US data.
Drug use initiation
For any individual, first use of marijuana,
Z
M
, is a random
variable drawn from a distribution describing the individual's
risk of initiating marijuana at each age. Each individual's
risk distribution depends on his or her drug use
propensity and age when first presented the opportunity
to use marijuana,
Y
M
. Youths with greater propensities
have a greater risk of use at every age, beginning with
their age at first opportunity to use a drug.
Specifically, given an individual's drug use propensity
and age of first opportunity to use marijuana, the cumulative
probability distribution for age of marijuana initiation
is given by 1
-
S
ZM
(
t
,
q
,
Y
M
), where
S
ZM
(
t
,
q
,
Y
M
) is the
conditional survival function for marijuana initiation.
For
t
=
8, 9 . . . 22,
(3)
where is the cumulative probability function for a normal
distribution with mean 0 and variance
b
2
. Thus, the
parameters
p
M
and
y
*
Mt
t
=
9 . . . 22 define for the model
the marginal probabilities
Pr
{
Z
M
<
9 |
Y
M
<
9} and the
marginal probabilities
Pr
{
Z
M
=
t
|
Y
M
£
t
,
Z
M
≥
t
}
=
E
[ (
y
*
Mt
- qi)], respectively. Age of initiation of hard
drugs, ZH, is drawn independent of YM and ZM from an
analogous distribution defined by the parameters b2, pH
and y*Ht, t = 9 . . . 22.
The value of b2 is the same for both marijuana
and hard drugs. This parameter affects the correlation
between ZM and ZH by controlling the influence of propensity
on the probability of initiation. It is chosen so that the
model produces a correlation between LM = ZM — YM and
LH = ZH — YH for youths who used both marijuana and
hard drugs by age 22 that matches the same correlation
observed in data on adolescents in the US. We set the
remaining parameter values so that the marginal
probabilities in the model (i.e. Pr {ZM < 9 | YM < 9},
Pr {ZH < 9 | YH < 9}, Pr {ZM = t | YM £ t, ZM ≥ t} and
Pr {ZH = t | YH £ t, ZH ≥ t}, t = 9 . . . 22) match the corresponding
estimates from our sample of data from the US
population.
The joint distribution for YM, ZM, YH and ZH is:
(4)
where f denotes the density function for a standard normal
random variable.
Figure 1 depicts our procedure for drawing random
observations from this distribution.
Marijuana use frequency
To examine the dose—response relationship between marijuana
use frequency and the risk of hard drug initiation,
we categorize each case that initiated use of marijuana
into one of five past year use frequencies (no past year use,
1—2 times, 3—11 times, 12—51 times and 52 or more
times) at each age, beginning with the age of marijuana
initiation. Cases are assigned a marijuana use intensity
random effect, xi, which is used to draw a marijuana use
frequency from the distribution of use frequencies
observed in the US sample with corresponding ages and
number of years since marijuana initiation.
We hypothesize that marijuana use frequency is positively
correlated with propensity to use drugs. However,
because propensity is unobservable, we know of no good
data for estimating this correlation. Therefore, we conduct
a sensitivity analysis in which the risk of hard drug
initiation at each marijuana use frequency is examined as
the correlation between xi and qi ranges from 0 to 1.
Parameter estimation
This section summarizes the statistical methods used to
estimate values for each of the model's parameters, b1,
S*YM, S*YH, b2, pM, pH and y*Mt and y*Ht t = 9 . . . 22. It also
describes the methods used to estimate the observed values
of the relative risk, ordering and dose—response effects
from a sample of data from the US population.
Data source
Estimates for the model parameters and observed values
of the relative risk, ordering and dose—response effects
were derived from the National Household Survey of
Drug Abuse (NHSDA). The NHSDA is an ongoing probability
sample survey of the US civilian, non-institutionalized
population aged 12 years and older (US Department
of Health and Human Services 1999). Data on all 58 846
respondents, 12—25 years of age, from birth cohorts
1964 through 1982, were pooled from the 1982 through
1994-A NHSDA in order to create stable estimates of
quite rare events. This pooling was justified by preliminary
analyses suggesting that drug use opportunity and
initiation survival probabilities were similar across birth
cohorts. NHSDA sample weights were applied to make
the pooled sample representative of the included birth
cohorts. The selected survey years included questions on
the ages of initiation and first opportunities to use marijuana,
heroin, cocaine and hallucinogens. More recent
data on drug use opportunities are not available because
these questions were dropped from subsequent administrations
of the NHSDA. First opportunity to use and initiation
into use of hard drugs were defined as the earliest
reported age of opportunity and use of heroin, cocaine or
hallucinogens. Because these data are self-reports of illicit
behavior and improper events, they are subject to a
variety of well-known biases. Nevertheless, longitudinal
investigations indicate that ordering of drug use initiation,
a central concern of the present analysis, is reported
reliably (Golub et al. 2000). Therefore, for our purposes,
recall bias is unlikely to significantly affect our principal
findings.
Statistical methods
Estimation of b1 To best match the correlation in ages of
first opportunities to use marijuana and hard drugs
observed in the NHSDA, we selected b1 = 3.22, the maximum
likelihood estimate of b1 for model (1 & 2) fit to a 5%
random sample of the NHSDA data, stratified by year of
survey administration and birth cohort. The estimate was
obtained using the S-Plus Software (MathSoft, Seattle,
WA, USA) using the methods described in Therneau &
Grambsch (2000).
Estimation of S*YM and S*YH The estimates of S*YM and S*YH
derived directly from the marginal survival functions
SYM (t) and SYH (t), which we estimate using data from the
NHSDA. We used the actuarial life table method (Miller
1981) to estimate the survival function for first opportunity
to use marijuana, SYM (t), defined as the probability
that a randomly chosen individual's first opportunity to
use marijuana occurs after age t. The actuarial life table
method estimates the probability of a first opportunity to
use at age t as the ratio of the number of individuals who
report the first opportunity at age t to the number of individuals
eligible to have a first opportunity at age t. Individuals
are ineligible if they had a previous opportunity to
use or if they are censored. Respondents are censored if
they are interviewed before age t and report no opportunities
to use prior to the interview. We used weighted
sums in the ratio to account for unequal probability of
selection in the NHSDA. The survival function at age t is
obtained by multiplying the age-specific probabilities of
an opportunity to use. We used analogous procedures to
estimate a survival function for the first opportunity to
use hard drugs, SYH (t), and survival functions for initiation
of marijuana use, SZM (t), and hard drug use, SZH (t)
(Fig. 2).
Because f (q) is distributed as a Gamma random variable
with mean one and variance b1, E [S*YM (t) f(q)] = 1 - b1
(Hogg & Craig 1978). Setting E [S*YM (t) f(q)]
equal to the estimated marginal survival function for
log SY*M t ( )-1 b1
the NHSDA sample yields, . Again,
a similar procedure is used to estimate S*YH from the estimates
of b1 and SYH (t).
Estimation of pM and pH Since pM = Pr {ZM < 9 | YM < 9},
we estimate this probability directly from the NHSDA as
the sum of the weights from respondents who report marijuana
initiation before age nine divided by the sum of the
weights from respondents who report an opportunity to
use marijuana before age nine. The procedure is repeated
for hard drugs.
Estimation of b2 As noted earlier, we set b2 so that the
model correlation between LM and LH matches the
NHSDA estimate. For all NHSDA respondents who
reported using both marijuana and hard drugs by age 22,
we calculated LM and LH and their correlation, r. We do
not have a closed form for the correlation between LM and
LH as a function of b2, r (b2) in our simulation model.
Therefore, we estimated the function via simulation. For a
given value of b2 we simulated 10 000 observations from
the distribution and calculated the correlation between
LM and LH. We then used the bisection method to search
over the values of b2 to find the value that solved r (b2) -
r = 0.
Estimation of y*Mt and y*Ht To estimate y*Mt we first estimate
from the NHSDA Pr {ZM = t | YM £ t, ZM ≥ t} as the
ratio of the sum of the weights for respondents who initiate
use at age t to the sum of the weights of respondents
with first opportunity to use marijuana before age t + 1
who did not initiate use prior to age t. We again did
not have a closed form for E [ (y*Mt - qi)] = Pr {ZM =
t | YM £ t, ZM ≥ t} as a function of y*Mt given a value for b2.
Instead we used the bisection method to find a value y*Mt
so the E [ (y*Mt - qi)] from the simulation model equals
our estimate of Pr {ZM = t | YM £ t, ZM ≥ t} from the
Fb2
Fb2
NHSDA. Values for the corresponding hard drug parameter
were calculated in a similar manner.
Estimation of the relative risk effect We estimate the risk
of hard drug use by 21 using the sample of NHSDA
respondents aged 22 or older. We estimate the probability
of hard drug use separately for respondents who reported
marijuana use by 21 and those who did not. Estimates
equal the weighted proportion by stratum. The relative
risk is the ratio of the risk for hard drug initiation for marijuana
users to the risk for others.
Estimation of ordering effect We used life table methods
to estimate the rate at which hard drug initiation precedes
marijuana initiation. For each age, t, we summed
the weights for respondents who had used neither marijuana
nor hard drugs by age t. Call this sum Et. We subtracted
from Et, Ct the sum of the weights for respondents
who were surveyed at age t and had used neither marijuana
nor hard drugs–i.e. the weights for censored
observations. Let Ut equal the sum of the weights for
youth who report initiating hard drugs at age t before initiating
marijuana use. We then estimate the probability
that hard drug use preceded marijuana use at age t as
Pt = AtUt / (Et — Ct), where At equals our estimate of the
probability that a youth's first use of hard drugs or marijuana
is after age t. The survival curve for initiating hard
drug use prior to marijuana use equals .
Estimation of the dose—response effect To examine the
marginal dose—response effect of the simulated marijuana
use frequency on the age of hard drug initiation, a
generalized linear model with a complimentary log-log
link (Hosmer & Lemeshow 1999) was fitted to the marijuana
use frequency and hard drug initiation data from a
random sample of 30 000 simulated cases. Whether or
not a case initiated hard drug use in a given year was
modeled as a function of past year marijuana use intensity
(no past year use, 1—2 times, 3—11 times, 12—51
times and 52 or more times) at age t (t = 12 . . . 21). Those
who did not initiate hard drug use were censored after age
21.
To compute a corresponding hazard ratio for the
NHSDA, we first selected the subset of respondents who
reported no hard drug initiation prior to the year preceding
the survey. We then stratified these respondents by
age at the time of the survey. For each respondent age
group we calculated the weighted proportion reporting
initiation of hard drug use in the past year by past year
marijuana use frequency. For example, we divided 12-
year-old respondents into those who did not use marijuana
in the past year, those who used marijuana 1—2
times, 3—11 times, 12—51 times or 52 or more times.
Within each use group we estimate separately the proportion
that initiated hard drugs. We repeat this for all other
age groups. The resulting proportions define the hazard
of hard drug initiation by age for each level of marijuana
use. We assume that the five resulting hazard functions
(one for each level of marijuana use) are age-specific, but
that a single proportional hazards model describes the
relative sizes of the five hazards at all ages. We compute
the proportionality constants as the weighted average of
the hazard ratios across ages in order to allow ages with
less variability to have more weight in the calculation.
This procedure for establishing dose—response hazards in
the NHSDA is inaccurate, since marijuana use frequency
could change after hard drug initiation in the past year.
However, we use this NHSDA estimate only for purposes
of comparison to analogous hazards observed in our modeled
data, not to establish parameters for the model. For
this comparison, our NHSDA dose—response estimates
are sufficient.
MODEL RESULTS
We drew 1 000 000 observations from the joint distribution,
from which three sets of outputs are recorded: simulated
marijuana and drug initiation survival functions,
and ; relative risk of initiating hard drugs by
age 21 for cases with and without prior marijuana initiation,
and the percentage of simulated cases for which
hard drug use preceded marijuana use by at least 1 year
prior to age 22. Because the NHSDA and our simulated
cases record age of drug use initiation in whole years, it is
not possible to determine if hard drug initiation preceded
marijuana initiation if both occurred in the same year.
Therefore, we describe hard drug initiation as preceding
marijuana initiation only if YH < YM.
Model precision
By design, modeled marijuana and hard drug initiation
survival functions, and , closely matched
those for the US population shown in Fig. 2. Indeed,
actual and modeled survival rates differed by 0.009 or
less for each drug at every age.
Gateway effects
Relative risk
In our model, by age 21, users of marijuana were 157
times more likely than non-users to have initiated a hard
drug. In comparison, respondents aged 22 or older in our
NHSDA sample who initiated marijuana use by age 21
were just 24 times more likely than non-marijuana users
to initiate hard drugs. Thus, our model produces a relative
risk phenomenon even greater than that observed in
the US data, even though the model incorporates no gateway
effect. We attribute little significance to the fact that
our model produces a relative risk substantially greater
than that observed in the NHSDA. The denominator in
this ratio is so small that even a slight imprecision in its
estimate could more than account for the difference
between observed and modeled risk ratios. Thus, for
instance, if the true value of Pr {ZH < 22 | ZM > 21} differs
from our NHSDA estimate by as little as 0.013, the true
relative risk could be greater than 190.
In addition, the elevated relative risk of hard drug initiation
among younger marijuana initiates vs. older ones
is also reproduced in the model. Among those aged 22
and older in our NHSDA sample, those who initiate marijuana
by age 15 have 1.60 times greater risk of becoming
a hard drug user by age 22 than those whose marijuana
initiation occurs after age 15. Our model produces the
larger, but still comparable, relative risk for these groups
of 3.44.
Ordering
The proportion of simulated cases for which hard drug
initiation preceded marijuana initiation was 0.011. This
compares with the corresponding estimate of 0.016 from
the NHSDA. Thus, initiation of hard drugs before marijuana was even more rare in our model than in the US
household data, suggesting that no gateway effect is
required to explain the strong ordering effect observed in
youths' drug initiation experiences.
Dose—response
Hazard ratios for hard drug initiation among users of
marijuana vs. those who did not use it in the past year are
presented in Fig. 3. The figure exhibits a strong dose—
response response relationship between marijuana use
frequency and the hazard of hard drug initiation at each
hypothesized correlation between the marijuana use
intensity random effect, x
i, and propensity, qi. Indeed,
even assuming zero correlation between these effects, a
rising dose—response curve is found, with the heaviest
users of marijuana having hazards of hard drug initiation
more than 10 times greater than those of non-users.
The corresponding dose—response curve from the
NHSDA data is plotted as a series of stars in Fig. 3. This
curve bears a striking resemblance to those produced by
the model. For the first two levels of marijuana use frequency
the US data corresponds closely to the assumption
that marijuana use frequency and drug use
propensity have a moderate correlation (r = 0.4). For the
highest marijuana frequencies, US hazard ratios fall
between the moderate and high (r = 0.8) correlation
assumptions.
DISCUSSION
Adolescent drug use initiation
The results reported here demonstrate that a simple common-
factor model with population-based parameters can
reproduce each of the phenomena previously used to
support claims of a marijuana gateway effect. Thus, the
strong relative risk, ordering and dose—response relationships
observed between marijuana use and hard drug initiation
do not require an assumption that marijuana
initiation, or even the first opportunity to use it, increases
the risk of either hard drug initiation or the opportunity
to use hard drugs. While not disproving the existence of a
marijuana gateway effect, our findings demonstrate that
the primary evidence supporting gateway effects is
equally consistent with an alternative model of adolescent
drug use initiation in which use, per se, of marijuana
has no effect on the later use of hard drugs.
Once a general propensity to use drugs is posited, the
relative risk of hard drug use among marijuana users vs.
non-users can be completely accounted for as a simple
consequence of the fact that users of any drug are likely to
have higher drug use propensities than non-users.
Indeed, our model produced hard drug initiation risk
ratios greater than those observed in the NHSDA both for
users vs. non-users of marijuana and for younger vs.
older initiates of marijuana.
With the assumption that use of any drug is conditioned
only on an individual's age, drug use propensity
and opportunity to use drugs, the observed ordering in
drug initiation can be attributed to the fact that opportunities
to use marijuana routinely precede opportunities
to use hard drugs–often by many years. Using just
these assumptions, our model produced rates of hard
drug use preceding marijuana use of just 11 per 1000
individuals, reflecting an even more invariant ordering
than that found in our NHSDA sample, in which 16
of every 1000 individuals try hard drugs before
marijuana.
Finally, even without the reasonable assumption of a
correlation between marijuana use intensity and the
more general propensity to use drugs, the assumptions of
the model suffice to produce a strong dose—response
relationship between marijuana use frequency and
the risk of hard drug initiation. However, introducing
such a correlation strengthens the dose—response relationship
considerably. Indeed, as demonstrated by our
sensitivity analysis, adjustments to the correlation
between marijuana use intensity and drug use propensity
suffice to account for the magnitude of the dose—response
relationship observed for populations of youths. Again,
the observed dose—response relationship between marijuana
use frequency and the risk of hard drug initiation
requires no marijuana gateway effect for its
explanation.
Exhibiting gateway effects by controlling for
common factors
Earlier studies have sought to support claims of a gateway
effect by showing that marijuana use, per se, remains a
powerful predictor of hard drug initiation, even after controlling
for a wide range of candidate 'common factors'
such as individuals' background characteristics, their
risk behaviors and the behaviors of their peers (Yamaguchi
& Kandel 1984b; Fergusson & Horwood 2000). This
approach presumes that the included factors are sufficiently
powerful indicators of any unobserved drug use
propensity that their inclusion should eliminate any spurious
appearance of a relationship between marijuana
use and hard drug initiation. Since we know drug use
propensities in our simulation model, we can examine the
limits of this assumption using a random sample of cases
drawn from our model. To do so, we construct variables
that are more or less reliable indicators of drug use propensity,
where the variances of the normally distributed
error terms are used to control the correlation between
the drug use propensity and its indicator. These indicators
are next included as covariates along with a marijuana
use indicator, m, in the following logistic model of hard
drug initiation by age 22:
(5)
Figure 4 presents the hard drug initiation odds ratios for
marijuana users vs. non-users, after controlling for drug
use propensity indicators (X) with reliabilities ranging
between 0 and 1. This figure demonstrates that drug use
propensity indicators need to be almost perfectly correlated
with true drug use propensity before strong relationships
between marijuana use and hard drug use are
eliminated. Even when the indicator fails to capture just
2% of the variance in drug use propensity (i.e. its reliability
is 0.99), marijuana users appear to have odds of initiating
hard drugs that are twice as great as non-users of
marijuana. Because it is very unlikely that the covariates
included in prior studies have anything like a 0.99 correlation
with drug use propensity, it is hardly surprising
that controlling for these covariates does not eliminate
the association between marijuana and hard drug use.
Model limitations
Several limitations and clarifications on the results are
warranted. Firstly, our model relies on a number of
untested assumptions and simplifications, such as a normal
distribution for propensity and the frailty model for
the joint distribution of age of first opportunity to use
marijuana or hard drugs. To the extent these assumptions
do not approximate corresponding phenomena in
the population of youths, the model represents the process
of adolescent drug use initiation less well. However,
to the extent the model assumptions are plausible, we
have demonstrated one possible process of drug use initiation
that produces all of the gateway phenomena without
requiring a gateway effect. The plausibility of our
model is demonstrated through comparisons with estimates
from the NHSDA. However, our estimates of the
rate at which gateway phenomena occur in the NHSDA
also depend on assumptions that may be wrong, like that
the hazards of hard drug initiation for different marijuana
use frequency groups remain proportional across
age groups. If the assumptions are wrong, our NHSDA
estimates will be biased and the comparisons provide less
good evidence for the plausibility of our simulation
model.
Secondly, we have produced a plausible model of adolescent
drug use initiation that derives many of its parameter
estimates from the NHSDA, a survey of US residents.
However, it is quite clear that many of these parameters,
like marijuana use prevalence, are specific to the population
of youths in the US during the period in which the
data used in this study were collected. As such, our estimates
of the rate at which gateway effects occur in the
NHSDA should not be expected to generalize to other
places or times. Similarly, our model is calibrated to correspond
to this US data, and might produce quite different
results if parameter estimates from a different country or
a different time were substituted for those estimates we
used.
A third clarification concerns the possible effects of
response bias on the appearance of gateway effects in this
study, and every other study relying primarily on selfreports
of drug use to demonstrate gateway effects. Suppose,
for instance, that the likelihood of initiating hard
drugs is, in fact, independent of whether or not someone
has initiated marijuana or the frequency with which they
use it. If there was a systematic under-reporting bias that
led some marijuana users to claim to have never used
either marijuana or hard drugs, or to under-report their
marijuana use frequencies and their use of hard drugs,
these biases could lead to the appearance of both the
relative risk and dose—response gateway phenomena,
although neither truly existed. If response bias accounts
for the gateway phenomena, then the propensity factor
we include in our model may correspond more to some
heterogeneous response bias trait than it does to a true
propensity to use drugs. It is for this reason that we have
been careful to define propensity in terms of the likelihood
of reporting drug use, rather than of engaging in drug
use.
Fourthly, we constructed the model in such a way that
use of hard drugs is independent of use of marijuana,
except insofar as they share a common propensity to use
drugs. This feature of the model holds true regardless of
the particular values selected for drug use opportunities,
use given opportunities or the correlation parameters.
Therefore, even though the data set we use to derive these
parameters might reflect the operations of a true gateway
effect (the NHSDA), we can be certain that model's outputs
do not result from any such effects.
The status of the marijuana gateway effect
The model and analyses described above do not disprove
the gateway effect. Instead, they demonstrate that each
of the phenomena that appear to support such an effect
are, in fact, equally consistent with a plausible alternative
that accounts for the known general liability to use drugs
and the known differences in when youths receive their
first opportunities to use drugs.
Something like a marijuana gateway effect probably
does exist, if only because marijuana purchases bring
users into contact with a black market that also increases
access to hard drugs (Goode 1970). However, this observation
does not refute the analysis presented above, since
there are at least two ways that gateway effects could
exist without undermining a model of drug use initiation
that fails to include them. Firstly, it is possible that any
true marijuana gateway effects can explain only a tiny
fraction of individuals' risk of hard drug use in comparison
with the risk attributable to their propensities to use
drugs, and is therefore a negligible factor in our model. A
second possibility is that marijuana use could increase
the risk of hard drug use for some youths, while decreasing
the risk for others. As such, true marijuana gateway
effects may be counterbalanced in the population by negative
marijuana gateway effects, with the net effect of
marijuana use on hard drug use being insignificant. Negative
gateway effects could occur if, for instance, marijuana
sated some youths' desires to experiment with illicit
drug use, or if unsatisfying (or penalized) marijuana use
experiences discouraged drug use progression among
some youths.
The purported marijuana gateway effect is frequently
invoked by policy makers as among the primary reasons
to resist efforts to relax marijuana policies, such as permitting
the medicinal use of marijuana (US Department
of Health and Human Services 1999). Whereas social scientists
often acknowledge that relative risk, ordering in
drug use initiation and dose—response phenomena do not
prove the existence of a marijuana gateway effect, they
too have frequently drawn policy conclusions that presuppose
such an effect. For instance, many have concluded
that by postponing youths' marijuana initiation,
prevention efforts will reduce the likelihood of hard drug
use and abuse (Yamaguchi & Kandel 1984b; Kandel et al.
1992; Golub & Johnson 2001). Our model demonstrates
how the observed correlations in the use of marijuana
and hard drugs may be entirely due to individuals' propensity
to use drugs and their opportunities to use them.
As such, marijuana policies would have little effect on
hard drug use, except insofar as they affected either an
individuals' propensity to use any drugs (as might be the
case with drug use prevention programs) or they resulted
in hard drugs becoming less available or available later in
youths' lives.
Because our model provides a straightforward, parsimonious
and plausible explanation for each of the phenomena
used to support claims of a marijuana gateway
effect, we believe the validity of that effect must remain
uncertain until new evidence is available directly comparing
it with the alternative common-factor model.
ACKNOWLEDGEMENTS
This research was supported by funds from the Center for
Substance Abuse Treatment (CSAT) of the Substance
Abuse and Mental Health Services Administration,
Department of Health and Human Services (grant
#TI11433, contract #270-97-7011), by the National
Institute on Alcohol Abuse and Alcoholism (grant #R01
AA12457) and by the Drug Policy Research Center at
RAND. The opinions expressed herein are those of the
authors and do not reflect official positions of the Government.
The authors thank Jonathan Caulkins, Mark Kleiman,
Robert Macoun, Rosalie Pacula and Peter Reuter
for helpful comments on earlier drafts, and Amanda
Geller and Mary Watson for administrative assistance.
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