Background

     How does simultaneous addiction (co-addiction) or sequential
(serial) addiction relate to the severity of pathological
gambling in gambling patients and Gamblers Anonymous members in
Maryland today?  Whether and to what extent compulsive gambling
patients are beset with other addictions is a question that
emerged from ongoing research for the Task Force.  When asked
whether they have ever had or do have an alcohol problem, 50.8
percent of Maryland compulsive gambling patients in the past five
years reply in the affirmative.  When asked whether they have
ever had or do have a drug problem, 26.7 percent of them answer
in the affirmative.  Among the Maryland Gamblers Anonymous (GA)
respondents, of whom about 80 to 90 percent returned the ques-
tionnaires during this past year, 26 percent reported having had
or having an alcohol problem while 14 percent reported having had
or having a drug abuse problem.  Because the closed-ended
responses of patient data did not distinguish between past and
present addiction, a confusion of simultaneous (co-addiction) and
sequential (serial) addiction could arise from these responses. 
Yet these percentages by themselves do not compel conclusive
inference.  It was the discovery that these variables were
potentially significant in the models that were developed that
necessitated further exploration of their nature.  


                        Problem Formulation

     The question of the severity of the gambling problem was
addressed with research for the Maryland Task Force on Gambling
Addiction.  The search for factors which aggravate this condition
was undertaken in hopes of identifying the sources of the prob-
lem, thereby sharpening the focus on ways to ameliorate or
eliminate the compulsive gambling problem.  A ratio of the amount
of the gambling debt to the annual income of the respondent was
constructed.  This ratio comprises an index as to the severity of
the gambling problem.  In the course of developing mathematical
models to help predict this index, it was found that co-addiction
or serial addiction could be significant.

     The ratio is then split into thirds so that it would have
three values: low, medium and high.  Thirty-three and three-
tenths percent of the responses are lumped into the low category,
the next third into the medium category, and the remaining ratios
reside in the high category.  An ordinal logit analysis was
performed using this ratio variable as a dependent variable. 
From this analysis, the significance, direction, and magnitude of
other variables on this gambling problem severity ratio were
identified, estimated, and fitted.  Next, the high and medium
categories were combined.  By collapsing this variable into two
values, a dichotomous variable was constructed  with coding that
differentiates between low and greater than low severity of
gambling ratios.  A logistic regression equation of variables
that were hypothesized to predict a form of this ratio was then
run.  The formulation of this ratio provides built-in variation
which can be analyzed as a tool to investigate which factors
contribute to the worsening of the condition and which factors
contribute to the amelioration of the problem.  One can determine
which factors appear to be associated with lower levels of this
severity and which factors appear to be associated with higher
levels of this severity.  The logistic regression equation
permits estimation of the probability of being in the higher two
categories over that of being in the lower category.  This
procedure was performed separately for both the patients and the
GA members.  For patients and GA members, models were fitted to
see what variables significantly predicted this kind of outcome.

     While the surveys were similar, they were not identical. 
Not all of the variables in one survey were in the other.  There
were some common variables in both the patient and GA models --
such as, past or present drug abuse, past or present alcohol
abuse, and educational level (high school dropout v. high school
graduate and beyond) of the respondent. 

     Nevertheless, each estimated and fitted model, whether
patient or GA, possessed variables that the other model did not
include.  The patient model contained a test of whether the
mother died before the respondent was 18 years of age, while the
GA models did not.  The GA models contained variables of whether
the gambler considered or attempted suicide, whether the family
had to resort to public assistance as a direct result of
gambling, and whether the gambler committed illegal acts as a
result of the gambling.  In the ordinal logit GA model, it was
found that whether the gambler sought counseling because of
gambling was significant.  These variables were dummy variables,
coded according to whether the GA member did or did not do these
things.  These variables were found to be significant in their
respective models.

     It was possible to determine whether the inclusion of these
variables improved the predictability of the models.  It was also
possible to ascertain the final predictability of these models. 
Moreover, with this form of analysis, which variables were
noteworthy and which were not could be discovered.  From the
model testing, identification of the direction of influence of
the variable was made possible -- those variables which had a
positive association with the outcome variable and which had a
negative link to that logit.  The size of the effect of each of
the variables was also computed.  Both models explained the
severity of the problem well.  The models were capable of
predicting more than 73 percent of the responses accurately.  


 


                           Patient Model

     Consider the model of the patients first.  The significant
independent (some persons think of these as predictor) variables
of this model were the number of years of education, existence of
physical or sexual abuse in the past or present, the existence of
past or present drug abuse, and whether the mother of the
respondent died before the respondent was 18 years of age.  All
of these variables had a significant positive relationship with
higher levels of severity, except that of drug abuse.  Drug abuse
had a significant negative relationship with the outcome variable
among the patients.  That is to say, the less the patient was
likely to have had or to have a drug problem, the more serious
the gambling problem would have been.  Conversely, the less
serious the gambling problem might have been, the more likely the
patient was to have had or have a drug problem.  Alcohol was not
significantly related to the severity of the gambling problem
among these patients at all.  

     The magnitude of these significant influences on the severi-
ty of the gambling problem is also of great interest.  The early
death of the mother was the most powerful predictor.  The past or
present physical or sexual abuse was the second most powerful
influence.  Third, following hard on the heels of such abuse, was
the level of the patient's education.  High school graduates were
more likely to get involved in this high-risk activity than were
those who dropped out of high school.  Finally, the drug problem
was found to be related, albeit negatively.  Although this was
not a strong relationship, the more the person was involved in
drug abuse, the less likely he was to have a more serious
gambling problem.  Valerie Lorenz suggested that clarity and
control may have been of major concerns here, not spending the
money on drugs.  To be sure, the more the money was spent on
drugs, the less it was available for gambling; the more it was
spent on gambling, the less available the money was for expendi-
ture on drugs.  The more severe the gambling addiction, the less
they might spend money on drugs.  The model for the patients can
be formulated by the following equation.

     That the model fit the data with very little difference
between the observed logit scores as they were found in the data
and those scores predicted by the formula is evidenced by the
lack of significance of difference in the Goodness of Fit 
statistic.  Also supporting this inference are the high
correlations between the observed and the predicted scores
indicated by Somer's Dxy and the Gamma correlation coefficients.

     The relative effect of the odds being in the upper of the
two binary categories can be found in the partial odds.  This
indicates the relative effect a variable had on the odds of a
predicted score being in the upper of the two categories of the
dependent variable.  To compute the odds of a particular person
having a greater than low severity of gambling problem, his
scores on each variable may be multiplied by the coefficients of
those scores and then summed.


             Introduction to Gamblers Anonymous Models

     With the Gamblers Anonymous sample, slightly different     
models were obtained.  Not all of the same variables were in the
two models.  One reason for this was that the surveys were not
identical.  The early death of the mother was not included in the
GA survey.  Nor was the past or present physical or sexual abuse. 
The coding on the education variable was a little different in
the GA survey from that in the patient survey.  Not only were
different questions asked, the target populations were different. 
The patients consisted of those persons receiving treatment for
their compulsive gambling at one of the three Maryland treatment
centers.  The GA respondents were the persons afflicted with a
gambling problem and attending GA self-help sessions in the State
of Maryland in 1989.

     In the GA models, we identified, estimated, and fitted
independent variables for the commission of illegal acts,
soliciting of public assistance by a family member, the
preference for casino gambling, and contemplation or attempted
suicide by the gambler.  All these variables significantly and
positively related to the severity of the gambling problem.
       
     The direction of the relationship between severity of the
gambling and having had or having an alcohol problem is signifi-
cantly negative.  While there appeared to be some co-dependency
of alcohol and gambling from the frequencies, the ordinal logit
and logistic regression models for the Gamblers Anonymous people
were more informative.  With respect to co- or cross-addiction,
the GA logit and regression models showed that drug abuse is not
significantly related to the severity of the problem at all, but
alcoholism is.  This means that gambling severity is inversely
related to the incidence of past or present alcohol dependency. 
Again there may be confusion between the concurrent and the
serial addiction since this distinction was not made in the
questions of both surveys.


                        Ordinal Logit Model

     The ordinal logit requires brief explanation.  The logit, or
natural log of the odds ratio of the gambling severity ratio, is
used for this analysis.  Because the dependent variable has three
underlying levels -- namely, low, medium, and high -- there can
be two cut points which divide this ratio.  The ratio can be cut
between the low and the medium level or we can cut it between the
medium and the high level.  Using these cut-points, the probabil-
ity of obtaining the upper level can be divided by the  probabil-
ity of obtaining the lower level for that cut-point.  When the
lower cut-point is used, then Alpha1 is used for the equation. 
Otherwise, the Alpha2 is used for the equation.  The upper
probability divided by the lower is the odds ratio.  The natural
log of this odds ratio is the logit.  Hence the ordinal logit
makes use of the ordering in the dependent variable.  The com-
puted GA ordinal logit model is very revealing.
     
     From the ordinal logit model developed and presented below,
it can be seen that the increased probability of severity of the
gambling problem is positively associated with the commission of
illegal acts, the seeking of public assistance on the part of a
family member or the gambler himself, whether the heaviest form
of gambling is done in the casino, or whether the gambler consid-
ered or attempted suicide.  The incidence of these events, each
coded as a dummy variable with values 1 for occurrence and 0 for
non-occurrence of the event, were all associated with a greater
severity of the gambling problem.  Only past or present alcohol
dependency was significantly negatively associated with increased
gambling problem severity, perhaps out of a need for clarity and
control.  Drug abuse is not significantly related to severity of
the gambling problem among those inclined to self-help, only
among those who feel the need to undergo treatment.  Again, there
is more reason to begin to doubt the likelihood of co-addictive
tendencies among the Maryland compulsive gamblers.  





     The model significantly improves the fit from the null model
as can be seen from the probability of the model chi-square. 
From the model summary statistics in Table 3, it can be seen that
this model fits the data well.  The nonparametric correlations
between the observed logit scores and those predicted by the
model are .58 and .61, for the Somers' Dxy and Gamma,
respectively.  

     The odds change in the severity of the gambling problem
associated with a unit change in the independent variable may be
computed by exponentiation of the beta coefficient.  The relative
effects of the independent variables on the odds are found in
Table 4.

-2 Log Likelihood = 116.23
Model Likelihood Ratio Chi-square= 32.02, df=5, p =.001**
Goodness of Fit Pearson Chi-square= 87.91, df=80, p=.260

                            Conclusions

     The co-addiction of alcohol, gambling and drugs is a serious
question that merits attention.  Our concern arises owing to the
negative coefficients in the logit models.  These coefficients
clearly indicate a significant, negative statistical relationship
between the severity of the gambling problem, on the one hand,
and serial or co-addiction, on the other.  That past or present
drug problems are negatively related to severity of the gambling
problem among patients is suggestive of an inverse association
between drug and gambling problems. 

      Among GA members, drug problems past or present did not
seems to be significantly related to the severity of the gambling
problem.  Instead, the GA members evinced a statistically
significant negative relationship between the severity of the
gambling problem, on one hand, and past or present alcohol abuse,
on the other.  Concern about the apparent inconsistency between
the severity of the gambling problem and other types of
addictions prompted further investigation. 


             The Question of the Addictive Personality

     In order to investigate the matter of the addictive person-
ality, the question of concomitance of addiction arises.  The
concomitance of addiction is not the same as the severity of the
addiction.  Instead, this question relates to whether different
addictions take place sequentially or simultaneously.  We do not
mean by concomitant addiction, that several addictions are
coterminous.  They may start at different times, overlap with one
another, and end at different times.  We distinguish concomitant
addiction from sequential addiction by saying there is overlap in
the former, and none in the latter.  

     The completeness of the data available to us in our
investigation of concomitant and sequential addiction required us
to consider several approaches in dealing with incomplete answers
to survey questions.  One approach, the standard, is listwise
deletion: the practice of deleting multiple observations whenever
the respondent fails to answer one of the questions involved in
an analysis.  There are very good reasons for taking this
approach.  This approach is a common one to render these results
comparable to those of other analyses.  If the respondent refuses
to answer any one of the questions, answers to which are
necessary for coming to a conclusion about the respondent, then
it might be presumptuous to impute characteristics to that
respondent without good reason.  Loosely based imputations lead
to erroneous conclusions, for which reason this practice ought to
be generally eschewed.  Who knows enough to draw these
conclusions is open to question.  Hence listwise deletion is a
reasonable and generally applicable research practice.  

     There may be circumstances where the standard approach may
not be warranted.  When respondents are hurried or impulsive,
they may not be methodical in their responses.  They may believe
that once they have indicated something the investigators can
draw logical inferences and that they need not complete other
questions addressing the same subject.  Sometimes, when questions
are personally embarrassing, respondents may be reluctant to
answer them.  When answering a question poses a threat to the
security of the respondent, respondents might also be reluctant
to be forthcoming.  Questions concerning substance or alcohol
abuse might appear to be threatening to some respondents.  

     Not answering a question of when a person ceased engaging in
an abuse may be a way of tacitly admitting continuing substance
abuse without expressly committing the answerer to the possible
liability.  For these reasons, a missing response to such a
question might allow an inference that the abuse continues. 
Limited inference thus might be used to complete unanswered
questions about when an addictive individual ceased practicing an
abuse.  But such inferences have to be drawn with great care.  

     If respondents do not answer other questions, it may still
be possible to fill in those missing answers.  Doctor Valerie
Lorenz observes that Gamblers Anonymous meetings in Maryland are
closed meetings, and suggests that attendees must be gamblers. 
It may be reasonable to assume that although a GA member
responding to our survey did not give the date of inception of
gambling addiction, nonetheless he very probably is a gambling
addict.  Such a conclusion will lead to more of a correct than an
incorrect assessment, she argues.

     In this section of this paper, we embark on an analysis that
uses two approaches: first, the standard listwise deletion
technique; second, applying reasonable assumptions in the absence
of explicit answers.  See Table 7 for a summary.

     When we examine simultaneous addiction to alcohol and
gambling, using standard listwise deletion, we first find that
there are seventeen, possibly eighteen, persons who indicate that
at some time in their lives they have been simultaneously
addicted to gambling and alcohol.  Setting aside standard
listwise deletion and assuming that all the respondents are
gambling, whether they say so or not, we find that 19, possibly
20 persons out of the total of 91 have at one time or other been
co-addicted to gambling and alcohol.  There is one person in
doubt because it is not clear whether his alcohol and gambling
addictions overlapped.  Nevertheless, approximately 19 to 22
percent of the GA members report having been simultaneously
addicted to gambling and alcohol.  Although this is not a large
proportion of these individuals, it appears to be a significant
proportion.  

     For co-addiction to gambling and drugs, we use both
approaches as well.  First, we make no assumptions about the
respondents' answers.  We find that eight respondents at one time
in their lives were co-addicted to gambling and drugs.  If we
assume that all of the GA respondents were addicted to gambling,
whether or not they so admitted, we find that ten of them report
co-addiction at one time in their lives.  The proportion of dual
addicts with gambling and drug problems ranges from 8.8 to 10.9
percent.  This, too, is a small percentage. 

     An even smaller proportion of the GA members were found to
have had a simultaneous three-way addiction.  Five persons of the
91 surveyed reported having at one time a simultaneous three-way
addiction problem with gambling, drugs and alcohol.  If we assume
that all respondents are gambling addicts, though they may not
have indicated such, there were six persons reporting a three-way
addiction.  This 5.5 to 6.6 percentage range we find to be much
smaller than either of the other two.

     How many of these persons have serial rather than dual
addiction?  We find that a small number of the individuals report
a strictly serial rather than a concurrent addiction.  Only one
person definitely indicates a purely serial addiction.  He began
with drugs and then went to gambling.  Another person may have
had a serial addiction or his addictions may have overlapped (he
gave the same age in years when he ended his alcohol problem and
began his gambling problem).  Only 1 to 2 percent of the GA
members exhibited evidence of strictly serial addiction.  

     How many of these persons exhibited serial as well as co-
addiction?  Three, possibly four persons reported serial as well
as simultaneous abuses.  Some persons began with a serial
addiction and moved to a simultaneous addiction.  They may become
dependent on drugs and then move to becoming concurrently
addicted to gambling and alcohol.  Others may become dependent on
alcohol and then abandon that dependency, only later to become
concurrently addicted to gambling and drugs.  Still others come
to gambling first, and later become simultaneously addicted to
drugs and alcohol.  Only 3.3 to 4.4 percent of the GA respondents
reported such a scenario of dependency.  

     The problem with these data is that they are not reliable. 
Except for the date of inception of gambling addiction, the
proportions of missing values for the dates of inception and
cessation of dependencies are unacceptably high.  When more than
thirty percent of the respondents did not answer a question, the
answers for that question should usually be thrown out and not
given serious credence.  The missing value rates for the
inception and cessation of these three dependencies are given
below.  Whether the questionnaire contained questions that were
too sensitive to produce adequately complete responses, or
whether there was a problem with the administration of the
questionnaire, the lack of response casts a shadow of doubt on
the validity of the answers given, as well as on the reliability
of this part of the report.