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Contents lists available at SciVerse ScienceDirect

Drug and Alcohol Dependence

jo u rn al hom epage: www.elsev ier .com/ locate /drugalcdep

odeling longitudinal drinking data in clinical trials: An application to theOMBINE study�

tacia M. DeSantisa,∗, Dipankar Bandyopadhyayc, Nathaniel L. Bakerb, Patrick K. Randalld,aymond F. Antond, James J. Prisciandaroe

University of Texas Health Sciences Center, 1200 Herman Pressler Dr, Houston, TX 77030, United StatesMedical University of South Carolina, 135 Cannon Street, Suite 303, Charleston, SC 29425, United StatesUniversity of Minnesota, A452 Mayo Building, 420 Delaware St., SE, Minneapolis, MN 55455, United StatesMedical University of South Carolina, 67 President Street, Charleston, SC 29425, United StatesMedical University of South Carolina, 125 Doughty Street, Suite 190, Charleston, SC 29425, United States

r t i c l e i n f o

rticle history:eceived 25 June 2012eceived in revised form 4 February 2013ccepted 8 February 2013vailable online xxx

eywords:linical triallcoholismaltrexonecamprosateognitive behavioral interventionero inflationoisson hurdle model

a b s t r a c t

Background: There is a lack of consensus in the literature as to how to define drinking outcomes in clinicaltrials. Typically, separate statistical models are fit to assess treatment effects on several summary drinkingmeasures. These summary measures do not capture the complexity of drinking behavior. We used theCOMBINE study to illustrate a statistical approach for examining treatment effects on high-resolutiondrinking data.Methods: This is a secondary data analysis of COMBINE participants randomly assigned to naltrexone,acamprosate, with medical management and/or combined behavioral intervention (CBI). Using a Poissonhurdle model, abstinence and number of drinks were simultaneously modeled as a function of treatmentand covariates. An emphasis was placed on the evaluation of “risky drinking” (3 drinks/day for womenand 4 for men).Results: During treatment, naltrexone increased the odds of abstinence vs placebo naltrexone (OR = 1.35[1.06, 1.65]) but receiving CBI in addition to naltrexone (vs not) obscured this effect; thus, the naltrexoneeffect was largest in the group not receiving CBI (OR = 1.87 [1.29, 2.46]). Naltrexone vs placebo naltrexone

also reduced the risk of drinking in those who resumed risky drinking (RR = 0.58 [0.24, 0.93]) and increasedthe odds of maintaining low risk drinking (OT = 1.99 [1.07, 2.90]). Both effects were strongest in theabsence of CBI when only “medical management” was provided.Conclusions: The hurdle model is an appropriate statistical tool for assessing the effect of treatment on thetwo part drinking process, abstinence and number of drinks. When applied to COMBINE, results bolster

romo

the use of naltrexone in p

. Introduction

The combined pharmacotherapies and behavioral interventionsor alcohol dependence (COMBINE) study was the largest studyver performed of pharmacotherapy for alcoholism in the Unitedtates (COMBINE Study Group, 2003; Anton et al., 2006). It wasesigned to assess the benefits of combining behavioral and phar-acological interventions in the treatment of alcohol dependence,

Please cite this article in press as: DeSantis, S.M., et al., Modeling longitudstudy. Drug Alcohol Depend. (2013), http://dx.doi.org/10.1016/j.drugalcde

leading preventable cause of morbidity and mortality and a majorontributor to health care costs (Mokdad et al., 2000; Grant et al.,004; McKenna et al., 2005). In the COMBINE study, naltrexone

� Supplementary material can be found by accessing the online version of thisaper.∗ Corresponding author. Tel.: +1 617 669 6258.

E-mail address: stacia.m.desantis@uth.tmc.edu (S.M. DeSantis).

376-8716/$ – see front matter © 2013 Elsevier Ireland Ltd. All rights reserved.ttp://dx.doi.org/10.1016/j.drugalcdep.2013.02.013

ting abstinence and reduction in risky drinking.© 2013 Elsevier Ireland Ltd. All rights reserved.

(Kranzler and Van Kirk, 2001), acamprosate (Mason, 2003; Mannet al., 2004), and combined behavioral intervention (CBI), weregiven in combination according to a placebo-controlled 2 × 2 × 2factorial design over 16 weeks (Table 1). It was hypothesized thatacamprosate would be effective in promoting abstinence while nal-trexone would be effective in reducing the amount of drinking onceany drinking had occurred; CBI was proposed to reinforce behav-iors toward abstinence and/or to reduce relapse once any drinkinghad occurred, and it was hypothesized to interact positively withnaltrexone (O’Malley et al., 1992; Anton et al., 1999). A medicalmanagement (MM) procedure designed to reflect what might occurin primary care practice was provided for participants in all but onestudy group.

inal drinking data in clinical trials: An application to the COMBINEp.2013.02.013

In the COMBINE study, the two a priori defined primary out-comes were ‘time to the first day of heavy drinking’ and ‘percentdays abstinent’ in the 16-week treatment period as derived fromcalendar recall; these summary measures are the most common

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Table 1Study design and randomization sample size. ACA = acamprosate, NTX = naltrexone,CBI = cognitive behavioral intervention.

Placebo ACA ACA

Placebo NTX 153 152No CBI

NTX 154 148Placebo NTX 156 151

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rimary outcomes specified in clinical trials of alcohol use dis-rders (Babor et al., 1994; Finney et al., 2003). Naltrexone (+MMlone) or CBI (+placebo acamprosate + naltrexone + MM) increasedime to first heavy drinking day compared to MM alone + placebocamprosate but, contrary to expectation, there was no additionaldvantage of combining CBI with naltrexone over each monother-py. No effects of either medication on percent days abstinent wereound. The failure to find main effects of acamprosate, (alone or inombination with CBI or naltrexone), was unexpected given theositive results from studies of acamprosate (Mason, 2003; Mannt al., 2004) and of the combination of acamprosate and naltrexoneonducted in Europe (Kefer et al., 2003; Feeney et al., 2006).

Experts disagree on what are the most relevant summary meas-res of drinking outcomes in clinical treatment trials (Cisler andweben, 1999; Meyer, 2001; Wang et al., 2002; Johnson et al., 2004;ckay et al., 2006; Shirley et al., 2010; Prisciandaro et al., 2012)

nd Cochrane reviews have demonstrated a lack of consensus inrimary outcome definitions across alcohol trials (Srisurapanontnd Jarusuraisin, 2008; Rosner et al., 2009). Further, when drinkingutcomes are analyzed as summary measures, for example, whenonsumption over a 16-week period is summarized into a singlendpoint (e.g., percent days abstinent), high resolution informa-ion about the complexity of drinking behavior is lost. As a result,he power to detect significant differences in drinking outcomes

ay be reduced. The limitations of two of the most commonly usedummary statistics are illustrated in Fig. 1. Fig. 1 displays 16 weeksf daily drinking data for 4 patients from the COMBINE study forhom summary measures may be uninformative. Patients 1 and

had one early onset heavy drinking day in the entire 16-weekreatment period but did not drink any other day in that period.atients 3 and 4 never officially met a predefined heavy drinkingay in those 16 weeks, even though they drank several drinks onany days since the start of the study. Therefore, in the “time

o first heavy drinking day” analysis of the original trial report,atients 1 and 2 are considered early treatment ‘failures’, whileatients 3 and 4 are considered a treatment ‘success’. Patients 3 and

have similar percent days abstinent even though patient 4 drinksore on non-abstinent days, a behavior that is undetectable when

nalyzing the summary statistic “percent days abstinent”. Thesellustrations underscore the limitations of summary endpoints inssessing drinking behavior.

Instead, abstinence and the number of drinks consumedhroughout the study period may be conceptualized as separate butorrelated processes. These outcomes are usually analyzed usingeneralized linear models (GML) but zero-inflated Poisson or bino-ial (ZIP, ZIB) regression may be used to model consumption if data

iolate the assumptions of GLMs. There have been several applica-ions of such zero inflated models in the substance use literatureLe and Galea, 2010; Hu et al., 2011; Meszaros et al., 2011; DeSantist al., 2011; Fielder et al., 2012; Peeters et al., 2012; Walley et al.,012). However, the statistical assumption of zero inflated mod-

Please cite this article in press as: DeSantis, S.M., et al., Modeling longitustudy. Drug Alcohol Depend. (2013), http://dx.doi.org/10.1016/j.drugalcde

ls is that zero drinking arises from a set of patients who haveero risk of drinking. Given that all patients in the COMBINE studyre substance-dependent at baseline, this assumption is unrea-onable. An alternative 2-part Poisson hurdle model that assumes

PRESSDependence xxx (2013) xxx– xxx

subjects remain at risk for drinking for the duration of the study ismore appropriate (e.g., Mullahy, 1986; McLachlan and Peel, 2000;Bandyopadhyay et al., 2011). Thus, the objective of this paper isto re-analyze the COMBINE data using a two-part hurdle model,to extend this model to accommodate low and high risk drinkingdefinitions, and formally to compare results to those obtained fromthe original trial report.

2. Methods

2.1. Participants and procedures

Participants in the COMBINE study included 1383 eligible alco-hol dependent individuals who were randomly assigned to 1of 9 groups for 16 weeks of treatment. In a 2 × 2 × 2 factorialdesign (consisting of n = 1226 patients), all eight groups receivedMM, 4 groups received more intensive counseling (CBI), andpatients in all 8 groups received either active/placebo naltrexone oractive/placebo acamprosate yielding 4 medication groups, withineach level of counseling (CBI/no CBI). This is illustrated in Table 1.Naltrexone, an opioid receptor antagonist, was studied based onevidence that it reduced the risk of heavy drinking in most stud-ies (Kranzler and Van Kirk, 2001; Srisurapanont and Jarusuraisin,2008) while acamprosate, thought to reduce glutamatergic hyper-activity associated with protracted abstinence, was thought tomaintain abstinence within varied behavioral treatment frame-works (Mason, 2003; Mann et al., 2004). Medical managementwas designed as a means of enhancing medication compliance andreinforcing sobriety that could be used in a primary care or man-aged care setting by nonspecialists (Pettinati et al., 2004, 2005;Miller, 2004; Longabaugh et al., 2005). A ninth group received CBIalone and no pills – as in previous COMBINE reports, this group wasnot analyzed here since it is outside the 2 × 2 × 2 factorial design.This results in a total sample size of 1226 of which data are availableon 1195 for the current analysis.

2.2. Measures

Individuals were assessed 9 times during the 16 weeks oftreatment and 3 additional times (i.e., 26, 52, and 68 weeks post-randomization) during the 52 weeks following treatment. Drinkingwas assessed via time line follow-back (TLFB), a calendar recallmethod that has been extensively validated to provide accuratemeasures of daily drinking. Secondary outcomes including moodand quality of life were also obtained. Primary and secondary anal-yses of the clinical trial have been reported (Anton et al., 2006;LoCastro et al., 2009; Witkiewitz et al., 2010; Gueorguieva et al.,2010; Prisciandaro et al., 2012) and data are publicly available fordownload following registration on the National Institute on Alco-hol Abuse and Addiction website. The reader is referred to theprimary report for further information on study design and meas-ures (Anton et al., 2006).

2.3. Statistical analyses

Abstinence and reduction in drinking are conceptualized asseparate but correlated processes; abstinence was the target ofacamprosate and reduction in drinking the target of naltrexone(Littleton and Zieglgansberger, 2003). Since it was initially hypoth-esized that the two medications might affect different facets of thealcohol consumption process (i.e., abstinence violation and sub-sequent alcohol consumption), the Poisson hurdle model, which

dinal drinking data in clinical trials: An application to the COMBINEp.2013.02.013

promotes a 2-stage decision making process that parallels this con-ceptualization, is a useful tool to assess treatment effects (Fielderet al., 2012). The first stage involves moving through a zero realiza-tion state (i.e., abstinence days). Once this “zero hurdle” is crossed,

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ntativ

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Fig. 1. Drinking patterns of 4 represe

hat is, once drinking has been re-established, the second stageetermines the number of drinks per day. The two processes areodeled via two regressions (logistic and Poisson), (i) generates

he “zeros”, i.e., patients who are believed to be at least tem-orarily abstinent and (ii) generates counts (drinks consumed)trictly greater than zero. Treatment assignment and covariates arellowed to predict the zeros and the counts in (i) and (ii). Correlationetween the two parts is induced by the introduction of shared ran-om intercept. Covariates enter the model via a logistic regressiono predict abstinence, and via a Poisson regression to predict con-umption after drinking is resumed. Full model details are shown inhe Supplementary material. The set of regression coefficients areenoted by ̌ and � for the logistic and Poisson regression compo-ents, respectively. The exponent of each component of ̌ is definedfor comparing treatments A:B) as “the odds of abstinence (zerorinking) in treatment A:B” and the exponent of each componentf � is defined as “the risk of increased drinking in treatment A:Bfter drinking has been resumed”.

To establish a longitudinal outcome variable of reasonableimension, the TLFB was summarized into average number ofrinks per day for each week. This was rounded to the nearest wholeumber, resulting in a zero inflated outcome since the majorityf patients did not drink during the treatment period. Covariatesshown in Supplementary Table 1) included ordinal week, threendicators for each of the three active treatments, three inter-ction terms formed by these treatment indicators, and a threeay interaction. To parallel the primary analysis, baseline aver-

ge number of drinks per day for the past 30 days and study centerere also adjusted for (Anton et al., 2006). A hurdle model with

hared random effects is subject to computational difficulty if tooany covariates are included. Thus, exploratory work that incor-

orated covariates in both the abstinence and drinking part of theodel was performed and determined that study center and prior

rinking better predicted abstinence. Thus, these covariates wereetained in the hurdle part of the model while week, which betterredicted drinking, was retained in the drinking part of the model.reatments and their interactions were included in both parts ofhe model.

Please cite this article in press as: DeSantis, S.M., et al., Modeling longitudstudy. Drug Alcohol Depend. (2013), http://dx.doi.org/10.1016/j.drugalcde

The NIAAA considers a heavy drinking day as being 5 or moretandard drinks for men and 4 or more for women (Falk et al.,010). Assessing the low level “harmful” or “risky” drinking cutoffdds another dimension to the existent literature. Since a hurdle

e patients from the COMBINE study.

can be placed at any number of drinks determined by experts,we utilized this NIAAA cutoff to formulate a “low risk drinkinghurdle model” rather than a zero hurdle model. To achieve this,a second model was developed and fit using the expert consen-sus that <4 drinks/day for women and <5 drinks/day for menrepresents non-harmful or low risk drinking. This involves a mod-ification to the denominator of the model likelihood where thesupport of the hurdle distribution is demarcated at greater than3 and 4 drinks for women and men. This model formulationand associated SAS code are shown in the Supplementary mate-rial.

To compare the zero drinking and risky drinking hurdle modelsto a commonly used longitudinal Poisson regression model (e.g., Leand Galea, 2010; Bandyopadhyay et al., 2011; Walley et al., 2012)three statistics were calculated. The Akaike information criteria(AIC) and Bayesian information criteria (BIC) were used to comparenon-nested models. Smaller values of these criteria indicate a bet-ter fit. The Vuong likelihood ratio-based test was used to comparenested models. In short, the Vuong test tests the null hypothe-sis that two models under comparisons are equally close to the“true” model for the data, against the alternative hypothesis thatone model is closer (Vuong, 1989). A significant p-value on theVuong test (p ≤ 0.05) indicates that the model in question is closerto the true model than the reference model (where the longitu-dinal Poisson regression is the reference model). Hurdle modelresults are presented in terms of relative risks (RR), odds ratios(OR) and 95% confidence intervals, or regression betas and standarderrors (SE).

Finally, to parallel the COMBINE study’s a priori hypotheses,treatment period (weeks 1–16) was analyzed separately from posttreatment period (weeks 17–26). The reason for separate modelingis that treatment was expected to be effective during the treatmentperiod but after cessation of treatment, maintenance of the effectis of interest. These are considered two independent a priori tests,thus the 3 models (zero hurdle, risky hurdle, and Poisson) were fitfor each period. For each time period assessed, one could envision acorrection for multiple testing for the three treatment variables, forthe invocation of a 2 part model (i.e., 2 correlated regressions each

inal drinking data in clinical trials: An application to the COMBINEp.2013.02.013

with treatment covariates), or for the other covariates in our model(prior drinking, week, center). However, corrections were not usedsince the treatment effects were hypothesized a priori, becausethe utility of the two part model is to help protect against type I

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rror rate inflation in the first place, and because the significancef remaining covariates were not of primary interest.

. Results

.1. Treatment period

Table 2 shows parameter estimates, standard errors, and asso-iated p-values for all variables for both hurdle models fit to thereatment period (weeks 1–16). For both models, there is a signif-cant effect of week on consumption, indicating increased alcoholonsumption over the treatment period. Although Table 2 revealshich treatment interactions are significant, due to the compli-

ated study design, post hoc contrasts were necessary to obtainhe main effect and the pairwise estimates presented in Table 2.able 2 displays odds ratios for abstinence and relative risks foronsumption, along with 95% confidence intervals, for all contrastsesulting from the zero hurdle model and the low risk drinking hur-le model. The main effects were obtained by averaging estimatesver the appropriate cells of the design in Table 1. The main effectstimates are interpreted, for example, as acamprosate vs placebocamprosate.

The zero hurdle model showed a significant naltrexone by CBInteraction in the negative direction ( ̌ = −0.67, SE = 0.22, p = 0.003)ndicating CBI reduced the effectiveness of naltrexone on absti-ence when given with MM only (no CBI). In the presence ofignificant interactions, main effects must be interpreted with cau-ion, thus all pairwise contrasts were examined (Table 3). Thereas a significant main effect of naltrexone on abstinence (OR = 1.35

1.06, 1.65]); however, due to the fact that CBI reduced the naltrex-ne effect, the comparison with the greatest OR of abstinence wasaltrexone + no CBI vs placebo naltrexone + no CBI (OR = 1.87 [1.29,.46]). Although there was no main effect of CBI on abstinence,here was an increased odds of abstinence in the CBI + placebo nal-rexone group vs the no CBI + placebo naltrexone group (OR = 1.561.08, 2.05]).

If any drinking is resumed, the Poisson part of the model assesseshe effects of each treatment on number of drinks consumed (bot-om of Table 2). Although there were no significant predictors ofonsumption in the zero hurdle model, the direction of the nal-rexone main effect was to reduce the risk of consumption afterrinking had occurred, but this did not reach statistical signifi-ance. Thus there is no evidence for the effectiveness of naltrexonen reduction of drinking after drinking is resumed.

The low risk drinking hurdle model also showed a significantaltrexone by CBI interaction in the negative direction (Table 2,

= −1.16, SE = 0.45, p = 0.001) indicating that CBI reduced the effectf naltrexone when given with MM only (no CBI) in preventing highisk drinking. There was also a significant negative interaction inhe negative direction in the Poisson part of the model (Table 2,

= −1.05, SE = 0.45, p = 0.02) indicating that CBI reduced the effectf naltrexone when given with MM only (no CBI) in decreasinghe risk of drinking if high risk drinking was resumed. There was atrong significant main effect of naltrexone in increasing the oddsf low risk drinking, and in reducing the risk of drinking if highisk drinking was resumed (Table 3). The effects were strongest forhe comparison of naltrexone vs placebo naltrexone in the absencef CBI (OR = 3.26 [1.21, 5.31]; RR = 0.32 [0.12, 0.53]). To summarizehese results, a person on naltrexone has 3.3 times the odds of main-aining low risk drinking and a 68% reduction in the risk of drinkingf high risk drinking is resumed, as compared to a person on placebo

Please cite this article in press as: DeSantis, S.M., et al., Modeling longitustudy. Drug Alcohol Depend. (2013), http://dx.doi.org/10.1016/j.drugalcde

altrexone (in the absence of CBI).All diagnostics indicate that the implementation of the hur-

le improves the model fit but that the best fit is provided byhe hurdle model for low/high risk drinking. AIC and BIC both

PRESSDependence xxx (2013) xxx– xxx

favored the hurdle models over the more commonly applied lon-gitudinal Poisson regression model that does not account for zeroinflation (Table 5). The Vuong statistic showed that the zero hur-dle model did not perform significantly better than the simplermodel (V = −1.23, p = 0.22); however, the low risk drinking hur-dle model performed significantly better than the simpler model(V = −55.63.73, p < 0.0001). The model fit statistics favoring the lowrisk drinking hurdle is interesting in light of the findings that thelow risk drinking hurdle model resulted in a larger and more sig-nificant effect size for naltrexone; thus the placement of the hurdleand 3 or 4 drinks better illustrates naltrexone’s effectiveness indecreasing “risky” or “harmful” drinking. This novel finding impliesthat naltrexone also blunts the progression of drinking once highrisk drinking is resumed, which has implications for mechanismand future drug development.

3.2. Post treatment period

The same three models were fit for the follow up period (weeks17–26) (Table 4). In all models, there was a significant linear effectof time toward increased risk of drinking. No significant treat-ment main effects or interactions were observed in any model thefollow-up period. The AIC and BIC both favored the hurdle mod-els over the longitudinal Poisson regression model and the Vuongtest significantly favored the low risk drinking hurdle model. Maineffects on the odds of abstinence and risk of drinking are shownin Supplementary Table 2. Pairwise effects are not shown since nointeractions were significant. The zero hurdle model only showednon-significant trends (p < 0.10) toward an effect of naltrexone onboth abstinence and risk of drinking.

4. Discussion

Alcohol researchers are often interested in understanding howinterventions affect abstinence from alcohol as well as amount ofdrinking once drinking is resumed over the course of treatment.Addressing these two questions usually requires defining multiplesummary drinking endpoints, which can increase the probabilityof a type I error rate. To better address these questions, we pre-sented a novel approach to model treatment effects on abstinenceand number of drinks per day utilizing a joint statistical framework.Applied to the COMBINE study, the approach allowed for the useof all available high resolution outcome data, applied the appropri-ate modeling assumption that all patients were at risk of drinkingthroughout the study period, and as a result, was able to detecttreatment effects on abstinence and drinking over prior reports.

Results from the present study both complement and add toprevious conclusions (Anton et al., 2006; Gueorguieva et al., 2010;Witkiewitz et al., 2010; Falk et al., 2010). The major contributionof this paper is rather in promoting consideration of alternativemodels than providing “definitive” answers on treatment effects.Since all analyses were secondary analyses and utilized statisticalapproaches that were not defined a priori, the current analyses maynot have been adequately powered. However, the paper is illus-trative in asmuch as it promotes the use of a statistical methodthat is capable of handling the subtle complexities of drinking data,and additionally, its findings bolster the use of naltrexone to pro-mote abstinence and reduction in risky drinking. For example, asin previous COMBINE reports, naltrexone was found to be effec-tive in positively impacting drinking behavior, and a modifyingeffect by CBI was observed. However, while the original report

dinal drinking data in clinical trials: An application to the COMBINEp.2013.02.013

found no main effects of naltrexone on percent days abstinent,the current analysis showed that naltrexone promotes abstinence.Furthermore, unlike previous COMBINE reports, the current studydemonstrated that naltrexone also promotes (pre-defined) low risk

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Table 2The left side contains results from the zero-drink hurdle model and the right side contains results from the ≤3 drink and ≤4 drink hurdle model fit to treatment period data(weeks 1–16). ACA = acamprosate, NTX = naltrexone, prior no. drink = average number of drinks per day for the month prior to the required abstinence period.

Variable Zero-drink hurdle model Low risk drinking hurdle model

Effect SE (effect) 95% CI p-Value Effect SE (effect) 95% CI p-Value

HurdleIntercept 1 1.29 0.17 0.96, 1.62 0.0001 4.95 0.35 4.26, 5.64 0.0001ACA 0.13 0.19 −0.25, 0.51 0.50 0.10 0.38 −0.65, 0.86 0.79NTX 0.64 0.19 0.26, 1.02 0.001 1.08 0.39 0.32, 1.84 0.006CBI 0.49 0.19 0.11, 0.87 0.01 0.99 0.39 0.24, 1.76 0.01ACAxNTX −0.02 0.22 −0.46, 0.42 0.91 0.24 0.45 −0.64, 1.11 0.60ACAxCBI −0.09 0.22 −0.53, 0.35 0.69 −0.27 0.45 −1.15, 0.60 0.54NTXxCBI −0.67 0.22 −1.11, −0.23 0.003 −1.16 0.45 −2.04, −0.28 0.001Prior No. drink −0.07 0.004 −0.07, −0.06 0.0001 −0.08 0.00 −0.09, −0.07 0.0001

Poisson regressionIntercept 2 1.80 0.14 1.52, 2.08 0.0001 5.05 0.33 4.40, 5.70 0.0001ACA 0.11 0.19 −0.26, 0.48 0.55 0.27 0.38 −0.48, 1.03 0.47NTX 0.22 0.19 −0.16, 0.59 0.25 1.17 0.39 0.41, 1.94 0.002CBI −0.11 0.19 −0.47, 0.26 0.58 0.58 0.45 −0.18, 1.33 0.14ACAxNTX −0.24 0.22 −0.67, 0.19 0.28 −0.06 0.45 −0.94, 0.82 0.89ACAxCBI −0.15 0.22 −0.58, 0.28 0.49 −0.17 0.45 −1.05, 0.71 0.71NTXxCBI 0.12 0.22 −0.31, 0.55 0.60 −1.05 0.45 −1.94, −0.17 0.02Week 0.02 0.00 0.02, 0.02 0.0001 0.01 0.002 0.01, 0.02 0.0001

Table 3Pairwise odds ratios and risk ratios and 95% confidence intervals for the treatment period.

Zero-drink hurdle model Low risk drinking hurdle modelEffect OR [95% CI] RR [95% CI] OR [95% CI] RR [95% CI]

ACA main effect 1.08 [0.84, 1.69] 1.08 [0.85, 1.31] 1.08 [0.57, 1.58] 0.84 [0.46, 1.23]NTX main effect 1.35 [1.06, 1.65]* 0.86 [0.67, 1.04]# 1.99 [1.07, 2.90]* 0.54 [0.30, 0.79]*

CBI main effect 1.15 [0.90, 1.41] 1.14 [0.89, 1.38] 1.57 [0.84, 2.30] 0.88 [0.47, 1.29]ACA + NTX vs PLB ACA + PLB NTX 1.46 [1.00, 1.91]* 0.93 [0.65, 1.21] 2.21 [0.79, 3.63] 0.47 [0.17, 0.76]*

ACA + PLB NTX vs PLB ACA + PLB NTX 1.09 [0.76, 1.43] 0.97 [0.68, 1.27] 1.02 [0.37, 1.68] 0.81 [0.30, 1.32]PLB ACA + NTX vs PLB ACA + PLB NTX 1.38 [0.95, 1.80] 0.76 [0.53, 0.99]* 1.84 [0.66, 3.03] 0.52 [0.19, 0.85]*

ACA + CBI vs PLB ACA + no CBI 1.24 [0.86, 1.62] 1.22 [0.85, 1.59] 1.65 [0.58, 2.71] 0.75 [0.26, 1.24]ACA + no CBI vs PLB ACA + no CBI 1.13 [0.78, 1.47] 1.00 [0.69, 1.31] 1.17 [0.40, 1.94] 0.77 [0.26, 1.28]PLB ACA + CBI vs PLB ACA vs no CBI 1.21 [0.83, 1.58] 1.06 [0.74, 1.38] 1.74 [0.62, 2.86] 0.81 [0.29, 1.33]NTX + CBI vs PLB NTX + no CBI 1.49 [1.03, 1.96]* 0.97 [0.68, 1.27] 2.45 [0.93, 3.96] 0.55 [0.21, 0.90]*

NTX + no CBI vs PLB NTX + no CBI 1.87 [1.29, 2.46]* 0.91 [0.63, 1.18] 3.26 [1.21, 5.31]* 0.32 [0.12, 0.52]*

PLB NTX + CBI vs PLB NTX + no CBI 1.56 [1.08, 2.05]* 1.20 [0.83, 1.56] 2.36 [0.90, 3.82] 0.61 [0.23, 0.98]*

dtCo

TTd

* Indicates significance at p < 0.05.# Indicates significance at p < 0.10.

Please cite this article in press as: DeSantis, S.M., et al., Modeling longitudstudy. Drug Alcohol Depend. (2013), http://dx.doi.org/10.1016/j.drugalcde

rinking and for those who reach a harmful level of drinking, nal-rexone significantly decreases the amount of drinks consumed.onsistent with prior findings, this effect is obscured in the contextf CBI, which itself has an effect in the same direction as naltrexone,

able 4he left side contains results from the zero-drink hurdle model and the right side containata (weeks 17–26). ACA = acamprosate, NTX = naltrexone, prior no. drink = average numb

Zero-drink hurdle model

Variable Effect SE (effect) 95% CI p-V

HurdleIntercept 1 0.93 0.25 0.45, 1.42 0.00ACA 0.001 0.29 −0.56, 0.57 1.00NTX 0.65 0.29 0.08, 1.22 0.02CBI 0.34 0.29 −0.23, 0.91 0.24ACAxNTX −0.38 0.33 −1.03, 0.28 0.26ACAxCBI 0.10 0.33 −0.55, 0.76 0.75NTXxCBI −0.27 0.33 −0.93, 0.38 0.42Prior no. drink −0.08 0.005 −0.09, −0.07 0.00

Poisson regressionIntercept 2 2.33 0.22 1.90, 2.76 0.00ACA 0.13 0.28 −0.42, 0.68 0.63NTX 0.31 0.28 −0.25, 0.86 0.28CBI −0.16 0.28 −0.71, 0.40 0.58ACAxNTX −0.24 0.33 −0.88, 0.40 0.47ACAxCBI −0.07 0.33 −0.71, 0.57 0.84NTXxCBI 0.10 0.33 −0.54, 0.74 0.77Week 0.01 0.002 0.01, 0.01 0.00

inal drinking data in clinical trials: An application to the COMBINEp.2013.02.013

but is not additive to it. Results derived from the current analyticframework provide greater insight into the mechanism of action ofnaltrexone on the two part clinical process of abstinence violationand alcohol consumption.

s results from the ≤3 drink and ≤4 drink hurdle model fit to post-treatment perioder of drinks per day for the month prior to the required abstinence period.

Low risk drinking hurdle model

alue Effect SE (effect) 95% CI p-Value

02 6.63 0.64 5.38, 7.88 0.0001 −0.004 0.58 −1.15, 1.14 0.99

0.83 0.57 −0.30, 1.95 0.15 0.85 0.57 −0.27, 1.97 0.14 −0.24 0.64 −1.50, 1.02 0.71 0.04 0.64 −1.22, 1.30 0.95 −0.90 0.65 −2.17, 0.37 0.1601 −0.07 0.007 −0.09, −0.06 0.0001

01 8.71 0.64 7.46, 9.96 0.0001 −0.01 0.59 −1.06, 0.96 0.92 0.44 0.58 −0.20, 1.78 0.12 0.35 0.58 −0.27, 1.73 0.15 −0.26 0.65 −1.54, 1.02 0.69 0.24 0.65 −1.04, 1.52 0.71 −0.51 0.65 −1.80, 0.77 0.4401 0.01 0.002 0.01, 0.00 0.001

ARTICLE IN PRESSG Model

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Table 5Model diagnostics comparing longitudinal Poisson regression with the two hurdle models.

AIC BIC Vuong statistic (V) p-Value

Treatment period Poisson regression 54,373 54,475 –Zero-hurdle 53,716 53,854 −1.23 0.22Low risk-hurdle 25,717 25,855 −55.63 0.0001

33

82

93

eaIerdodtfa

rtrotr2meadtrga(coa

rdebnuaAmbea

R

Na

C

Post-treatment period Poisson regression 54,3Zero-hurdle 33,7Low risk-hurdle 20,6

In addition, the hurdle model was extended in a novel way tovaluate a cut-point for drinking that may be useful for delineating

priori definitions of low from harmful, or higher risk, drinking.n determining naltrexone’s mechanism of impact, there is ben-fit to conceptualizing low risk (i.e., short of high-risk drinking)ather than assuming low risk drinking equates to zero drinks peray. In fact, regression diagnostics indicated that the model fit wasptimal, and results indicated that naltrexone reduces the risk ofrinking 68% after high risk drinking is resumed, which supportshis cutoff as a meaningful definition of low risk drinking. Of course,urther research into a data driven definition of low risk or “accept-ble” drinking endpoints is still needed.

Secondary analyses of these data were warranted for severaleasons: (1) given the degree of conflicting evidence in the litera-ure regarding the effectiveness of naltrexone and acamprosate ineducing drinking and maintaining abstinence, (2) given the lackf consensus on outcome definitions in alcohol trials and (3) dueo the misuse of zero inflated models that assume zero-drinking-isk patients in the substance use literature (Bandyopadhyay et al.,011). The proposed approach has many advantages over com-only used approaches (e.g., Loeys and Moerkerke, 2012; Fielder

t al., 2012). First, the hypothesized mechanism of action ofcamprosate in promoting abstinence and naltrexone in reducingrinking lends itself to a joint model of abstinence and consump-ion. Second, clinical “improvement” may signify abstinence or aeduction in quantity of alcohol consumed, both of which are inte-ral parts of a hurdle model. Third, performing many separatenalyses of summary endpoints for abstinence and heavy drinkingas reported in the primary paper) reduces the amount of out-ome data utilized and may inflate type I error rate. Lastly, the easef implementation in SAS software makes the current approachdaptable to other alcohol datasets.

Limitations of this study must be recognized. Since the TLFBeports were heavily zero inflated, i.e., a large number of abstinentays were reported throughout the study, the 2-part model is notxpected to be as powerful to detect treatment effects as it woulde in a dataset with larger variations in counts. However, a largeumber of abstinent days is often a statistical issue in substancese clinical trials and resulting parameter estimates achieved herere still valid since the model converged to a sensible maximum.lso, while analysis did not control for the testing of multiple treat-ents and interactions, interaction p-values were small enough to

e deemed significant even after a Bonferroni correction for 3 mainffects was employed. Thus, it was justifiable to report results fromll pairwise comparisons.

ole of funding source

This secondary analysis of the COMBINE study is funded by theational Institutes of Health National Institute on Alcohol Abusend Addiction (Grant number R03 AA020648-01).

Please cite this article in press as: DeSantis, S.M., et al., Modeling longitustudy. Drug Alcohol Depend. (2013), http://dx.doi.org/10.1016/j.drugalcde

ontributors

None.

54,475 –33,918 −0.98 0.3320,829 −36.67 0.0001

Conflict of interest

No conflict declared.

Appendix A. Supplementary data

Supplementary data associated with this article can be found,in the online version, at http://dx.doi.org/10.1016/j.drugalcdep.2013.02.013.

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