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New Insights into the Efficacy of Naltrexone Based on Trajectory-Based Reanalyses of Two Negative Clinical Trials

      Background

      The heterogeneity of clinical findings in studies evaluating the efficacy of naltrexone in the treatment of alcohol dependence has led to growing efforts to explore novel approaches to data analysis. The objective of this study was to identify distinct trajectories of daily drinking over time in two negative clinical trials and to determine whether naltrexone affected the probability to follow a particular trajectory.

      Methods

      The Veterans Affairs (VA) Cooperative Study #425 and the Women’s Naltrexone Study failed to demonstrate efficacy on primary outcome variables. Separately for each study, we analyzed daily indicators of any drinking and heavy drinking using a semiparametric group-based approach.

      Results

      We estimated three distinct trajectories of daily drinking (both any and heavy drinking) which we described as “abstainer,” “sporadic drinker,” and “consistent drinker.” Naltrexone doubled the odds of following the abstainer trajectory instead of the consistent drinker trajectory but did not significantly change the odds of following the abstainer trajectory as contrasted with the sporadic drinker trajectory.

      Conclusions

      Naltrexone may have a clinically meaningful effect for alcohol-dependent patients with a high chance of consistent drinking, even in studies where it failed to show efficacy in planned analyses.

      Key Words

      The heterogeneity of clinical findings in studies evaluating the efficacy of naltrexone in the treatment of alcohol dependence has led to growing efforts to explore novel approaches to study design and data analysis. Naltrexone is approved by the Food and Drug Administration (FDA) for the treatment of alcoholism, but evidence for its efficacy is not unequivocal. A number of small to medium size studies (
      • Anton R.F.
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      ) and two large clinical trials (
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      • et al.
      Efficacy and tolerability of long-acting injectable naltrexone for alcohol dependence.
      ) reported that naltrexone was effective in delaying relapse heavy drinking, reducing the intensity of drinking, or increasing percent days abstinence. Several systematic reviews indicated that naltrexone efficacy was associated with a small to moderate effect size (
      • Berglund M.
      A better widget? Three lessons for improving addiction treatment from a meta-analytical study.
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      ). In contrast, a large randomized Veterans Affairs (VA) clinical trial (
      • Krystal J.H.
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      • Kirk G.F.
      • Rosenheck R.A.
      Naltrexone in the treatment of alcohol dependence.
      ) and other clinical trials (
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      A multicentre, randomized, double-blind, placebo-controlled trial of naltrexone in the treatment of alcohol dependence or abuse.
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      Naltrexone and brief counseling to reduce heavy drinking in hazardous drinkers.
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      • et al.
      Lack of efficacy of naltrexone in the prevention of alcohol relapse: Results from a German multicenter study.
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      • Killeen T.K.
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      • et al.
      Effectiveness of naltrexone in a community treatment program.
      ,
      • Kranzler H.R.
      • Modesto-Lowe V.
      • Van Kirk J.
      Naltrexone vs. nefazodone for treatment of alcohol dependence: A placebo-controlled trial.
      ) found no significant benefit associated with naltrexone treatment. Some meta-analyses also found no effect of naltrexone on abstinence (
      • Bouza C.
      • Angeles M.
      • Munoz A.
      • Amate J.M.
      Efficacy and safety of naltrexone and acamprosate in the treatment of alcohol dependence: A systematic review.
      ,
      • Garbutt J.C.
      • West S.L.
      • Carey T.S.
      • Lohr K.N.
      • Crews F.T.
      Pharmacological treatment of alcohol dependence: A review of the evidence.
      ).
      The sources of heterogeneity in these clinical trials are not clear. Since naltrexone is not an aversive treatment, it is not expected to stop people from drinking but may decrease frequency and volume of drinking. Hence, it may affect some measures of drinking but not others, which may explain the findings in some studies of a protective effect of naltrexone on heavy drinking but not on any drinking. Naltrexone is thought to act by reducing craving, thereby promoting self-management of drinking behavior. The efficacy of naltrexone might also be directly related to changes in compliance. Furthermore, multisite study effect sizes are generally smaller than single-site study effect sizes due to their larger population heterogeneity (
      • Feinn R.
      • Kranzler H.R.
      Does effect size in naltrexone trials for alcohol dependence differ for single-site vs. multi-center studies?.
      ). The possibility that subgroups of alcohol-dependent patients might differ predictably in their response to naltrexone also has been suggested on the basis of molecular genetic data (
      • Oslin D.W.
      • Berrettinni W.
      • Kranzler H.R.
      • Pettinati H.
      • Gelernter J.
      • Volpicelli J.R.
      • et al.
      A functional polymorphism of the mu-opioid receptor gene is associated with naltrexone response in alcohol-dependent patients.
      ).
      The impact of heterogeneous patient responses to naltrexone on clinical trial results may be exacerbated by the reliance of all published studies on summary drinking measures. The use of analytic approaches that evaluate patterns of drinking rather than single events or summary measures may be better suited to evaluate naltrexone efficacy (
      • O’Malley S.S.
      • Froehlich J.C.
      Advances in the use of naltrexone: An integration of preclinical and clinical findings.
      ,
      • Wang S.J.
      • Winchell C.J.
      • McCormick C.G.
      • Nevius S.E.
      • O’Neill R.T.
      Short of complete abstinence: An analysis exploration of multiple drinking episodes in alcoholism treatment trials.
      ). We hypothesize that by using daily drinking data and by accounting for compliance, we will not only be able to elicit meaningful patterns of alcohol use over time but may also see an increase in power for detecting treatment effects.
      Recent advances in longitudinal statistical modeling (
      • Rose J.S.
      • Chassin L.
      ) provide methods that enable the use of daily drinking data. Traditional growth modeling (
      • Diggle P.J.
      ,
      • Goldstein H.
      ,
      • Lindsey J.K.
      ,
      • Longford N.T.
      ,
      • Raudenbush S.W.
      • Bryk A.S.
      ) assumes that every individual follows the same type of trajectory over time, while latent-class based approaches (
      • Dolan C.V.
      • Schmittman V.R.
      • Lubke G.H.
      • Neale M.C.
      Regime switching in the latent growth curve mixture model.
      ,
      • Muthén B.O.
      • Muthén L.
      Integrating person-centered and variable-centered analyses: Growth mixture modeling with latent trajectory classes.
      ,
      • Muthén B.O.
      • Muthén L.K.
      The development of heavy drinking and alcohol-related problems from ages 18 to 37 in a U.S. national sample.
      ,
      • Nagin D.S.
      Analyzing developmental trajectories: A semiparametric, group-based approach.
      ) allow data-driven identification of distinct classes of developmental trajectories. Thus, it is possible to identify subgroups of subjects who show distinct patterns of clinical response within a clinical trial based on the structure of the data generated by that trial, i.e., subgroups that might not have been hypothesized a priori by the investigative team.
      In the field of alcoholism research, trajectory-based analyses have been selectively applied to large-scale observational studies of developmental patterns of alcohol use (
      • Chassin L.
      • Pitts S.C.
      • Prost J.
      Binge drinking trajectories from adolescence to emerging adulthood in a high risk sample: Predictors and substance abuse outcomes.
      ,
      • Del Boca F.K.
      • Darkes J.
      • Greenbaum P.E.
      • Goldman M.S.
      Up close and personal: Temporal variability in the drinking of individual college students during their first year.
      ,
      • Greenbaum P.E.
      • Del Boca F.K.
      • Darkes J.
      • Wang C.P.
      • Goldman M.S.
      Variation in the drinking trajectories of freshmen college students.
      ,
      • Hill K.G.
      • White H.R.
      • Chung I.J.
      • Hawkins J.D.
      • Catalano R.F.
      Early adult outcomes of adolescent binge drinking: Person and variable-centered analyses of binge drinking trajectories.
      ,
      • Khoo S.K.
      • Muthén B.O.
      Longitudinal data on families: Growth modeling alternatives.
      ,
      • Muthén B.O.
      Methodological issues in random coefficient growth modeling using a latent variable framework: Applications to the development of heavy drinking in ages 18–37.
      ,
      • Muthén B.O.
      • Muthén L.
      Integrating person-centered and variable-centered analyses: Growth mixture modeling with latent trajectory classes.
      ,
      • Muthén B.O.
      • Muthén L.K.
      The development of heavy drinking and alcohol-related problems from ages 18 to 37 in a U.S. national sample.
      ). To our knowledge, however, trajectory-based approaches have not yet been applied to treatment research studies. The objective of this work was to determine whether trajectory-based methods would provide insights into two adequately powered trials that failed to demonstrate significant naltrexone efficacy.

      Methods and Materials

      Veterans Affairs Cooperative Studies Program Study #425 Naltrexone in the Treatment of Alcohol Dependence

      In this double-blind randomized trial (
      • Krystal J.H.
      • Cramer J.A.
      • Krol W.F.
      • Kirk G.F.
      • Rosenheck R.A.
      Naltrexone in the treatment of alcohol dependence.
      ), 627 veterans with chronic, severe alcohol dependence were assigned to 3 months of naltrexone, 12 months of naltrexone, or placebo. Of the 627 subjects, 567 (10 female subjects) provided drinking data and were included in the analyses. Patients receiving naltrexone started with 25 mg once daily for 2 days, followed by 50 mg once daily for 3 or 12 months. Time to first day of heavy drinking (six or more drinks for men and four or more drinks for women) was defined as the primary outcome measure in the first 13 weeks of the trial.

      Women’s Naltrexone Trial

      The second double-blind randomized clinical trial was conducted at the Substance Abuse Treatment Unit of the Connecticut Mental Health Center and enrolled 103 women with current alcohol dependence (

      O’Malley S, Sinha R, Grilo CM, Capone C, Farren C, McKee SA, et al (in press): Naltrexone and cognitive behavioral coping skills therapy for the treatment of alcohol drinking and eating disorder features in alcohol dependent women: A randomized, double-blind, placebo controlled trial. Alcohol Clin Exp Res.

      ). Eligible subjects were randomized to either naltrexone or matching placebo for 12 weeks. Of the 103 subjects, 98 had drinking data and were included in analyses. Patients receiving naltrexone started with 25 mg once daily for 2 days, followed by 50 mg once daily. The primary outcomes included time to first day of drinking and time to first day of heavy drinking defined as consuming four or more drinks on an occasion.
      In both trials, no significant naltrexone effects were observed on the primary outcome measures (
      • Krystal J.H.
      • Cramer J.A.
      • Krol W.F.
      • Kirk G.F.
      • Rosenheck R.A.
      Naltrexone in the treatment of alcohol dependence.
      ,

      O’Malley S, Sinha R, Grilo CM, Capone C, Farren C, McKee SA, et al (in press): Naltrexone and cognitive behavioral coping skills therapy for the treatment of alcohol drinking and eating disorder features in alcohol dependent women: A randomized, double-blind, placebo controlled trial. Alcohol Clin Exp Res.

      ).
      In both studies, the Timeline Follow-Back (TLFB) was used to retrospectively collect daily drinking data. Timeline Follow-Back is the most comprehensive self-report measure and has good reliability and internal consistency on summary drinking measures (
      • Sobell L.C.
      • Sobell M.B.
      Timeline follow-back: A technique for assessing self-reported ethanol consumption.
      ,
      • Sobell L.C.
      • Sobell M.B.
      Alcohol consumption measures.
      ). In the trajectory-based reanalysis, we focused on the daily binary indicator of drinking (1 if any drinks were consumed by the subject on that day, 0 otherwise) or heavy drinking (1 if six or more drinks were consumed by male subjects and four or more drinks were consumed by female subjects on that day, 0 otherwise). Although there is large individual variability in accuracy of reporting daily drinking (
      • Searles J.S.
      • Helzer J.E.
      • Walter D.E.
      Comparison of drinking pattern measures by daily reports and timeline follow back.
      ), the trajectory-based approach smoothes the day-to-day data, thus creating stable data-driven patterns with much smaller variability than daily measures. At the same time, this approach captures drinking over time more precisely than traditional summary measures.
      We used the approach of
      • Nagin D.S.
      Analyzing developmental trajectories: A semiparametric, group-based approach.
      and
      • Nagin D.S.
      • Tremblay R.E.
      Analyzing developmental trajectories of distinct but related behaviors: A group-based method.
      to identify distinct trajectories of drinking patterns during the first 3 months of the trials (considered separately) and to estimate how naltrexone affects the probability of following a particular trajectory. The models assumed fixed polynomial trends over time within each trajectory class and modeled the effect of treatment and covariates on trajectory membership via a generalized logistic regression model. Model selection (number of trajectory classes and degree of the polynomial trends over time) was based on the Schwartz Bayesian criterion. Baseline covariates (age, percent drinking days and drinks per drinking day in the 90 days prior to study entry, posttraumatic stress disorder and major depression diagnosis in last month prior to study entry) were entered as main effects one at a time and jointly, and their effects on trajectory membership and on the relationship between naltrexone and trajectory membership were assessed. Lifetime cocaine dependence was also tested as a covariate in the VA trial. Medication compliance was measured using a microelectronic monitoring system (MEMS) (
      • Cramer J.A.
      • Mattson R.H.
      • Prevey M.L.
      • Scheyer R.D.
      • Ouellette V.L.
      How often is medication taken as prescribed? A novel assessment technique.
      ) of the medication bottle to remove the single daily pill (APREX Corporation, Fremont, California), recorded as a binary variable (1 if bottle was opened on a particular day, 0 otherwise), and treated as a time-dependent covariate in the analyses.
      This modeling strategy allowed the data to guide the choice of the number of trajectories that best fit the data and to determine the shape of each trajectory over time. It also allowed estimation of the proportion of the population whose treatment response corresponds most closely to each trajectory group. For the analysis, we used a customized SAS procedure (PROC TRAJ, SAS Institute, Cary, North Carolina) developed by
      • Jones B.
      • Nagin D.S.
      • Roeder K.
      A SAS procedure based on mixture models for estimating developmental trajectories.
      .
      We performed parallel analyses of the two clinical trials and then calculated a weighted average of the naltrexone effect estimates to obtain a meta-analytic estimate of the overall naltrexone effect. For model selection, we considered two and three class models and quadratic and cubic polynomials.

      Results

      Any Drinking Outcome

      Figure 1, Figure 2 plot the estimated trajectories in the VA and women’s clinical trials, respectively. The three trajectory patterns over time were similar for the two studies and were interpreted as “abstainers,” “sporadic drinkers,” and “consistent drinkers.” The abstainers were not necessarily complete abstainers but had close to 0% chance of drinking on any particular day. Estimated percentages of each treatment group that conform most closely to each trajectory and estimated odds ratios for the naltrexone effect adjusted for compliance are presented in Table 1. In both studies, subjects on naltrexone were more likely to be abstainers than were subjects on placebo, were about as likely to be sporadic drinkers, and were less likely to be consistent drinkers. In the VA trial, the odds of being an abstainer versus a consistent drinker and of being a sporadic drinker versus a consistent drinker were doubled for subjects on naltrexone as compared with subjects on placebo and these comparisons were statistically significant (odds ratio [OR] = 2.02, 95% confidence interval [CI]: 1.16, 3.52 and OR = 1.85, 95% CI: 1.06, 3.22, respectively). In the trial in women, the corresponding odds were also doubled but these comparisons were not statistically significant. The combined estimates from the two studies confirmed that subjects on naltrexone had significantly higher odds to be abstainers or sporadic drinkers versus consistent drinkers than subjects on placebo (OR = 2.05, 95% CI: 1.24, 3.39 and OR = 1.90, 95% CI: 1.08, 3.34, respectively). The odds ratio estimates for comparing abstainers and consistent drinkers in the VA trial and in the combined results were still significant after Bonferroni correction, while the odds ratio estimates for comparing sporadic drinkers and consistent drinkers were no longer statistically significant.
      Figure thumbnail gr1
      Figure 1Trajectory analysis of any drinking in VA clinical trial. Medication compliance is considered as a time-dependent covariate. Solid lines without symbols represent model-based probabilities of any drinking over time for each trajectory group corresponding to average daily compliance rates. Solid lines with symbols represent sample-based probabilities of any drinking based on all subjects weighted by the posterior probability of trajectory membership. VA, Veterans Affairs.
      Figure thumbnail gr2
      Figure 2Trajectory analysis of any drinking in women’s clinical trial. Medication compliance is considered as a time-dependent covariate. Solid lines without symbols represent model-based probabilities of any drinking over time for each trajectory group corresponding to average daily compliance rates. Solid lines with symbols represent sample-based probabilities of any drinking based on all subjects weighted by the posterior probability of trajectory membership. VA, Veterans Affairs.
      Table 1Estimated Probabilities of Any Drinking for a Particular Trajectory by Treatment and Adjusted Odds Ratios for Naltrexone Effect
      Study GroupProbability Trajectory 1 (Abstainers)Probability Trajectory 2 (Sporadic Drinkers)Probability Trajectory 3 (Consistent Drinkers)Odds Ratio (Abstainers vs. Sporadic Drinkers)Odds Ratio (Abstainers vs. Consistent Drinkers)Odds Ratio (Sporadic vs. Consistent Drinkers)
      VA (98% men)65.2%24.1%10.8%
       Naltrexone67.4%24.2%8.4%1.09 (0.71, 1.68)2.02 (1.16, 3.52)1.85 (1.06, 3.22)
       Placebo60.8%23.9%15.3%
      Women45.7%35.7%18.6%
       Naltrexone48.3%39.2%12.4%1.01 (.40, 2.57)2.23 (.68, 7.37)2.20 (.67, 7.28)
       Placebo41.7%34.3%24.0%
      Combined1.08 (.73, 1.60)2.05 (1.24, 3.39)1.90 (1.08, 3.34)
      VA, Veterans Affairs.

      Heavy Drinking Outcome

      Figure 3 plots the estimated trajectories for heavy drinking in the VA clinical trial. In the women’s trial, due to the small sample size, stable identification of trajectories of heavy drinking was not possible. In Figure 3, the three trajectory patterns over time were similar to the trajectories for any drinking and were depicted as abstainers from heavy drinking, sporadic heavy drinkers, and consistent heavy drinkers. Estimated percentages of each treatment group that conform most closely to each trajectory and estimated odds ratios for the naltrexone effect adjusted for compliance are presented in Table 2. Subjects on naltrexone appeared slightly more likely to be abstainers from heavy drinking than subjects on placebo, were about as likely to be sporadic heavy drinkers, and were less likely to be consistent heavy drinkers. The odds of being an abstainer from heavy drinking versus being a consistent heavy drinker were doubled for subjects on naltrexone as compared with subjects on placebo (OR = 2.07, 95% CI: 1.11, 3.84). This comparison was statistically significant before but not after Bonferroni correction.
      Figure thumbnail gr3
      Figure 3Trajectory analysis of heavy drinking in VA clinical trial. Medication compliance is considered as a time-dependent covariate. Solid lines without symbols represent model-based probabilities of heavy drinking over time for each trajectory group corresponding to average daily compliance rates. Solid lines with symbols represent sample-based probabilities of any drinking based on all subjects weighted by the posterior probability of trajectory membership. VA, Veterans Affairs.
      Table 2Estimated Probabilities of Heavy Drinking for a Particular Trajectory by Treatment and Adjusted Odds Ratios for Naltrexone Effect
      Study GroupProbability Trajectory 1 (Abstainers from Heavy Drinking)Probability Trajectory 2 (Sporadic Heavy Drinkers)Probability Trajectory 3 (Consistent Heavy Drinkers)Odds Ratio (Abstainers vs. Sporadic Heavy Drinkers)Odds Ratio (Abstainers vs. Consistent Heavy Drinkers)Odds Ratio (Sporadic vs. Consistent Heavy Drinkers)
      VA72.9%18.9%8.2%
       Naltrexone75.2%18.4%6.4%1.19 (.75, 1.89)2.07 (1.11, 3.84)1.74 (.85, 3.57)
       Placebo68.2%19.9%11.9%
      VA, Veterans Affairs.

      Covariate Analyses

      None of the baseline covariates significantly altered the effect of naltrexone on trajectory membership for both outcomes. Ignoring medication compliance did not change the significance of the findings regarding the efficacy of naltrexone on any drinking but decreased the significance of the efficacy of naltrexone on heavy drinking. Medication compliance had a significant effect on the trends over time by decreasing the odds of drinking in all trajectories (p < .01). For consistent drinkers in the VA trial, the odds of drinking on a particular day for compliers were only one third of the odds of noncompliers (OR = .35, 95% CI: .30, .40). For sporadic drinkers and abstainers in the VA trial, the odds of drinking on a particular day for compliers were about one half of the odds of noncompliers (OR = .45, 95% CI: .40, .50 and OR = .47, 95% CI: .34, .65). For all trajectory groups in the women’s trial, the odds of drinking on a particular day for compliers were slightly less than one half of the odds of noncompliers (OR = .46, 95% CI: .35, .60 for consistent drinkers; OR = .43, 95% CI: .32, .57 for sporadic drinkers; OR = .44, 95% CI: .23, .84 for abstainers). The effect of medication compliance on heavy drinking was most pronounced for the consistent heavy drinkers where the odds of heavy drinking on a particular day for compliers were only one fifth of the odds of noncompliers (OR = .20, 95% CI: .17, .23). For sporadic heavy drinkers, the odds of heavy drinking on a particular day for compliers were only one third of the odds of noncompliers (OR = .35, 95% CI: .30, .40), while for abstainers from heavy drinking, the odds were halved with compliance (OR = .54, 95% CI: .37, .80).

      Number Needed to Treat Analyses

      Number needed to treat (NNT) analyses provide a clinical context of how many people need to receive naltrexone to have them move from one trajectory to another. The adverse outcome is membership in the consistent drinkers or consistent heavy drinkers trajectory. Using the probability estimates of trajectory membership from Table 1, we estimate that 15 and 9 subjects need to be treated with naltrexone to have 1 subject move out of the consistent drinkers trajectory in the VA and women’s trials, respectively. Using the probability estimates from Table 2, we estimate that 19 subjects need to be treated with naltrexone to have 1 subject move out of the consistent heavy drinkers trajectory in the VA trial.

      Discussion

      In the trajectory-based reanalysis of the VA clinical trial, we found statistically significant effects of naltrexone on increasing the likelihood of abstinence from any drinking and decreasing the likelihood of heavy drinking. These findings stand in contrast to the findings of no effect of naltrexone on the originally specified summary measures of alcohol consumption in the same data set. We hypothesize that both original studies failed to find a significant naltrexone effect because of the high abstinence rates and because of the reliance on summary measures of alcohol consumption. Since all patients in both studies received a form of psychotherapy in addition to medication, both studies explored, in essence, the ability to show a medication effect in addition to an active treatment. This may account for the high abstinence rates. When the abstinence group is highly represented, the clinical effects appear small and most clinical trials using standard analytic techniques will fail to find group differences. The trajectory-based analytic approach may be one useful strategy in these situations.
      We found a significant effect of naltrexone in the VA trial that recruited almost entirely men but no significant effect of naltrexone in the trial in women. While this could be interpreted to concur with the finding of
      • Garbutt J.C.
      • Kranzler H.R.
      • O’Malley S.S.
      • Gastfriend D.R.
      • Pettinati H.M.
      • Silverman B.L.
      • et al.
      Efficacy and tolerability of long-acting injectable naltrexone for alcohol dependence.
      of differential effects by gender, the sample size of the VA trial was six times larger than that of the trial in women. Moreover, the similarities in both the shape of the estimated trajectories and in the magnitude of effects between the VA and the women’s studies suggest that the lack of statistical significance in the women’s study is more likely due to low power and that the naltrexone effect is actually consistent across the gender.
      Not surprisingly, medication adherence was found to decrease the chance of drinking regardless of treatment (
      • Cramer J.
      • Rosenheck R.
      • Kirk G.
      • Krol W.
      • Krystal J.
      Medication compliance feedback and monitoring in a clinical trial: Predictors and outcomes.
      ). Accounting for daily medication compliance strengthened the effect of naltrexone both for any drinking and for heavy drinking. This is consistent with previous findings that suggest the effect of naltrexone can be enhanced by improving medication compliance (
      • Volpicelli J.R.
      • Rhines K.C.
      • Rhines J.S.
      • Volpicelli L.A.
      • Alterman A.I.
      • O’Brien C.P.
      Naltrexone and alcohol dependence: Role of subject compliance.
      ).
      A limitation of our compliance analyses is that the model we used (
      • Nagin D.S.
      Analyzing developmental trajectories: A semiparametric, group-based approach.
      ) does not allow direct testing of interactions between baseline variables (including treatment) and time-dependent covariates. Hence, we were not able to assess whether effects of compliance differed by treatment or baseline covariates. Compliance may also be affected by treatment and mediate treatment response, but we could not establish such relationships in the model used.
      Our analysis is predicated on the assumption that different classes of trajectories exist. When no categorically different trajectories exist, a substantial percent of subjects will not be reliably classified into any one trajectory. In our analysis, over 86% of subjects had a posterior probability greater than 95% to belong to one of the trajectory classes and over 99% of the subjects had a posterior probability greater than 60% to belong to one trajectory class. This gives reassurance that in the clinical trials we reanalyzed, categorically different trajectory classes indeed exist.
      We considered models limited to either two or three trajectory classes because of limited sample sizes and computational feasibility. In the analysis of developmental behavioral data, a larger number of distinct developmental trajectory classes have typically been identified, although the additional classes have usually been formed by splitting already existing classes. Since ours is the first trajectory-based analysis of treatment data, it is not clear whether more trajectory classes would significantly improve the fit of our models to the data. Even if more trajectory classes are needed to adequately describe the data, stable identification of these trajectories will require even larger sample sizes to ensure precise estimation of probabilities of class membership for each trajectory class. It is thus possible that we may have missed a finer categorization of the trajectories over time.
      The problem of negative or failed clinical trials for medications where there is substantial evidence supporting efficacy is a major problem in psychiatric research (
      • Greist J.H.
      • Mundt J.C.
      • Kobak K.
      Factors contributing to failed trials of new agents: Can technology prevent some problems?.
      ,
      • Katz M.M.
      • Halbreich U.M.
      • Bowden C.L.
      • Frazer A.
      • Pinder R.M.
      • Rush A.J.
      • et al.
      Enhancing the technology of clinical trials and the trials model to evaluate newly developed, targeted antidepressants.
      ,
      • Khan A.
      • Schwartz K.
      Study designs and outcomes in antidepressant clinical trials.
      ,
      • Yang H.
      • Cusin C.
      • Fava M.
      Is there a placebo problem in antidepressant trials?.
      ). The current findings suggest that trajectory-based statistical methods may play a role in the analysis of clinical trials by empirically estimating the heterogeneity in the study population and identifying subgroups of subjects with similar response patterns for whom treatment is effective.
      Supported by Department of Veterans Affairs Cooperative Study Program and Alcohol Research Center, the Center for Translational Neuroscience of Alcoholism (P50 AA012870-05), and Grants RO1-AA10225 and K05-AA014715.
      In addition to the authors, the members of the Department of Veterans Affairs Cooperative Study 425 Group were as follows: K. Drexler, F. Mohammad, L. Siklosky, K. Walker, C. Arnold-Hunter, and R. Head, Atlanta; J. Hermos, H. Behr, B. Kinne, D. Savage, and J. Wickis, Boston; L. Rugle, O. Kausch, H. Zegarna, K. Conti, H. Adkins, G. Harris, and C. Cartier, Cleveland; B. Adinoff, L. Burney, J. Fields, B. Hudson, J. Corder, and A. Quintero, Dallas; J. Grabowski, R. Wancha, Y. Ruiz, S. Chermack, S. Fleming, K. Gamel, and B. Sullivan, Detroit; L. Madlock, R. Murray, J. Williams, R. Lewandowski, and T. Owens, Memphis, Tennessee; M. FeBornstein, J. Pena, B. Cotton-Brown, M. Cowie, A. Connelly, W. Hill, A. Holmes, and J. Fiery, New Orleans; P. Casadonte, S. Kushner, S. Johnson, J. Siegris, N. Lynch, E. Richardson, and A. Butcher, New York; S. Nixon, C. Shaw, R. Joswick, D. Bertoch, and H. Engebretson, Oklahoma City; L. Haynes-Tucker, L. Moffet, J. Weintraub, R. Lutz, S. Clinton, F. Pohlman, R. Royal, and S. Harris, Menlo Park, California; I. Maany, J. DeStefano, M. Andem, C. Hackett, J. McNeely, S. Dyanick, D. Torpey, S. Poole, E. Moeller, and A. Scheamania, Philadelphia; G. Kaplan, H. MacAskill, P. Charnley, and C. Williams, Providence, Rhode Island; C. Stock, P. Stevenson, S. Plumb, M. Dean, and J. Hunter, Salt Lake City; P. Banys, I. Rhew, S. Staccone, J. Kelly, and S. Shives, San Francisco; A. Saxon, M. Willey-Allen, J. Williams, K. Lunna, V. Ruscigno, S. Brown, and K. Shaffer, Seattle; J. Collins, S. Kilby, T. Burke, L. Linzy, C. Dalzell, M. Rhoads, J. Kelly, N. Banks, J. Arflin, and D. Briones, Perry Point, Maryland; and M. Miller and C. Messick, Albuquerque, New Mexico.

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