Multiple substance use is common in cocaine patients, making it a challenge to obtain samples of “pure” or singly dependent subjects for clinical trials research. The response has been to broaden the eligible subject pool by allowing concurrent use or abuse of other substances, although recent articles have debated the degree of acceptable heterogeneity for pharmacotherapy efficacy research (O’Brien and Lynch, 2003; Rounsaville et al., 2003). Moreover, when patients who use multiple drugs are included in a cocaine clinical trial, the investigation needs to take into account this increased variability. Not all clinical trials have consistently reported the impact of concomitant substance use on response to cocaine treatment.

Marijuana use is especially prevalent among patients with cocaine dependence (Miller et al., 1990a,b; Aharonovich et al., 2005, 2006). In an earlier report our research group described some interesting characteristics associated with marijuana-using individuals presenting for medication treatment trials (Lindsay et al., 2009). Among the large percentage (46.4%) of concurrent marijuana users seeking treatment for cocaine dependence, those who used marijuana frequently (i.e., 10 or more days over the past 30) showed a profile of greater clinical impairment, exemplified by more severe addiction severity scores, and heavier patterns of drug use, than those who used marijuana occasionally or not at all.

The extent to which marijuana-using cocaine-dependent patients fare worse in treatment compared to their non-marijuana-using counterparts is unclear. Aharonovich et al. (2006) examined the impact of continued cannabis use during methylphenidate treatment of comorbid cocaine dependence and ADHD and found that moderate or intermittent use of cannabis was associated with better retention in treatment than heavy use or abstinence. The effect of cannabis use on cocaine abstinence rates was not significant, contrary to previous findings (Aharonovich et al., 2005). Other studies have failed to find an effect of marijuana use on retention or cocaine treatment outcomes (Budney et al., 1996; Higgins et al., 2003). In a recent retrospective analysis of data from three clinical trials of contingency management, Alessi et al. (2011) found that pretreatment marijuana use did not dampen the benefit of this behavioral treatment in reducing cocaine use. In sum, the small literature shows mixed results on the impact of cannabis use on cocaine treatment outcome, underscoring the need to better understand this potential interaction, especially as it relates to the development of effective medications for treatment of cocaine dependence.

The prognostic significance of baseline marijuana use on treatment outcome is the focus of the present study. Having reported positive results from earlier trials of levodopa pharmacotherapy for cocaine dependence (Mooney et al., 2007; Schmitz et al., 2008), we carried out a secondary analysis to determine whether levodopa treatment effects varied as a function of marijuana use at baseline. Observations by Lindsay et al. (2009) led us to expect that marijuana use would moderate the effect of levodopa by reducing overall treatment effectiveness. Specifically, we hypothesized that within the subgroup of cocaine subjects having high levels of baseline marijuana use, treatment with levodopa pharmacotherapy would be less effective.

The second aim of this study is to demonstrate a more appropriate, statistical method for conducting secondary analysis of subgroup treatment effects. Analytically, evaluation of subgroup effects entails testing the interaction of treatment and some baseline, subgroup measurement. A large literature has criticized the use of traditional, Frequentist approaches as inadequate due to their often low power, and dichotomous evaluation of the evidence (i.e., significance testing; Dixon and Simon, 1991; Simon et al., 1996; Simon and Freedman, 1997; Simon, 2002; Green et al., 2009). For instance, Brookes et al. (2001) showed that a trial with 80% power to detect a main effect of treatment possessed only 29% power to detect an interaction effect as large as the main effect. Positing an interaction effect matching the magnitude of a main effect reflects an extremely optimistic scenario. Stated another way, if the interaction was as large as the anticipated main effect, the sample size would still require quadrupling in order to maintain 80% power to detect the interaction. The same literature, criticizing conventional Frequentist methods for analyzing treatment-by-subgroup interaction effects, has recommended Bayesian methods as an alternative.

Bayesian analytical methods avoid issues of reduced power and significance testing by evaluating the probability that the alternative (H_A) hypothesis exists, given the observed data, and any prior evidence for H_A. These probabilities can be meaningfully refined, unlike p values that cannot, by using informative prior probability distributions (for more extensive review of the limitations of p values, and the advantages of Bayesian statistical approaches see Dixon and Simon, 1991; Schervish, 1996; Goodman, 1999, 2005; Berry, 2006). Thus, the researcher is able to attach a probability value to the parameter of interest, in this case, the interaction effect, e.g., “given the observed data, the probability that an interaction of at least magnitude X exists is Y.” The Bayesian approach provides a natural analysis for the present situation, in which we sought to incorporate information from a previous study to improve precision in estimating the interaction parameter. Referred to as the Bayesian power prior approach, this paper demonstrates how to pool historical data from an earlier randomized clinical trial with current data, and produce more precise conclusions regarding the hypothesis of interest, i.e., that heterogeneity in response to treatment is a function of baseline marijuana use.

Baseline marijuana use characteristics of pharmacotherapy groups from their respective studies are provided in Table 1.

Table 2 displays Bayesian estimates for a₀ = 0 and a₀ = 1 as well as frequentist estimates of the interaction term. Estimates of the interaction coefficient for a₀ = 0 and a₀ = 1 and a₀ = 1 are R.R. = 0.887 (95% C.B.I. 0.781–1.022) and R.R. = 0.899 (95% C.B.I. 0.808–1.016) respectively. That is, relative to patients in the placebo condition, participants receiving levodopa demonstrated a decrease in TES by a factor of 0.887 (i.e., 11.3%) or 0.899 (i.e., 10.1%) for the two most extreme weights that might be attached to the historical evidence (i.e., a₀ = 0 and a₀ = 1 respectively). Note that the point estimates are quite similar and that the 95% Credible Interval for a₀ = 0 entirely contains the corresponding interval for a₀ = 1. The broader credible interval for a₀ = 0 which encompass the interval for a₀ = 1 reflects the decrease in uncertainty that occurs as the historical data receives greater weight in the analysis; a reasonable result given that inclusion of more information from the historical data permits greater precision in the resulting estimates. Inspection of Figures 1 and 2 show that, at different levels of a₀, the value of the parameter estimate for the interaction, as well as the probability that increased baseline marijuana use predicts decreased TES scores in the levodopa condition, remains relatively constant. Inspection of Figure 3 shows the magnitude of the decrease in the Credible Interval range and the variance of the posterior distribution as a percentage of its width at a₀ = 0, as a function of altering a₀. In the current case, the range of the Credible Interval decreases by approximately 14% while the variance of the posterior distribution of the exponentiated coefficient decreases by almost 26%. Finally, Figure 4 shows the posterior distributions of the parameter value for the interaction coefficient. The distributions, displayed for a₀ = 0, 0.5, and 1.0, appear to be quite similar. Given the failure to demonstrate that alterations in a₀ result in substantial changes to the estimated value of the interaction coefficient, coupled with the increase in precision for the estimate, it is reasonable to give the historical data a weight comparable to the current data (i.e., a₀ = 1).

From a substantive perspective, using a₀ = 1, the probability that baseline marijuana use predicts differential response to treatment with levodopa/carbidopa is 0.96 (i.e., where θ is less than or equal to a R.R. of 1.0; Figure 4). Based on the Frequentist Likelihood Ratio Test statistics presented in Table 1, neither the historical, current nor the combined data sets lead to rejection of the null hypothesis.

Inspecting the simple effects of baseline marijuana use indicates that among participants receiving levodopa/carbidopa the probability that baseline marijuana confers harm in terms of treatment outcome is 0.981 (Figure 5). The probability that marijuana confers harm within the placebo condition is 0.163 (Figure 5). For every additional day of marijuana use reported at baseline, participants in the levodopa/carbidopa condition demonstrate a 5.4% decrease in TES (R.R. 0.946, 95% C.B.I. 0.864–1.069; Figure 6). For every additional day of marijuana use reported at baseline, participants in the placebo condition demonstrate a 4.9% increase in TES (R.R. 1.049, 95% C.B.I. 1.002–1.115; Figure 6).

Subgroup analyses are informative for characterizing heterogeneity in response to treatment for cocaine dependence. Inadequate power minimizes the usefulness of conventional, Frequentist tests of the salient interaction terms. As such Bayesian methods provide a more appropriate, probabilistic measure of the evidence for subgroup effects. Improved precision for estimates of subgroup effects can result from incorporation of historical data into the analysis of a current data set. Doing so raises questions regarding the comparability of the data sets, and the weight subsequently accorded the historical data. Power priors offer a mechanism for formalizing the degree to which historical data is incorporated into the analysis of a newer data set.

In the current context this type of analysis points, with high probability, to the existence of a subgroup effect of baseline marijuana use on response to treatment for cocaine dependence with levodopa/carbidopa. Specifically, higher marijuana use predicted lower treatment effectiveness (cocaine-negative urines) in the levodopa/carbidopa condition, but not in the placebo condition. It is possible that higher marijuana use at baseline operates as a proxy for cocaine severity that has been shown to distinguish subpopulations in terms of treatment response. Repeating our analysis with baseline cocaine use as a covariate, however, failed to alter any substantive conclusions. To the extent that frequent marijuana use at baseline continued during treatment, this pattern of concomitant use may have influenced levodopa’s efficacy via providing competing drug reinforcement, perhaps counteracting the putative dopamine-restoring effects of levodopa. Although generally a well-tolerated medication in cocaine-dependent patients, levodopa may interact with marijuana to produce less tolerable effects and thus reduce compliance and efficacy. Based on these findings, future research should examine how marijuana use during treatment interacts with cocaine use in moderating the effects of levodopa treatment: (i) chronic marijuana use may produce changes in cannabinoid-1 and/or dopamine receptor availability which may alter the effects of levodopa in cocaine-dependent subjects; (ii) intoxication following acute marijuana use may alter the probability of concurrent cocaine use in the levodopa condition relative to placebo via drug–drug interactions not yet fully understood.

Limitations of the current study include the post hoc/secondary nature of the data analysis. A large literature has discussed the problem of post hoc subgroup analyses (Adams, 1998; Assmann et al., 2000; Pocock et al., 2002; Cook et al., 2004; Rothwell, 2005). The clear danger is that post hoc selection of subgroups for analysis may result in capitalization on chance variability in the data. While this is somewhat mitigated by the finding that the interaction remains consistent, pooling across the two samples, it is still possible that idiosyncrasies in recruitment, or secular trends in the population from which sampling occurred resulted in biased estimates of the interaction effect. Prospective confirmation of these findings have broad implications for analyzing patient heterogeneity in response to treatment, the design of clinical trials to account for population heterogeneity through stratified randomization, as well as more specific implications for the potential usefulness of levodopa pharmacotherapy in treatment cocaine dependence.

Robert Agnelli who was instrumental in programming the SAS statistical code is an employee of SAS, Inc., Cary, NC, USA. The other authors conducted the current research in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.