We analyzed data from a randomized controlled trial comparing injectable DAM vs. oral MMT conducted in Andalusia, Spain, from February 2003 to December 2004. Study design, methods and results have been published elsewhere . Briefly, 62 long-term, opioid dependent individuals with severe health and other drug related problems were randomized to receive either injectable DAM (plus oral methadone) or oral methadone alone. A total of 44 participants completed the 9 month treatment period and 50 completed the follow-up evaluations.
For the present study we analyse data from the Andalusian trial using a multi-domain outcome measure reported in a previous study conducted in The Netherlands, also comparing injectable DAM and oral MMT . The MDO is a dichotomous index, imputing success when the patient shows at least 40% improvement at 9 months, compared to the baseline values, in physical health (MAP-H) , or mental status (SCL-90), or social functioning (illegal activities and/or contact with non drug users), without a deterioration superior to 40% in any of these dimensions and no substantial increase (20%) in cocaine use. More details about this MDO can be found elsewhere .
Statistical analyses were performed using a Bayesian approach in order to take advantage of previous information, a strategy highly appropriated when working with small sample sizes (small samples are very common in trials aimed at treating conditions with low-incidence in the community). Previous information in big samples would have virtually no impact in the results. We calculated success rates, the relative risk (RR) and the respective 95% confidence intervals (CI). Using data derived from the Dutch study, a priori information was obtained for analysis of the Andalusian study data using Bayesian methods [18–21]. Analyses were performed by intention to treat, with no imputation for missing values. We denote by θ
1 the percentage of patients who responded to the experimental treatment (DAM), while θ
2 represents the percentage of those responding to the conventional treatment (methadone). Bayesian analysis enables us to calculate the probability of θ
1 being greater than θ
2 by a specified magnitude, based on the data from our trial and prior information from the Dutch trial. Upon clinical judgment and based on the target populations (i.e. treatment-refractory opioid-dependent individuals) and outcome expectations (i.e. stabilization, long-term treatment), we assumed as clinically relevant a minimal difference of 15% between the rates of responders in each group, and assessed the probability of this being fulfilled under different assumptions.
For each of the parameters θ
1 and θ
2 we selected three a priori distributions from the family of beta distributions with parameters a and b which approximately represent the implicit number of responders and non-responders in the prior distribution. These three scenarios represent different degrees of incorporation of prior evidence. In the first scenario ('No use' of historical data) Jeffreys' priors were used, which are non-informative prior beta distributions with parameters a = b = 0.5 for both, θ
1 and θ
2. The remaining two pair of priors were set on the basis of the knowledge derived from a previous clinical trial using injected DAM.  The respective CI associated with these prior data were calculated, and parameters were chosen (a and b in the beta distribution) such that the maximum density intervals of these distributions coincided approximately with the CI obtained previously. The second scenario ('Partial use') down-weighted the Dutch study by dividing a and b by 5. Finally, we repeated the process using the values a and b without modification ('Full use'), essentially equivalent to a full pooling of the trial results in a meta-analysis.
In order to perform a sensitivity analysis, several scenarios need to be imagined. The one considered when we do a 'partial use' of previous data is placed between two extreme situations: no use of previous data (meaning there are no similarities between contexts) and full use of them (meaning both contexts are equal). These extreme positions are extreme, since we cannot assume the Dutch and Andalusian context are the same, or that they have nothing in common either. The chosen halfway scenario takes into account this argument. A division by 5 of the parameters derived from the Beta-distribution was chosen in order to substantially increase the distribution dispersion attributed to previous data, allowing an adequate sensitivity analysis.
For each one of these prior choices, we obtained the conjugate beta distributions for the response rate in each arm of the trial using our binomial data. A total of 20.000 simulations were made from these a posteriori distributions, and the corresponding 20.000 differences θ
1 - θ
2 were calculated providing an a posteriori distribution of the difference between the proportions: Δ = θ
1 - θ
2. This was used to derive simulation-based estimates of the probability of relevant magnitudes concerning Δ: P(Δ larger than 0), P(Δ larger than 0.15) and a maximum density interval (probability interval for Δ) at 95%. EPIDAT 3.1 was used for all computations .