Statistical Methods

The results section is composed of two parts; the first part is concerned with the between-groups analysis, i.e. the comparison between the CM and ST groups, and the second part is dedicated to detailed within-group analyses of the CM group.

III.3.1. Between-Group Analyses

Data analyses of the demographic and baseline characteristics for the standard treatment and the contingency management groups were conducted using Mann-Whitney U tests for continuous and ordinal variables, and chi-square for categorical variables (Appendix VI).

The data for the three measured timepoints 1, 2 and 3 were examined using Mann-Whitney U tests for between group differences, and Friedman tests to compare the three timepoints for the standard treatment and contingency management groups separately (Appendix VI). Where appropriate, post-hoc analyses with Wilcoxon signed-rank tests were conducted with a Bonferroni correction applied. That is, pairwise contrasts between timepoints were conducted with χ2 tests using α levels determined by dividing the conventional α of .05 by the number of pairwise comparison made. For the three timepoints, the following outcome variables from the TOP questionnaires were examined; crack, cocaine, alcohol, opiates, cannabis use, days attended work and/or college, criminal involvement, psychological health, physical health, quality of life, and the two extracted outcome variables from the CISS questionnaire; measured quality of the working relationship between drug worker and client, and compliance and reliability with treatment requirements.

The following outcome measures of the TOP will not be presented in the results section, due to no or too few responses: (a) None of the participants reported any cocaine use (b) Acute housing problem and/or at risk of eviction; two participants reported problems with their accommodation at timepoint 2. (c) Injecting risk behaviour; three participants reported high-risk injection practices. (d) One person reported using amphetamines twice a month and two participants reported the use of illicit diazepam 1 – 3 times a month at timepoint 2. Regarding the questionnaire items ‘days paid work’ and ‘days attended college or school’, the responses to these two separate, but related measures were consolidated to one category because there were too few participants responding positively to either of the questions.

III.3.2. Within-Group Analyses

Conditional Probabilities of Change and Clinical Improvement

Regarding the within-group analyses for the CM group, study results were investigated for evidence of clinically meaningful changes on an individual participant level. We operationalised the statistical method of conditional probabilities of change and the criteria of clinically meaningful change to assess outcome. These conventions were also used by Gawin et al., (1989), Stitzer et al., (1992) and Iguchi et al. (1997) to evaluate CM programme outcome. The definition of conditional probabilities of change is as follows; participants who could improve were defined as those whose baseline rate of cocaine free urines was 90% or less;

these participants were classified as improved if their rate of cocaine free urines increased by 10% or more during the intervention. Participants who could deteriorate were defined as those whose baseline cocaine free urine rate was 10% or more; these participants were classified as deteriorated if their rate of cocaine free urines decreased by 10% or more during the intervention. Clients whose cocaine positive urine test rate for baseline versus intervention period remained within ±10% were classified as unchanged. The 10% urine improvement criterion was selected to eliminate small changes based on chance fluctuations (Gawin et al., 1989; Higgins et al., 1991; Carroll, Rounsaville & Gawin, 1991; Stitzer et al., 1992; Iguchi et al., 1997).

In order to apply an even more stringent definition of clinical improvement, a further standardised evaluation of treatment for crack cocaine misusing clients, namely the requirement of 3 consecutive cocaine free weeks was employed. The rationale for the 3 week requirement of cocaine free urines was that this represented a clinically meaningful period of abstinence and, at the same time, constituted an achievable goal for the population of chronic supplemental users of cocaine in a 12 week intervention period (Stitzer et al., 1992; Iguchi et a., 1997).

To give equal weight to urine results of early dropouts and those retained throughout the evaluation, data analyses were based on the overall percentage of cocaine positive urine samples given by each participant during baseline and during the portion of the intervention in which s/he participated. In this way, data from each

client contributed equally to the analysis whether or not the client stayed through the entire intervention period (Stitzer et al., 1992). Therefore, urine specimens not collected from participants leaving treatment prior to the end of the intervention period were counted as cocaine positive and missing urine samples were considered positive samples, which is predicated on a widely used approach in CM trials (for example, Silverman et al., 1996; Budney et al., 2000).

Baseline and Crack Use During CM Intervention

A non-parametric procedure, the Spearman’s rank order correlation coefficient (i.e., Spearman's rho) was performed to address the question whether self-reported baseline cocaine consume (timepoint 1) was associated with crack cocaine abstinence during the CM intervention period (Appendix VI).

Survival Analysis

A survival analysis Kaplan-Meier product-limit procedure (non-parametric) was employed to estimate time-to-event models and to examine the distribution of the time-to-event variables (Appendix VI). A great advantage and a unique characteristic of this method is that it accounts for censored observations, i.e. cases where the critical event (event of interest) has not occurred in the observed intervention period, and cases that are lost to analysis because of participants leaving treatment prior to the end of the intervention period. The latter are so-called ‘right censored cases’, of which the present sample comprised a fair amount.

Two modelling strategies for retention data were used. For the first model, the outcome (‘event’) was determined as time to study dropout. The event was defined as the second consecutive occasion a scheduled reinforcement session was not attended and the absence was not authorised prior to the appointment. The second non-attendance was selected because several participants missed one scheduled reinforcement session but did not dropout of the study at that point.

For the second model, outcome was specified as time to first positive cocaine urinalysis or second consecutive unexcused non-attendance (see first model). The event was specified as occurring when the first positive cocaine urinalysis or second unexcused non-attendance was produced (whichever occurred first).

For both models, the event (i.e. time to dropout or first positive cocaine urinalysis) was calculated from the first day of the study. If the event did not occur during the 12-week period, data were censored at the last day of the intervention (usually Day 84). Retention analyses are reported using the estimated survival function, mean, median and 95% confidence intervals (CIs).

III.3.3. Changes in the Planned Data Analyses

At the time of the proposal for the study (in 2008), the drug and alcohol service held a caseload of 270 opiate maintenance clients. In order to qualify for opiate substitution treatment, the policy at the service required weekly or fortnightly urine tests. An examination of 52 random urine samples revealed that 32 tests were positive for cocaine, that is 62%. It was extrapolated that approximately 167 clients (62% from 270 clients) consume cocaine or crack cocaine. Thus, the assumption was that approximately 50 clients use crack cocaine on a regular basis, have a desire to abstain from crack use and are interested to participate in a CM intervention.

Within the realm of the (methodological) restrictions from the NTA, the study was designed. One of the aims was to investigate predictors of CM treatment outcome (please see section, I.10. Background of the Study, Research Aims and Questions), for example the two implemented measures from the CISS; treatment compliance and working relationship. To investigate these treatment outcome predictors, the statistical method of a logistic regression would have been indicated. However, the small sample size and the relatively few participants that remained abstinent for extended durations of time prevented the application of this method. Advanced statistical methods, such as logistic regression models, require greater sample sizes.

Bergtold, Yeager, Jason and Featherstone (2011) established that sample size can affect parameter estimates and hence, the robustness of the inferences from logistic regression analysis. Equally, using a survival analysis model (for example, a Log rank (Mantel Cox test)) to establish whether gender differences can be observed with regard to treatment response was not feasible.