Community Reinforcement Approach Drinking Trial With Homeless Alcohol-Dependent Individuals (Smith, Meyers, & Delaney, 1998)

Nine-month follow-up drinking outcomes for the N = 88 homeless alcohol-dependent participants in Smith, Meyers, and Delaney's (1998) randomized clinical trial of the Community Reinforcement Approach (CRA), published in the Journal of Consulting and Clinical Psychology. Participants were recruited from the Salvation Army Adult Rehabilitation Center in Albuquerque, New Mexico across two consecutive cohorts and were randomized to CRA, to CRA augmented with disulfiram, or to standard care. The outcome is the participant's average number of standard drinks per week at the nine-month follow-up, reported in both raw form (markedly right-skewed) and after a base-ten log transformation that approximately normalizes the distribution used in the original published analyses. The data are reproduced in Maxwell, Delaney, and Kelley (2027, Designing Experiments and Analyzing Data: A Model Comparison Perspective, 4th ed., Routledge), Chapter 3, Section 3.10.4, as the textbook's worked example of a between-subjects analysis of variance with a heavily skewed outcome.

Usage

drinks_trial

Format

A data frame with 88 observations on 5 variables.

id: Sequential participant identifier, 1 to 88.
cohort: Factor with levels 1 and 2. The study enrolled two consecutive cohorts. Cohort 1 compared three conditions (Standard, CRA, and CRA + Disulfiram); Cohort 2 dropped the disulfiram cell on the basis of Cohort 1 results and compared Standard against CRA only.
treatment: Factor with levels Standard, CRA, and CRA + Disulfiram, the randomly assigned treatment condition.
drinks_per_week: Average number of standard drinks per week at the nine-month follow-up. Bounded below at zero and markedly right-skewed (range 0 to 624.6, mean 36.9, median 3.8).
log_drinks: Common-log transformation \(\log_{10}(\code{drinks\_per\_week} + 1)\), the scale on which Smith, Meyers, and Delaney (1998) ran their primary between-groups analyses to obtain approximate normality. The plus-one inside the logarithm keeps the zero values finite (and mapped to zero).

Source

Smith, J. E., Meyers, R. J., and Delaney, H. D. (1998). The community reinforcement approach with homeless alcohol-dependent individuals. Journal of Consulting and Clinical Psychology, 66(3), 541–548. doi:10.1037/0022-006X.66.3.541

Also reproduced in Maxwell, Delaney, and Kelley (2027), Chapter 3.

The data are distributed openly with the companion materials of Maxwell, Delaney, and Kelley (2027), Designing Experiments and Analyzing Data: A Model Comparison Perspective, and are redistributed here on that basis.

Details

Per-cell sample sizes. The (cohort, treatment) crosstab is incomplete by design:

	Standard	CRA	CRA + Disulfiram
Cohort 1	17	15	19
Cohort 2	20	17	(not run)

Treatment marginals sum to 37 Standard, 32 CRA, and 19 CRA + Disulfiram; cohort marginals sum to 51 in Cohort 1 and 37 in Cohort 2.

The authors, the published article, and the textbook. The trial was conducted and reported by Jane Ellen Smith, Robert J. Meyers, and Harold D. Delaney, all then in the Department of Psychology at the University of New Mexico. Smith and Meyers were the substantive PIs of an extensive program of CRA research; Meyers (with N. H. Azrin) is widely associated with the dissemination of CRA and is the developer of the related Community Reinforcement and Family Training (CRAFT) intervention. Delaney is a quantitative psychologist who served as the trial's methodologist. In DMAR the data are included as a worked-example benchmark because they appear in Maxwell, Delaney, and Kelley (2027), Chapter 3, Section 3.10.4, as the running example for the consequences of skipping a normalizing transformation when fitting an analysis of variance to a markedly skewed outcome.

The original published article is

Smith, J. E., Meyers, R. J., and Delaney, H. D. (1998). The community reinforcement approach with homeless alcohol-dependent individuals. Journal of Consulting and Clinical Psychology, 66(3), 541–548. doi:10.1037/0022-006X.66.3.541

and the textbook reproduction (with Section 3.10.4 of MDK 2027 devoted to the worked analysis) is

Maxwell, S. E., Delaney, H. D., & Kelley, K. (2027). Designing experiments and analyzing data: A model comparison perspective (4th ed.). Routledge.

The Community Reinforcement Approach (CRA). CRA is a behavioral treatment for alcohol-use disorder developed by Nathan Azrin and colleagues in the 1970s. It uses operant conditioning principles to align vocational, marital, social, and recreational reinforcers in the patient's natural environment with abstinence rather than drinking. CRA had previously been evaluated in housed populations; Smith, Meyers, and Delaney (1998) extended its evidence base to homeless alcohol-dependent individuals, the population represented in these data.

Disulfiram (Antabuse). The CRA + Disulfiram condition added disulfiram, a long-standing pharmacological adjunct that produces an aversive reaction on alcohol consumption. The Cohort 1 finding that adding disulfiram offered little incremental benefit over CRA alone motivated dropping the disulfiram cell in Cohort 2.

Design and analysis. The published analyses fit a one-way analysis of variance to log_drinks (the raw drinks_per_week variable violates the normality assumption badly enough that the omnibus inference is misleading without transformation; see Maxwell, Delaney, and Kelley, 2027, Section 3.10.4). Useful contrasts include CRA versus Standard within each cohort, CRA versus CRA + Disulfiram within Cohort 1 to estimate the incremental benefit of disulfiram, and pooling across cohorts to estimate an overall CRA-versus-Standard effect.

Use as a DMAR benchmark. This data set is the canonical DMAR example for one-way between-subjects analysis with a heavily right-skewed continuous outcome. Methods that pair naturally with the data set include the one-way analysis of variance, planned contrasts (contrast_test), the standardized mean difference (smd, ci_smd), Cliff's delta (cliff_delta), the probability of superiority, and accuracy in parameter estimation sample size planning (ss_aipe_smd, ss_power_smd). The contrast between an ANOVA fit to drinks_per_week and one fit to log_drinks is a clean teaching example for the consequences of skipping a normalizing transformation.

What is and is not here. The published paper reports drinking outcomes at multiple follow-up timepoints (2, 6, 9, and 12 months) along with several demographic and clinical covariates. The values distributed here cover the nine-month follow-up only and contain no demographic or covariate information. Anyone wanting the full longitudinal trajectories or the covariate set should consult Smith, Meyers, and Delaney (1998) directly.

References

Maxwell, S. E., Delaney, H. D., & Kelley, K. (2027). Designing experiments and analyzing data: A model comparison perspective (4th ed.). Routledge. (See Chapter 3 on between-subjects analysis of variance and Section 3.10 on transformations.)

Kelley, K. (2026). DMAR: Methods for the design, measurement, and analysis of human-centered outcomes in R [R package]. https://github.com/yelleKneK/DMAR

Author

Ken Kelley

Examples

data(drinks_trial)
str(drinks_trial)
#> 'data.frame':	88 obs. of  5 variables:
#>  $ id             : int  1 2 3 4 5 6 7 8 9 10 ...
#>  $ cohort         : Factor w/ 2 levels "1","2": 1 1 1 1 1 1 1 1 1 1 ...
#>  $ treatment      : Factor w/ 3 levels "Standard","CRA",..: 2 2 2 2 2 2 2 2 2 2 ...
#>  $ drinks_per_week: num  11 21.7 98.3 6.9 19.1 ...
#>  $ log_drinks     : num  1.078 1.357 1.997 0.898 1.303 ...

# Per-cell sample sizes by cohort and treatment.
with(drinks_trial, table(cohort, treatment))
#>       treatment
#> cohort Standard CRA CRA + Disulfiram
#>      1       17  15               19
#>      2       20  17                0

# Right skew of the raw outcome versus the log-transformed scale
# used in the published analyses.
summary(drinks_trial$drinks_per_week)
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#>   0.000   0.000   3.846  36.879  36.434 624.615 
summary(drinks_trial$log_drinks)
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#>  0.0000  0.0000  0.6834  0.8408  1.5724  2.7963 

# One-way analysis of variance on the log scale, treating the
# five filled (cohort, treatment) cells as the design.
fit <- aov(log_drinks ~ cohort:treatment, data = drinks_trial)
summary(fit)
#>                  Df Sum Sq Mean Sq F value Pr(>F)  
#> cohort:treatment  4   9.04  2.2597    3.48 0.0112 *
#> Residuals        83  53.90  0.6494                 
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

# Standardized mean difference (Cohen's d) for every pairwise
# (two-way) comparison of the three treatments, on the normalizing
# log scale. The loop assembles a table of d with its 95%
# confidence interval for each of the three possible pairs.
groups <- split(drinks_trial$log_drinks, drinks_trial$treatment)
cmp    <- combn(names(groups), 2)
smd_table <- do.call(rbind, lapply(seq_len(ncol(cmp)), function(j) {
  g1 <- groups[[cmp[1, j]]]
  g2 <- groups[[cmp[2, j]]]
  d  <- smd(group_1 = g1, group_2 = g2)$value
  ci <- ci_smd(smd = d, n_1 = length(g1), n_2 = length(g2))
  data.frame(
    comparison = paste(cmp[1, j], "vs", cmp[2, j]),
    d          = round(d, 3),
    ci_lower   = round(ci$value[ci$term == "lower_limit"], 3),
    ci_upper   = round(ci$value[ci$term == "upper_limit"], 3)
  )
}))
smd_table
#>                     comparison     d ci_lower ci_upper
#> 1              Standard vs CRA 0.555    0.071    1.036
#> 2 Standard vs CRA + Disulfiram 0.725    0.152    1.292
#> 3      CRA vs CRA + Disulfiram 0.170   -0.400    0.738