The Single-Case Design in Family Therapy Evaluation Research

This paper discusses the need for the development of new research designs for family therapy evaluation, and a manner for meeting that need. The single-case research design has gained acceptance as bona fide experimental designs for evaluating the effectiveness of intervention techniques in drug and psychotherapy outcome research. Although the need for more outcome studies on the effectiveness of family therapy has been frequently noted, there has been virtually no use of the single-case design in family therapy outside of the behavior modification literature on families. This paper presents potential benefits of the application of single case-design for the practice of family therapy. Preliminary guidelines are suggested for the application of these designs.     

Single-case experimental designs: Characteristics,changes, and challenges

Tactics of Scientific Research (Sidman, 1960) provides a visionary treatise on single-case designs, their scientific underpinnings, and their critical role in understanding behavior. Since the foundational base was provided, single-case designs have proliferated especially in areas of application where they have been used to evaluate interventions with an extraordinary range of clients, settings, and target foci. This article highlights core features of single-case experimental designs, how key and ancillary features of the designs have evolved, the special strengths of the designs, and challenges that have impeded their integration in many areas where their contributions are sorely needed. The article ends by placing the methodological approach in the context of other research traditions. In this way, the discussion moves from the specific designs toward foundations and philosophy of science issues in keeping with the strengths of the person and book we are honoring.     

A Gradual Effects Model for Single-Case Designs

Single-case designs are a class of repeated measures experiments used to evaluate the effects of interventions for small or specialized populations, such as individuals with low-incidence disabilities. There has been growing interest in systematic reviews and syntheses of evidence from single-case designs, but there remains a need to further develop appropriate statistical models and effect sizes for data from the designs. We propose a novel model for single-case data that exhibit nonlinear time trends created by an intervention that produces gradual effects, which build up and dissipate over time. The model expresses a structural relationship between a pattern of treatment assignment and an outcome variable, making it appropriate for both treatment reversal and multiple baseline designs. It is formulated as a generalized linear model so that it can be applied to outcomes measured as frequency counts or proportions, both of which are commonly used in single-case research, while providing readily interpretable effect size estimates such as log response ratios or log odds ratios. We demonstrate the gradual effects model by applying it to data from a single-case study and examine the performance of proposed estimation methods in a Monte Carlo simulation of frequency count data.     

Meta- and statistical analysis of single-case intervention research data: Quantitative gifts and a wish list

In this commentary, we add to the spirit of the articles appearing in the special series devoted to meta- and statistical analysis of single-case intervention-design data. Following a brief discussion of historical factors leading to our initial involvement in statistical analysis of such data, we discuss: (a) the value added by including statistical-analysis recommendations in the What Works Clearinghouse Standards for single-case intervention designs; (b) the importance of visual analysis in single-case intervention research, along with the distinctive role that could be played by single-case effect-size measures; and (c) the elevated internal validity and statistical-conclusion validity afforded by the incorporation of various forms of randomization into basic single-case design structures. For the future, we envision more widespread application of quantitative analyses, as critical adjuncts to visual analysis, in both primary single-case intervention research studies and literature reviews in the behavioral, educational, and health sciences.     

Characteristics of single-case designs used to assess intervention effects in 2008

This article reports the results of a study that located, digitized, and coded all 809 single-case designs appearing in 113 studies in the year 2008 in 21 journals in a variety of fields in psychology and education. Coded variables included the specific kind of design, number of cases per study, number of outcomes, data points and phases per case, and autocorrelations for each case. Although studies of the effects of interventions are a minority in these journals, within that category, single-case designs are used more frequently than randomized or nonrandomized experiments. The modal study uses a multiple-baseline design with 20 data points for each of three or four cases, where the aim of the intervention is to increase the frequency of a desired behavior; but these characteristics vary widely over studies. The average autocorrelation is near to but significantly different from zero; but autocorrelations are significantly heterogeneous. The results have implications for the contributions of single-case designs to evidence-based practice and suggest a number of future research directions.     

Single-case effect size calculation: Comparing regression and non-parametric approaches across previously published reading intervention data sets

Growing from demands for accountability and research-based practice in the field of education, there is recent focus on developing standards for the implementation and analysis of single-case designs. Effect size methods for single-case designs provide a useful way to discuss treatment magnitude in the context of individual intervention. Although a standard effect size methodology does not yet exist within single-case research, panel experts recently recommended pairing regression and non-parametric approaches when analyzing effect size data. This study compared two single-case effect size methods: the regression-based, Allison-MT method and the newer, non-parametric, Tau-U method. Using previously published research that measured the Words read Correct per Minute (WCPM) variable, these two methods were examined by comparing differences in overall effect size scores and rankings of intervention effect. Results indicated that the regression method produced significantly larger effect sizes than the non-parametric method, but the rankings of the effect size scores had a strong, positive relation. Implications of these findings for research and practice are discussed.     

Using response ratios for meta-analyzing single-case designs with behavioral outcomes

Methods for meta-analyzing single-case designs (SCDs) are needed to inform evidence-based practice in clinical and school settings and to draw broader and more defensible generalizations in areas where SCDs comprise a large part of the research base. The most widely used outcomes in single-case research are measures of behavior collected using systematic direct observation, which typically take the form of rates or proportions. For studies that use such measures, one simple and intuitive way to quantify effect sizes is in terms of proportionate change from baseline, using an effect size known as the log response ratio. This paper describes methods for estimating log response ratios and combining the estimates using meta-analysis. The methods are based on a simple model for comparing two phases, where the level of the outcome is stable within each phase and the repeated outcome measurements are independent. Although auto-correlation will lead to biased estimates of the sampling variance of the effect size, meta-analysis of response ratios can be conducted with robust variance estimation procedures that remain valid even when sampling variance estimates are biased. The methods are demonstrated using data from a recent meta-analysis on group contingency interventions for student problem behavior.     

Course-oriented single-case studies in clinical practice--methodology and examples for use

Although the relevance of single-case methodology for clinical research is stressed frequently in the literature, clinicians do seldom use this approach. The present contribution is an attempt to stimulate and exemplify the realization of single-case designs clinical settings. In the first part of this paper single-case designs and strategies of statistical analysis for practical use are discussed. In the second part three empirical studies are reported: (1) An A/B-design for evaluation of a relaxation program for treatment of chronic headache; (2) an A/B/A/B-design to analyze the effect of cognitive-behavioral treatment in anxiety; and (3) an A/B/C/B/C-desing to test psychological treatment in rehabilitation of a schizophrenic patient.     

Randomization tests for multiple-baseline designs: An extension of the SCRT-R package

Multiple-baseline designs are an extension of the basic single-case AB phase designs, in which several of those AB designs are implemented simultaneously to different persons, behaviors, or settings, and the intervention is introduced in a staggered way to the different units. These designs are well-suited for research in the behavioral sciences. We discuss the advantages and limitations for valid inferences, and suggest a statistical technique—randomization tests—for use with multiple-baseline data, to complement visual analysis. In addition, we provide an extension of our SCRT-R package (which already contained means for conducting randomization tests on single-case phase and alternation designs), for multiple-baseline AB data.     

The conditional power of randomization tests for single-case effect sizes in designs with randomized treatment order: A Monte Carlo simulation study

The conditional power (CP) of the randomization test (RT) was investigated in a simulation study in which three different single-case effect size (ES) measures were used as the test statistics: the mean difference (MD), the percentage of nonoverlapping data (PND), and the nonoverlap of all pairs (NAP). Furthermore, we studied the effect of the experimental design on the RT’s CP for three different single-case designs with rapid treatment alternation: the completely randomized design (CRD), the randomized block design (RBD), and the restricted randomized alternation design (RRAD). As a third goal, we evaluated the CP of the RT for three types of simulated data: data generated from a standard normal distribution, data generated from a uniform distribution, and data generated from a first-order autoregressive Gaussian process. The results showed that the MD and NAP perform very similarly in terms of CP, whereas the PND performs substantially worse. Furthermore, the RRAD yielded marginally higher power in the RT, followed by the CRD and then the RBD. Finally, the power of the RT was almost unaffected by the type of the simulated data. On the basis of the results of the simulation study, we recommend at least 20 measurement occasions for single-case designs with a randomized treatment order that are to be evaluated with an RT using a 5% significance level. Furthermore, we do not recommend use of the PND, because of its low power in the RT.     

It has been said that, “There are three degrees of falsehoods: Lies,damn lies,and statistics”

Applied behavior analysis (ABA) researchers have historically eschewed population-based, inferential statistics, preferring to conduct and analyze repeated observations of each participant's responding under carefully controlled and manipulated experimental conditions using single-case designs (SCDs). In addition, early attempts to adapt traditional statistical procedures for use with SCDs often involved trade-offs between experimental and statistical control that most ABA researchers have found undesirable. The statistical methods recommended for use with SCDs in the current special issue represent a welcome departure from such prior suggestions in that the current authors are proposing that SCD researchers add statistical methods to their current practices in ways that do not alter traditional SCD practices. Further refinement and use of such methods would (a) facilitate the inclusion of research using SCDs in meta-analyses and (b) aid in the development and planning of grant-funded research using SCD methods. Collaboration between SCD researchers and statisticians, particularly on research that demonstrates the benefit of these methods, may help promote their acceptance and use in ABA.     

A generalized least squares regression approach for computing effect sizes in single-case research: application examples

A new method for deriving effect sizes from single-case designs is proposed. The strategy is applicable to small-sample time-series data with autoregressive errors. The method uses Generalized Least Squares (GLS) to model the autocorrelation of the data and estimate regression parameters to produce an effect size that represents the magnitude of treatment effect from baseline to treatment phases in standard deviation units. In this paper, the method is applied to two published examples using common single case designs (i.e., withdrawal and multiple-baseline). The results from these studies are described, and the method is compared to ten desirable criteria for single-case effect sizes. Based on the results of this application, we conclude with observations about the use of GLS as a support to visual analysis, provide recommendations for future research, and describe implications for practice.     

Behavioral treatment of thunder and lightning phobias.

The use of four different behavioral techniques in the treatment of six female clients with thunder and lightning phobia is described. The techniques (Systematic desensitization. Covert reinforcement. Stress inoculation training, and Self administered desensitization with tape recorder) were evaluated in single-case experimental designs, using both self-report, behavioral, and physiological data.The immediate and follow-up results showed that five of the clients were completely recovered and the sixth markedly improved after their respective treatment (10–14 session). These results and the questions concerning continuous assessment in single-case design and external validity of laboratory assessment in phobic conditions are discussed.     

Bayesian estimates of autocorrelations in single-case designs

Researchers in the single-case design tradition have debated the size and importance of the observed autocorrelations in those designs. All of the past estimates of the autocorrelation in that literature have taken the observed autocorrelation estimates as the data to be used in the debate. However, estimates of the autocorrelation are subject to great sampling error when the design has a small number of time points, as is typically the situation in single-case designs. Thus, a given observed autocorrelation may greatly over- or underestimate the corresponding population parameter. This article presents Bayesian estimates of the autocorrelation that greatly reduce the role of sampling error, as compared to past estimators. Simpler empirical Bayes estimates are presented first, in order to illustrate the fundamental notions of autocorrelation sampling error and shrinkage, followed by fully Bayesian estimates, and the difference between the two is explained. Scripts to do the analyses are available as supplemental materials. The analyses are illustrated using two examples from the single-case design literature. Bayesian estimation warrants wider use, not only in debates about the size of autocorrelations, but also in statistical methods that require an independent estimate of the autocorrelation to analyze the data.     

An R package for single-case randomization tests

Randomization tests are nonparametric statistical tests that obtain their validity by computationally mimicking the random assignment procedure that was used in the design phase of a study. Because randomization tests do not rely on a random sampling assumption, they can provide a better alternative than parametric statistical tests for analyzing data from single-case designs. In this article, an R package is described for use in designing single-case phase (AB, ABA, and ABAB) and alternation (completely randomized, alternating treatments, and randomized block) experiments, as well as for conducting statistical analyses on data gathered by means of such designs. The R code is presented in a step-by-step way, which at the same time clarifies the rationale behind single-case randomization tests.     

Directions in Consultation Research: Bridging the Gap Between Science and Practice

The authors promote the application of research findings to consultation and suggest directions for practice-relevant consultation research. The authors suggest that consultation research is in an early evolutionary stage and that further development depends on resolving several fundamental issues. Three approaches to consultation research are discussed: naturalistic studies, single-case designs, and alternative means of determining significance. Representative research in three areas of interest (consultant practice, consulting process, and consultation interventions) is reviewed, and criteria for evaluating research are discussed. The authors conclude with comments on operationalizing the scientist-practitioner ideal in consultation research and practice.     

Rational stage-directed therapy: A cognitive experiential system using hypnosis,imagery, cognitive restructuring,and developmental staging

Conclusion Although RSDT is a relatively new form of therapy, we believe there is reason for great optimism regarding the efficacy of the RSDT model. Communications from our colleagues using the model in a variety of settings have been very favorable. We believe the experimental studies that have been conducted on the RSDT model demonstrate that it has generated significantly better outcomes when compared with other therapeutic models and those results obtained from no therapy controls. We think the effectiveness of RSDT has been admirably demonstrated through comprehensive research designs In comparison with outcome studies conducted on other forms of therapy. We look toward the future with optimism as more practitioners begin to use the RSDT model and additional evaluation studies are conducted.     

SATIATION THERAPY: A PROCEDURE FOR REDUCING DEVIANT SEXUAL AROUSAL

Two single-case experiments demonstrated the efficacy of satiation therapy with adult males who had long-standing deviant sexual interests. The procedure involves the pairing of prolonged masturbation (1 hour) with the verbalization by the patient of his deviant sexual fantasies and in both cases the designs permitted the attribution of control over aberrant responding to the satiation therapy. The results are discussed in terms of the possible active ingredients of the procedure.     

The Use of Single-Case Experimental Research to Examine Physical Activity,Exercise, and Physical Fitness Interventions: A Review

This review identified studies that have utilized single-case experimental methods to evaluate physical activity, exercise, and physical fitness interventions. A total of 10 studies met the inclusion criteria. Single-case experimental design studies were inclusive to clinical populations and able to demonstrate an intervention effect. Future researchers should use validated and reliable assessments of physical activity or physical activity capacity, establish stable baseline assessments of their target behavior prior to the introduction of any intervention, use statistical tests to establish clinical and statistical significance, and move away from simple A-B designs that do not rule out the effects of extraneous variables.