Further developments in summarising and meta-analysing single-case data: An illustration with neurobehavioural interventions in acquired brain injury

How to assess and take into account trend in single-case experimental design data

One of the data features that are expected to be assessed when analyzing single-case experimental designs (SCED) data is trend. The current text deals with four different questions that applied researchers can ask themselves when assessing trend and especially when dealing with improving baseline trend: (a) What options exist for assessing the presence of trend?; (b) Once assessed, what criterion can be followed for deciding whether it is necessary to control for baseline trend?; (c) What strategy can be followed for controlling for baseline trend?; and (d) How to proceed in case there is baseline trend only in some A-B comparisons? Several options are reviewed for each of these questions in the context of real data, and tentative recommendations are provided. A new user-friendly website is developed to implement the options for fitting a trend line and a criterion for selecting a specific technique for that purpose. Trend-related and more general data analytical recommendations are provided for applied researchers.Trial registration: ClinicalTrials.gov identifier: NCT04560777.

Does the choice of a linear trend-assessment technique matter in the context of single-case data?

Trend is one of the data aspects that is an object of assessment in the context of single-case experimental designs. This assessment can be performed both visually and quantitatively. Given that trend, just like other relevant data features such as level, immediacy, or overlap does not have a single operative definition, a comparison among the existing alternatives is necessary. Previous studies have included illustrations of differences between trend-line fitting techniques using real data. In the current study, I carry out a simulation to study the degree to which different trend-line fitting techniques lead to different degrees of bias, mean square error, and statistical power for a variety of quantifications that entail trend lines. The simulation involves generating both continuous and count data, for several phase lengths, degrees of autocorrelation, and effect sizes (change in level and change in slope). The results suggest that, in general, ordinary least squares estimation performs well in terms of relative bias and mean square error. Especially, a quantification of slope change is associated with better statistical results than quantifying an average difference between conditions on the basis of a projected baseline trend. In contrast, the performance of the split-middle (bisplit) technique is less than optimal.

Deep-Breathing Biofeedback Trainability in a Virtual-Reality Action Game: A Single-Case Design Study With Police Trainers

It is widely recognized that police performance may be hindered by psychophysiological state changes during acute stress. To address the need for awareness and control of these physiological changes, police academies in many countries have implemented Heart-Rate Variability (HRV) biofeedback training. Despite these trainings now being widely delivered in classroom setups, they typically lack the arousing action context needed for successful transfer to the operational field, where officers must apply learned skills, particularly when stress levels rise. The study presented here aimed to address this gap by training physiological control skills in an arousing decision-making context. We developed a Virtual-Reality (VR) breathing-based biofeedback training in which police officers perform deep and slow diaphragmatic breathing in an engaging game-like action context. This VR game consisted of a selective shoot/don’t shoot game designed to assess response inhibition, an impaired capacity in high arousal situations. Biofeedback was provided based on adherence to a slow breathing pace: the slower and deeper the breathing, the less constrained peripheral vision became, facilitating accurate responses to the in-game demands. A total of nine male police trainers completed 10 sessions over a 4-week period as part of a single-case experimental ABAB study-design (i.e., alternating sessions with and without biofeedback). Results showed that eight out of nine participants showed improved breathing control in action, with a positive effect on breathing-induced low frequency HRV, while also improving their in-game behavioral performance. Critically, the breathing-based skill learning transferred to subsequent sessions in which biofeedback was not presented. Importantly, all participants remained highly engaged throughout the training. Altogether, our study showed that our VR environment can be used to train breathing regulation in an arousing and active decision-making context.

Fitting Bayesian Models for Single-Case Experimental Designs

Abstract. Single-case experimental designs (SCEDs) are interrupted time-series designs that have recently gained recognition as being able to provide a strong basis for establishing intervention effect. Typically, SCED data are short time series and autocorrelated, which renders maximum likelihood and parametric analyses inadequate for data analysis, respectively. Although Bayesian methods overcome these challenges, most practitioners do not use Bayesian estimation because of: (a) its steep learning curve, (b) lack of Bayesian training, and (c) lack of knowledge of Bayesian software solutions. This study demonstrates two Bayesian interrupted time-series models using freeware programs R and JAGS. Practitioners could modify these codes and run them for their own data by changing the values in the codes where indicated. Providing practitioners with such tools to facilitate their analysis is one way to improve methodological rigor in applied research.

Quantifying differences between conditions in single-case designs: Possible analysis and meta-analysis

The current paper is a call for and illustration of a way of closing the gap between basic research and professional practice in the field of neurorehabilitation. Methodologically, single-case experimental designs and the guidelines created regarding their conduct are highlighted. Statistically, we review two data analytical options, namely (a) indices quantifying the difference between pairs of conditions in the same metric as the target behavior and (b) a formal statistical procedure offering a standardized overall quantification. The paper provides guidance in the analysis and suggests free software in order to illustrate, in the context of data from behavioral interventions with children with developmental disorders, that informative analyses are feasible. We also show how the results of individual studies can be made eligible for meta-analyses, which are useful for establishing the evidence basis of interventions. Nevertheless, we also point at decisions that need to be made during the process of data analysis.

Linear Trend in Single-Case Visual and Quantitative Analyses

The frequently used visual analysis of single-case data focuses on data aspects such as level, trend, variability, overlap, immediacy of effect, and consistency of data patterns; most of these aspects are also commonly quantified besides inspecting them visually. The present text focuses on trend, because even linear trend can be operatively defined in several different ways, while there are also different approaches for controlling for baseline trend. We recommend using a quantitative criterion for choosing a trend line fitting technique and comparing baseline and intervention slopes, instead of detrending. We implement our proposal in a free web-based application created specifically for following the What Works Clearinghouse Standards recommendations for visual analysis. This application is especially destined to applied researchers and provides graphical representation of the data, visual aids, and quantifications of the difference between phases in terms of level, trend, and overlap, as well as two quantifications of the immediate effect. An evaluation of the consistency of effects across replications of the AB sequence is also provided. For methodologists and statisticians, we include formulas and examples of the different straight line fitting and detrending techniques to improve the reproducibility of results and simulations.

Recommendations for Choosing Single-Case Data Analytical Techniques

The current paper responds to the need to provide guidance to applied single-case researchers regarding the possibilities of data analysis. The amount of available single-case data analytical techniques has been growing during recent years and a general overview, comparing the possibilities of these techniques, is missing. Such an overview is provided that refers to techniques that yield results in terms of a raw or standardized difference and procedures related to regression analysis, as well as nonoverlap and percentage change indices. The comparison is provided in terms of the type of quantification provided, data features taken into account, conditions in which the techniques are appropriate, possibilities for meta-analysis, and evidence available on their performance. Moreover, we provide a set of recommendations for choosing appropriate analysis techniques, pointing at specific situations (aims, types of data, researchers' resources) and the data analytical techniques that are most appropriate in these situations. The recommendations are contextualized using a variety of published single-case data sets in order to illustrate a range of realistic situations that researchers have faced and may face in their investigations.

How Can Single-Case Data Be Analyzed? Software Resources, Tutorial, and Reflections on Analysis

The present article aims to present a series of software developments in the quantitative analysis of data obtained via single-case experimental designs (SCEDs), as well as the tutorial describing these developments. The tutorial focuses on software implementations based on freely available platforms such as R and aims to bring statistical advances closer to applied researchers and help them become autonomous agents in the data analysis stage of a study. The range of analyses dealt with in the tutorial is illustrated on a typical single-case dataset, relying heavily on graphical data representations. We illustrate how visual and quantitative analyses can be used jointly, giving complementary information and helping the researcher decide whether there is an intervention effect, how large it is, and whether it is practically significant. To help applied researchers in the use of the analyses, we have organized the data in the different ways required by the different analytical procedures and made these data available online. We also provide Internet links to all free software available, as well as all the main references to the analytical techniques. Finally, we suggest that appropriate and informative data analysis is likely to be a step forward in documenting and communicating results and also for increasing the scientific credibility of SCEDs.

Analyzing Two-Phase Single-Case Data with Non-overlap and Mean Difference Indices: Illustration, Software Tools, and Alternatives

Two-phase single-case designs, including baseline evaluation followed by an intervention, represent the most clinically straightforward option for combining professional practice and research. However, unless they are part of a multiple-baseline schedule, such designs do not allow demonstrating a causal relation between the intervention and the behavior. Although the statistical options reviewed here cannot help overcoming this methodological limitation, we aim to make practitioners and applied researchers aware of the available appropriate options for extracting maximum information from the data. In the current paper, we suggest that the evaluation of behavioral change should include visual and quantitative analyses, complementing the substantive criteria regarding the practical importance of the behavioral change. Specifically, we emphasize the need to use structured criteria for visual analysis, such as the ones summarized in the What Works Clearinghouse Standards, especially if such criteria are complemented by visual aids, as illustrated here. For quantitative analysis, we focus on the non-overlap of all pairs and the slope and level change procedure, as they offer straightforward information and have shown reasonable performance. An illustration is provided of the use of these three pieces of information: visual, quantitative, and substantive. To make the use of visual and quantitative analysis feasible, open source software is referred to and demonstrated. In order to provide practitioners and applied researchers with a more complete guide, several analytical alternatives are commented on pointing out the situations (aims, data patterns) for which these are potentially useful.