Intervention Analysis Models for Single-Case Designs

• In Event: 30.075 - The Meta-Analysis of Single-Subject Experimental Design Data: Methodological Challenges and Approaches

Abstract

Much of the recent research on methods for statistical analysis or meta-analysis of single-case designs (SCDs) has focused on models for multiple baseline designs, with relatively less attention to treatment reversal designs (i.e., ABAB designs). Multiple baseline are a comparatively simple case because, for a given case, the design involves just one baseline phase and one treatment phase. In contrast, treatment reversal designs involve more than one baseline and more than one treatment phase. For instance, the What Works Clearinghouse guidelines (Kratochwill et al., 2010) indicate that treatment reversal designs must have at minimum two baseline and two treatment phases in order to meet design standards. This makes it more difficult to develop credible—and causally interpretable—models for treatment reversal designs.
An implicit assumption of treatment reversal designs is that the effects of intervention are transient rather than permanent. For the effects of treatment to reverse or decline after their removal necessarily implies that the total effect of treatment is a consequence of the sustained application of an intervention, rather than a permanent effect that would be sustained even if the treatment were removed. To date, most case-level models for single-case designs have focused on linear change within phases (e.g. Gorsuch, 1983; Center, Skiba, and Casey, 1985; Maggin et al., 2011), or models for nonlinear growth after treatment that do not model a complementary decay after treatment has been removed (Moeyaert et al., 2014; Shadish, Kyse, & Rindskopf, 2013; Hembry et al., 2015; Rindskopf 2013). In this study, we build on work by (citation removed for masked review) and develop a simple non-linear model for treatment reversal designs that allows for both nonlinear growth due to application of treatment and non-linear decay as a consequence of removal of treatment. The model is an extension of the set of models for the analysis of interventions proposed by Box and Tiao (1976).
This paper investigates the performance of the model under several different data-generating models. Similar to many previous investigations, we begin by studying performance under models with normal errors with AR(1) autocorrelation. Additionally, we investigate quasi-Poisson and quasi-binomial error structures that more closely match the features of the count- or rate-measures often used in SCD studies of behavior. We present results of Monte Carlo simulation investigations and applications of the model to several empirical examples.

Authors

• Daniel Swan, The University of Texas - Austin

• James Eric Pustejovsky, The University of Texas - Austin