Estimating Causal Effects With Multiple-Baseline Data

• In Event: Methodological Dilemmas Encountered in Analyses and Meta-Analyses of Single-Case Design Research

Abstract

Causal effect inferences can be made from single-case data through the use of randomization tests, which require few assumptions when treatment assignment is randomized (e.g., Edgington, 1980; Kratochwill & Levin, 2010). Researchers are encouraged, however, to move beyond inferences about the presence of an effect and to estimate the size of the effect (American Psychological Association, 2010). An individual causal effect can be defined as the difference between what would be observed for the individual under the treatment condition and what would be observed for that individual under the control condition, thus the causal effect is the difference in two potential responses (Gadbury & Iyer, 2000; Holland, 1986; Rubin, 1974). To estimate causal effects from single-case data assumptions are typically made about how the outcome changes with time and then these assumptions along with baseline observations are used to make projections about what would have happened had we not intervened. If our assumptions are inaccurate, our estimates may be biased. The sensitivity of treatment effect estimates to bias from misspecification (e.g., unaccounted for maturation or history effects) is a substantial methodological problem for single-case researchers.
For the special case where there are two groups of participants, one group assigned to a short baseline and one to a long baseline, it is possible if participants are randomly assigned to the two groups to estimate the average causal effect by comparing those in treatment with those still in baseline, a causal effect estimate which requires minimal assumptions (Ferron, 2011). Most applications of multiple-baseline designs, however, involve three or four baselines lengths, rather than two, and at least three baseline lengths are needed to meet design standards by the What Works Clearinghouse (Kratochwill, Hitchcock, Horner, Levin, Odom, Rindskopf, & Shadish, 2010). The purpose of this poster is to extend the work on estimating causal effects to the more general multiple-baseline case where there can be any number of baseline lengths.
The approach that will be illustrated in the poster is based on (1) random assignment of participants to baseline lengths, (2) temporal staggering of the baselines by t +1 points in time, (3) partitioning of the time series data to make partitions which include the observations exactly t points into treatment along with the baseline observations at these same points in time, and (4) estimation of a multilevel model that is parameterized to yield an estimate of the average causal effect based on the difference in the predicted levels of those in treatment for t points in time and those still in baseline using the previously described partitions of the dataset and which by using the data not in these partitions also yields a more traditional estimate of the treatment effect that is based on the difference between baseline and treatment fitted trajectories. The poster will illustrate this method using data from the multiple-baseline study by Rantz, Dickinson, Sinclair, and Van Houten (2009). Implications for the design and analysis of multiple baseline studies are discussed.

Author

• John M. Ferron, University of South Florida