Bayesian Unknown Change-Point Models to Investigate Immediacy in Single Case Designs

• Published in: Psychological methods 2017-12, Vol.22 (4), p.743-759
• Main Authors: Natesan, Prathiba, Hedges, Larry V
• Format: Article
• Language: English
• Subjects: Bayes Theorem; Data Interpretation, Statistical; Humans; Markov Chains; Models, Statistical; Monte Carlo Method; Research Design - statistics & numerical data; Simulation; Statistical Estimation; Statistical Probability
• ISSN: 1082-989X; 1939-1463
• DOI: 10.1037/met0000134

Although immediacy is one of the necessary criteria to show strong evidence of a causal relation in single case designs (SCDs), no inferential statistical tool is currently used to demonstrate it. We propose a Bayesian unknown change-point model to investigate and quantify immediacy in SCD analysis. Unlike visual analysis that considers only 3-5 observations in consecutive phases to investigate immediacy, this model considers all data points. Immediacy is indicated when the posterior distribution of the unknown change-point is narrow around the true value of the change-point. This model can accommodate delayed effects. Monte Carlo simulation for a 2-phase design shows that the posterior standard deviations of the change-points decrease with increase in standardized mean difference between phases and decrease in test length. This method is illustrated with real data. Translational Abstract An immediate change in the dependent variable following introduction of treatment is called immediacy. Immediacy is a necessary condition to show strong evidence of causality in single case designs (SCDs). Currently no objective and inferential statistical tools are used to investigate immediacy. We propose a Bayesian unknown change-point model to investigate and quantify immediacy in SCD analysis. This model assumes that the change-point between baseline and treatment phases is unknown and estimates the change-point. Unlike visual analysis that considers only 3-5 observations in consecutive phases to investigate immediacy, this model considers all data points. Immediacy is indicated when the change-point is estimated accurately and with less uncertainty. This model can accommodate delayed effects where immediacy may not be possible due to the nature of some treatments taking longer to take effect. The use of Bayesian methods helps overcome some of the most common drawbacks of single case designs such as small sample sizes and lack of independence of observations. The model performs well for data with at least 8 observations per phase and a mean difference of at least 3 standard deviations between the baseline and treatment phases. This method is illustrated with real data.