A Markov approach for increasing precision in the assessment of data-intensive behavioral interventions

Health interventions using real-time sensing technology are characterized by intensive longitudinal data, which has the potential to enable nuanced evaluations of individuals' responses to treatment. Existing analytic tools were not developed to capitalize on this opportunity as they typically focus on first-order findings such as changes in the level and/or slope of outcome variables over different intervention phases. This paper introduces an exploratory, Markov-based empirical transition method that offers a more comprehensive assessment of behavioral responses when intensive longitudinal data are available. The procedure projects a univariate time-series into discrete states and empirically determines the probability of transitioning from one state to another. State transition probabilities are summarized separately in phase-specific transition matrices. Comparing transition matrices illuminates intricate, quantifiable differences in behavior between intervention phases. Statistical significance is estimated via bootstrapping techniques. This paper introduces the methodology via three case studies from a secondhand smoke reduction trial utilizing real-time air particle sensors. Analysis enabled the identification of complex phenomena such as avoidance and escape behavior in response to punitive contingencies for tobacco use. Additionally, the largest changes in behavior dynamics were associated with the introduction of behavioral feedback. The Markov approach's ability to elucidate subtle behavioral details has not typically been feasible with standard methodologies, mainly due to historical limitations associated with infrequent repeated measures. These results suggest that the evaluation of intervention effects in data-intensive single-case designs can be enhanced, providing rich information that can ultimately be used to develop interventions uniquely tailored to specific individuals.