Pain and physical activity for one individual

A comparison of models

Abstract

Aims: there is increasing awareness that for effective patient care we need more than only randomized controlled trials with groups of participants and that carefully collected single case (N = 1) data have several important advantages over traditional group-level studies. With the advance of technology, collecting relevant data from a single case is becoming easier by the day, and this offers tremendous opportunities for understanding how behaviors displayed by an individual can be influenced by one or several key variables. For example, how pain experienced influences the amount of time spent on physical exercise. 
Method: using publicly available observational single case data, five models are compared: a classical ordinary least squares (OLS) linear regression model; a dynamic regression model (DRM); a two-level random-intercepts model (2LRI); a continuous covariate first-order autoregressive correlation model (CAR1); and an ordinary least squares model with time trend (OLST). These models are compared in terms of overall model fit statistics, estimates of the relation between physical activity (response variable of interest) and pain (covariate of interest), and residual statistics. 
Results: 2LRI outperforms all other models on both overall model fit and residual statistics, and provides covariate estimates that are in between the relative extremes provided by other models. CAR1 and OLST demonstrate an almost identical performance and one that is substantially better than OLS – which performs worst – and DRM. 
Conclusion: for observational single case data, DRM, CAR1, OLST, and 2LRI account for the serial correlation that is typically present in single case data in somewhat different ways under somewhat different assumptions, and all perform better than OLS. Implications of these findings for observational, quasi-experimental, and experimental single case studies are discussed.