Descriptions of the Assertive Community Treatment (ACT) model for people with severe mental illnesses imply a nonlinear relationship between patient function (in specific domains) and time. Specifically, it is postulated that prior to receipt of ACT services, the domain-specific functioning of a patient is characterized by a certain level and relative stability (or gradual change) around that level. As the clinical and support services of ACT begin to exert beneficial influences in patient's lives over the first 6 months or year of services, patients' functioning undergoes a period of rapid change (hopefully improvement), until it restabilizes at a new level. While virtually all longitudinal studies of ACT interventions have been conducted over timeframes that subsume this period of rapid change, none have attempted to explicitly model it. In this project, we propose to develop a nonlinear multilevel model of ACT effects and to apply them to data collected as part of two recent ACT trials in Charleston, South Carolina. Like most mental health services data, the data collected for these trials is irregularly spaced and incomplete - a situation well suited to the multilevel modeling framework. Within the family of multilevel models entertained, we will consider several plausible autocorrelation error structures that allow for irregularly spaced observations. We have also uncovered indirect evidence that at least two different mechanisms may be operating to generate missing data in data set. Through a combination of selection and pattern mixture models, we propose to take the influence of both missing data mechanisms into account when estimating nonlinear treatment effects over time.
