Assessing the impact of complex interventions on measurable health outcomes is a growing concern in health care and health policy. Interrupted time series (ITS) designs borrow from traditional case-crossover designs and function as quasi-experimental methodology that enables researchers to retrospectively analyze the impact of an intervention. Statistical models used to analyze ITS data a priori restrict the interruption's effect to a predetermined time point or censor data for which the intervention effects may not be fully realized, and neglect changes in the temporal dependence and variability. In addition, current methods limit the analysis to one hospital unit or entity and are not well specified for discrete outcomes (e.g., patient falls). This dissertation develops novel ITS methods based on segmented regression that address the aforementioned limitations.

We propose the 'Robust-ITS' model, a single-unit model able to estimate (rather than merely assume) the lagged effect of an intervention on a health outcome. Robust-ITS accounts for plausible differences in the mean, temporal dependence and variability of an outcome pre- and post-intervention. Next, we develop the 'Robust Multiple ITS' model as an extension of Robust-ITS for multi-unit data. Alongside Robust Multiple ITS, we propose the 'supremum Wald test', able to formally test for the existence of a change point across unit specific mean functions. Lastly, we present the 'Generalized Robust ITS' model, appropriate for outcomes whose underlying distribution belongs to the family of exponential distributions. Generalized Robust ITS expands the available methodology to adequately model multi-unit binary, count and rate ITS. The methods proposed allow researchers to test for the existence of and estimate the change point, borrow information across units in multi-unit settings, and test for differences in the mean function and correlation structure pre- and post-intervention. Throughout, the methodology is illustrated by analyzing patient centered data from a hospital that implemented and evaluated a new care delivery model in multiple units.