The Avalanche Hypothesis and Compression of Morbidity: Testing Assumptions through Cohort-Sequential Analysis.

BACKGROUND: The compression of morbidity model posits a breakpoint in the adult lifespan that separates an initial period of relative health from a subsequent period of ever increasing morbidity. Researchers often assume that such a breakpoint exists; however, this assumption is hitherto untested. PURPOSE: To test the assumption that a breakpoint exists--which we term a morbidity tipping point--separating a period of relative health from a subsequent deterioration in health status. An analogous tipping point for healthcare costs was also investigated. METHODS: Four years of adults' (N = 55,550) morbidity and costs data were retrospectively analyzed. Data were collected in Pittsburgh, PA between 2006 and 2009; analyses were performed in Rochester, NY and Ann Arbor, MI in 2012 and 2013. Cohort-sequential and hockey stick regression models were used to characterize long-term trajectories and tipping points, respectively, for both morbidity and costs. RESULTS: Morbidity increased exponentially with age (P<.001). A morbidity tipping point was observed at age 45.5 (95% CI, 41.3-49.7). An exponential trajectory was also observed for costs (P<.001), with a costs tipping point occurring at age 39.5 (95% CI, 32.4-46.6). Following their respective tipping points, both morbidity and costs increased substantially (Ps<.001). CONCLUSIONS: Findings support the existence of a morbidity tipping point, confirming an important but untested assumption. This tipping point, however, may occur earlier in the lifespan than is widely assumed. An "avalanche of morbidity" occurred after the morbidity tipping point-an ever increasing rate of morbidity progression. For costs, an analogous tipping point and "avalanche" were observed. The time point at which costs began to increase substantially occurred approximately 6 years before health status began to deteriorate.

Estimation and inference concerning ordered means in analysis of covariance models with interactions.

When interactions are identified in analysis of covariance models it becomes important to identify values of the covariates for which there are significant differences or, more generally, significant contrasts among the group mean responses. Inferential procedures that incorporate a priori order restrictions among the group mean responses would be expected to be superior to those that ignore this information. In this paper we focus on analysis of covariance models with pre-specified order restrictions on the mean response across the levels of a grouping variable when the grouping variable may interact with model covariates. In order for the restrictions to hold in the presence of interactions, it is necessary to impose the requirement that the restrictions hold over all levels of interacting categorical covariates and across pre-specified ranges of interacting continuous covariates. The parameter estimation procedure involves solving a quadratic programming minimization problem with a carefully specified constraint matrix. Simultaneous confidence intervals for treatment group contrasts and tests for equality of the ordered group mean responses are determined by exploiting previously unconnected literature. The proposed methods are motivated by a clinical trial of the dopamine agonist pramipexole for the treatment of early-stage Parkinson's disease.