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

<div><p>Background</p><p>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.</p><p>Purpose</p><p>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.</p><p>Methods</p><p>Four years of adults’ (<i>N</i> = 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.</p><p>Results</p><p>Morbidity increased exponentially with age (<i>P</i><.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 (<i>P</i><.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 (<i>Ps</i><.001).</p><p>Conclusions</p><p>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.</p></div

Model estimates for costs and for the rates at which costs increase.

<p>A: Cohort-sequential model estimates for costs. B: Hockey stick regression model estimates for rates at which costs increase. The tipping point indicates the estimated age at which a significant increase is observed in the rate of change <i>of the rate of change</i>. Model estimates are shown in their original metrics. Note that the y axis in Fig 5A represents annual cost estimates, while that of Fig 5B represents changes over time in costs. Thus, slopes shown in Fig 5A and 5B represent 1st and 2nd derivatives, respectively. Both y axes are reverse scaled, such that values positioned higher on the page indicate more favorable outcomes (lower costs or slower rates of growth in costs). Shaded regions indicate 95% confidence intervals. Cost estimates were adjusted to 2009 values using the Consumer Price Indices of the U.S. Bureau of Labor Statistics [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0123910#pone.0123910.ref017" target="_blank">17</a>].</p

Cohort-sequential model for morbidity.

<p>Model fit was adequate (χ²(508) = 749.078, <i>P</i><.001; χ ²/<i>df</i> [NC] = 1.475; CFI = .997; RMSEA = .019). M_i was constrained to equality across age cohorts, as were D_i and M_s. Autoregressive pathway coefficients are listed in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0123910#pone.0123910.s002" target="_blank">S1 Table</a>. Asterisks indicate <i>P</i><.001; dagger, parameter constrained to 0; M_i, mean intercept; D_i, intercept variance (disturbance term); M_s, mean slope; D_s, slope variance; Morb., morbidity.</p

Model estimates for morbidity and rates of morbidity progression.

<p>A: Cohort-sequential model estimates for morbidity. B: Hockey stick regression model estimates for rates of morbidity progression. The tipping point indicates the estimated age at which a significant increase is observed in the rate of change <i>of the rate of change</i>. Model estimates are shown in their original metrics. Note that the y axis in Fig 4A represents model-estimated morbidity scores, while that of Fig 4B represents changes over time in morbidity. Thus, slopes shown in Fig 4A and 4B represent 1^st and 2^nd derivatives, respectively. Both y axes are reverse scaled, such that values positioned higher on the page indicate more favorable outcomes (better health status or slower morbidity progression). Shaded regions indicate 95% confidence intervals.</p

Effects of exclusion criteria on sample size.

<p>Effects of exclusion criteria on sample size.</p

Implicit Mercantilism, Oligopoly, and Trade*

The authors propose a new model of trade between developing and advanced economies to capture the effects of important asymmetries in the organizations of their industries. This model demonstrates how the industrial structure of a developing economy can evolve to produce what the authors call “implicit mer-cantilism. ” Free entry plus domestic oligopoly in a developing economy, when combined with competitive behavior in developed countries, generates several distinct stages of mercantilism hitherto unrecognized in the literature. Each stage has its own pattern of interaction with a competitive trading world. As the pro-duction costs and techniques of the mercantile society converge to world standards, its citizens will first lose from this progress, only later to gain. Both effects are due to certain relationships between home prices and world prices, newly identified in this paper. The analysis is particularly relevant to the structure of Asian economies, and to policy debates about their reform. 1