The value of a statistical year of life implied by dialysis practice currently averages $129,090 per QALY ($61,294 per year), but is distributed widely within the dialysis population. The spread suggests that coverage decisions using dialysis as the benchmark may need to incorporate percentile values (which are higher than the average) to be consistent with the Rawlsian principles of justice of preserving the rights and interests of society's most vulnerable patient groups.
The PageRank model pioneered by Google is the most common approach for generating web search results. We present a two-stage algorithm for computing the PageRank vector where the algorithm exploits the lumpability of the underlying Markov chain. We make three contributions. First, the algorithm speeds up the PageRank calculation significantly. With web graphs having millions of webpages, the speedup is typically in the two-to three-fold range. The algorithm can also embed other acceleration methods such as quadratic extrapolation, the Gauss-Seidel method, or the Biconjugate gradient stable method for an even greater speed-up; cumulative speedup is as high as 7 to 14 times. The second contribution relates to the handling of dangling nodes. Conventionally, dangling nodes are included only towards the end of the computation. While this approach works reasonably well, it can fail in extreme cases involving aggressive personalization. We prove that our algorithm is the generally correct way of handling dangling nodes using probabilistic arguments. We also discuss variants of our algorithm, including a multistage extension for calculating a generalized version of the PageRank model where different personalization vectors are used for webpages of different classes. The ability to form class associations may be useful for building more refined models of web traffic.
Published evidence suggests that frequent hemodialysis (more than three times per week) for patients with ESRD may improve health-related quality of life and has the potential to increase longevity and reduce hospitalization and other complications. Here, a Monte Carlo simulation model was used to compare varying combinations of in-center hemodialysis frequency (three to six treatments per week) and session length (2 to 4.5 h per session) with regard to unadjusted and quality-adjusted life-years and total lifetime costs for a cohort of 200,000 patients, representing the prevalent ESRD population. The incremental cost-effectiveness ratio was calculated for the various regimens relative to a conventional hemodialysis regimen (three treatments per week, 3.5 h per session). Using conservative assumptions of the potential effects of more frequent hemodialysis on outcomes, most strategies achieved a costeffectiveness ratio of Ͻ$125,000, although all had a cost-effectiveness ratio of Ͼ$75,000. The costeffectiveness ratio increased with the frequency of hemodialysis. More frequent in-center hemodialysis strategies could become cost-neutral if the cost per hemodialysis session could be reduced by 32 to 43%. No other change in model assumptions achieved cost neutrality. In conclusion, given the extraordinarily high costs of the ESRD program, the viability of more frequent hemodialysis strategies depends on significant improvements in the economic model underlying the delivery of hemodialysis.
Dialysis is the most common therapy for patients afflicted with chronic kidney failure. Currently, little is known about the relationship between the timing of dialysis initiation and the therapy's cost and effectiveness. This paper examines the cost-effective initiation of dialysis and compares standard initiation criteria from the clinical literature to computationally derived strategies. Comparisons make use of a simulation model that integrates submodels of disease progression, hospitalization, transplantation, cost, and quality of life. The simulation model is also used by an approximate dynamic programming (ADP) algorithm to derive approximately optimal strategies that maximize patient welfare. Patient welfare is measured from the society's perspective and is defined as the product of the expected discounted quality-adjusted life years (QALYs) and a “value-of-life” parameter, minus the expected total discounted medical expenditures. Also considered is an alternative formulation in which the goal is to minimize the expected total discounted medical expenditures without affecting patient QALYs relative to current medical practice. Numerical results show that: (i) standard early initiation strategies, where once started on dialysis patients are kept on a fixed weekly program, have a limited potential, and (ii) early dialysis at an incrementally increasing dose customized to each patient can yield a significant cost advantage. These findings demonstrate computationally intensive models of disease progression, and therapy effectiveness can identify novel strategies for managing expensive medical therapies and a more efficient use of scarce health-care resources.
The model produces reliable results and is robust. It enables the cost-effectiveness analysis of dialysis strategies.
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