Checking unimodality using isotonic regression: an application to breast cancer mortality rates

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• 作者：C. Rueda ; M. D. Ugarte ; A. F. Militino
• 关键词：Change point ; Isotonic regression ; Order restricted inference ; Temporal trends ; Joint point regression ; Segmented regression
• 刊名：Stochastic Environmental Research and Risk Assessment (SERRA)
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：30
• 期：4
• 页码：1277-1288
• 全文大小：510 KB
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• 作者单位：C. Rueda (1)
  M. D. Ugarte (2) (3)
  A. F. Militino (2) (3)
  
  1. Department of Statistics and Operations Research, Facultad de Ciencias, Valladolid University, 47005, Valladolid, Spain
  2. Department of Statistics and Operations Research, Public University of Navarre, Pamplona, Spain
  3. INAMAT, Public University of Navarre, Campus de Arrosadia, 31006, Pamplona, Spain
  
• 刊物类别：Earth and Environmental Science
• 刊物主题：Environment
  Mathematical Applications in Environmental Science
  Mathematical Applications in Geosciences
  Probability Theory and Stochastic Processes
  Statistics for Engineering, Physics, Computer Science, Chemistry and Geosciences
  Numerical and Computational Methods in Engineering
  Waste Water Technology, Water Pollution Control, Water Management and Aquatic Pollution
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1436-3259

文摘

In some diseases it is well-known that a unimodal mortality pattern exists. A clear example in developed countries is breast cancer, where mortality increased sharply until the nineties and then decreased. This clear unimodal pattern is not necessarily applicable to all regions within a country. In this paper, we develop statistical tools to check if the unimodality pattern persists within regions using order restricted inference. Break points as well as confidence intervals are also provided. In addition, a new test for checking monotonicity against unimodality is derived allowing to discriminate between a simple increasing pattern and an up-then-down response pattern. A comparison with the widely used joinpoint regression technique under unimodality is provided. We show that the joinpoint technique could fail when the underlying function is not piecewise linear. Results will be illustrated using age-specific breast cancer mortality data from Spain in the period 1975–2005.