Summary
When analyzing trends in cancer rates, it is common to rely on the so-called Annual Percent Change (APC). For dealing with such a measure of trend, directly age-adjusted rates are usually considered. Classical methods such as pooled t-tests are often applied for comparing APCs of two groups of individuals in a simple way under independence assumption. In practice, it is quite common to find groups of interest for which the independence assumption fails because their regions or periods of time overlap. No one of the papers that deal this problem consider the case where more than two APCs are compared. In this work we propose a Wald-type test-statistic which is not difficult to compute once we provide the estimators of two or more APCs to be compared. These estimators are the minimum power divergence estimators that cover as special case those obtained by maximum likelihood.
This work is related to the stay of Nirian Martín in Harvard University (September 2008 - August 2009), supported by the Real Colegio Complutense. She met Marisa just the first day after arriving in Spain, September 1. In the last conversation Marisa told Nirian that both will meet soon again. Due to her optimistic character it was impossible to imagine they both could not meet again. This paper has been written in memory to Marisa.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Dik, J.J., de Gunst, M.C.M.: The distribution of general quadratic forms in normal variables. Statistica Neerl. 39, 14–26 (1985)
Horner, M.J., Ries, L.A.G., Krapcho, M., Neyman, N., Aminou, R., Howlader, N., Altekruse, S.F., Feuer, E.J., Huang, L., Mariotto, A., Miller, B.A., Lewis, D.R., Eisner, M.P., Stinchcomb, D.G., Edwards, B.K. (eds.): SEER Cancer Statistics Review. National Cancer Institute, Bethesda (1975-2006)
Martín, N., Li, Y.: A new class of minimum power divergence estimators with applications to cancer surveillance. J. Multivar. Anal (2011) (in press)
Pardo, L.: Statistical Inference Based on Divergence Measures. Chapman & Hall/CRC, New York (2006)
Pardo, L., Martin, N.: Homogeneity/Heterogeneity Hypotheses for Standardized Mortality Ratios Based on Minimum Power-divergence Estimators. Biomet. J. 51, 819–836 (2009)
Li, Y., Tiwari, R.C., Zou, Z.: An age-stratified model for comparing trends in cancer rates across overlapping regions. Biomet. J. 50, 608–619 (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Martín, N., Li, Y. (2011). Multiple Comparison of Change Trends in Cancer Mortality/Incidence Rates Taking with Overlapping Regions and Time-Periods. In: Pardo, L., Balakrishnan, N., Gil, M.Á. (eds) Modern Mathematical Tools and Techniques in Capturing Complexity. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20853-9_33
Download citation
DOI: https://doi.org/10.1007/978-3-642-20853-9_33
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-20852-2
Online ISBN: 978-3-642-20853-9
eBook Packages: EngineeringEngineering (R0)