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Biostatistics Advance Access published online on March 29, 2009
Biostatistics, doi:10.1093/biostatistics/kxp007
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© 2009 The Author(s)
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/2.0/uk/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Frailty modeling of bimodal age-incidence curves of nasopharyngeal carcinoma in low-risk populations

Marion Haugen*

Department of Biostatistics, Institute of Basic Medical Sciences, University of Oslo, PO Box 1122 Blindern, N-0317 Oslo, Norway marion.haugen{at}medisin.uio.no

Freddie Bray

Department of Biostatistics, Institute of Basic Medical Sciences, University of Oslo, PO Box 1122 Blindem, N-0317 Oslo, Norway and The Cancer Registry of Norway, Institute of Population-based Cancer Research, Montebello, N-0310 Oslo, Norway

Tom Grotmol and Steinar Tretli

The Cancer Registry of Norway, Institute of Population-based Cancer Research, Montebello, N-0310 Oslo, Norway

Odd O. Aalen

Department of Biostatistics, Institute of Basic Medical Sciences, University of Oslo, PO Box 1122 Blindern, N-0317 Oslo, Norway and The Cancer Registry of Norway, Institute of Population-based Cancer Research, Montebello, N-0310 Oslo, Norway

Tron A. Moger

Department of Biostatistics, Institute of Basic Medical Sciences, University of Oslo, PO Box 1122 Blindern, N-0317 Oslo, Norway and Institute of Health Management and Health Economics, PO Box 1089 Blindern, N-0317 Oslo, Norway

* To whom correspondence should be addressed.

The incidence of nasopharyngeal carcinoma (NPC) varies widely according to age at diagnosis, geographic location, and ethnic background. On a global scale, NPC incidence is common among specific populations primarily living in southern and eastern Asia and northern Africa, but in most areas, including almost all western countries, it remains a relatively uncommon malignancy. Specific to these low-risk populations is a general observation of possible bimodality in the observed age-incidence curves. We have developed a multiplicative frailty model that allows for the demonstrated points of inflection at ages 15–24 and 65–74. The bimodal frailty model has 2 independent compound Poisson-distributed frailties and gives a significant improvement in fit over a unimodal frailty model. Applying the model to population-based cancer registry data worldwide, 2 biologically relevant estimates are derived, namely the proportion of susceptible individuals and the number of genetic and epigenetic events required for the tumor to develop. The results are critically compared and discussed in the context of existing knowledge of the epidemiology and pathogenesis of NPC.

Keywords: Carcinogenesis; Compound Poisson; Frailty; Nasopharyngeal carcinoma; Survival analysis

Received July 9, 2008; revised November 3, 2008; revised January 29, 2009; accepted for publication February 23, 2009.


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