# American Institute of Mathematical Sciences

August  2004, 4(3): 813-821. doi: 10.3934/dcdsb.2004.4.813

## Testing increasing hazard rate for the progression time of dementia

 1 Division of Biostatistics, Washington University in St. Louis, St. Louis, MO 63110, United States, United States, United States 2 Department of Surgery, Washington University in St. Louis, St. Louis, MO 63110, United States 3 Department of Neurology and Pathology and Immunology, Washington University in St. Louis, St. Louis, MO 63110, United States

Received  January 2003 Revised  January 2004 Published  May 2004

In the longitudinal studies of certain diseases, subjects are assessed periodically. In fact, many Alzheimer's Disease Research Centers (ADRC) in the United States typically assess their subjects annually, resulting in grouped or interval censored data for the progression time from one stage of dementia to a more severe stage of dementia. This paper studies the likelihood ratio test for increasing hazard rate associated with the progression time of dementia based on grouped progression time data. We first give the maximum likelihood estimators (MLEs) for model parameters under the assumption that the hazard rate of the progression time is nondecreasing. We then present the likelihood ratio test for testing the null hypothesis that the hazard rate is constant against the alternative that it is increasing. Finally, the methodology is applied to the dementia progression time from the Consortium to Establish a Registry for Alzheimer's Disease (CERAD). The statistical methodology developed here, although specifically referred to the study of dementia in the paper, can be easily applied to other longitudinal medical studies in which the disease status is categorized according to the severity and the hazard rate associated with the transition time among disease stages is to be tested.
Citation: C. Xiong, J.P. Miller, F. Gao, Y. Yan, J.C. Morris. Testing increasing hazard rate for the progression time of dementia. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 813-821. doi: 10.3934/dcdsb.2004.4.813
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