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Prof. Wenjiang Fu
University of Houston, USA
A Novel Statistical Method for Age-standardization With Applications to Marketing Researchand Public Health Studies
In public health, economics, marketing research and business management, it is importantto estimate the temporal trend of disease rates, sales of products, or themarket share of a business during a period of time. Often the disease rates vary with the age of patients (e.g. cancer mortality)or the sales of products vary with the age ofconsumers (e.g. sales of cosmeticproducts or life insurance policies). To estimate the temporal trend across a number of years, asummary value (e.g. yearly rate or percentage) needs to be estimated based on a sequence of age-specific rates or percentages. However, such a task is well known to be complex because of the Simpson’s paradox and becausethe age structure varies with time due to aging of the population.  Thismakesthe crude rate heavily depend on the age structureand vary drastically across time periods even if the age-specific rates remain the same, resulting ininappropriatecomparison and trend estimation. To address this issue,a direct age-standardization procedure has been employed in the literature to calculate asummary valueusing the age-structure of a standard population, such as the US 2000 population age structure.
Although this direct age-standardization method has become the “standard” procedure in marketing research, demography, sociology, and public health research, it has been criticized for the lack of theoretical justification and for generating statistical illusions. In this work, I will study the direct age-standardization method using statistical theory, point out that age-standardization inevitably introduces bias, and further provide an upper bound of such bias. In particular, I demonstrate that using the age structure of the US 2000 Standard Population leads to severe overestimation of cancer mortality and the sales of US life insurance policies.I will then introduce a novel mean reference population method, which minimizes the bias andlargelyimproves the estimationaccuracy. This method further addresses the controversy about the selection of the reference population for the age-standardization. Finally,I will discuss some related statistical issues.This is a joint work with Shuangge Ma, David Todem and Martina Fu. 
Dr. Wenjiang Fu is Professor of Statistics in the Department of Mathematics of the University of Houston. His research interest covers a wide range of research areas in theoretical and applied statistics, including variable selection via regularization methods, statistical computing via the coordinate-descent algorithm, high dimensional data models and genome data analysis, statistical models for age-period-cohort analysis with applications to public health studies, demography, sociology, economics and marketing research. He has collaborated with clinicians and sociologists in a number of research areas, including cancer, pediatrics, neural science, patient safety, etc. He received PhD degree in biostatistics from the University of Toronto in Canada on the Lasso method, theory and applications. Before joining the University of Houston, he was Assistant and Associate Professor in the College of Human Medicine of Michigan State University andResearch Associate Professor in the Department of Statistics, Texas A&M University. He has visited the Australian National University and the National University of Singapore. His research has been funded by the US National Cancer Institute, the National Institute of Child and Human Development, the National Institute of Allergy and Infectious Diseases, the Centers for Disease Control and Prevention, Michigan State University, Michigan Health and Hospital Association, and the Hunt-For-A-Cure Foundation for cystic fibrosis.
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