数学与物理交叉部
学术报告会
报告人: Prof. Wenjiang Fu (Michigan State University, USA)
题 目: Bias and Artifact Trade-off in Modeling Temporal Trend of Archived Data with Applications to Demography, Marketing Research, Public Health and Sociology
时 间：07.31 (星期五), 15:00--16:00
地 点：数学院南楼N212室
摘 要:
In economics, marketing research, business management, and public health studies, it is important to estimate accurately the temporal trend of sales of products, the market share of a business, or disease trend during a period of time. Often the sales of products vary with the age of consumers (e.g. sales of life insurance policies, cosmetics,) and the disease mortality rate varies with the age of patients. To estimate the temporal trend across a number of years, two approaches are commonly taken, but both involve a difficult modeling issue. One leads to a well-known identifiability problem in age-period-cohort model. The other requires a summary value (e.g. yearly sales or rate) to be estimated based on a sequence of age-specific sales or rates. However, such a task is well known to be complex because of the Simpson’s paradox and because the age structure varies with time due to aging of the population. It is known that the crude rate method heavily depends on the age structure and drastically varies cross time periods even if the age-specific sales or percentages remain the same, resulting in inappropriate trend estimation or comparison across time periods. A direct age-standardization method has been employed in the literature to calculate a summary value using the age-structure of a standard population. For example, using the US 2000 population age structure to calculate the age-adjusted percentage or sales of US life insurance policies. The same method has been applied to demography, public health and sociology.
Although the direct age-standardization method has become the “standard” procedure, it has been criticized in the literature for the lack of justification and for generating statistical illusions. In this talk, I will study the direct age-standardization using statistical framework, point out that the age-standardization procedure 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 the sales of US life insurance policies and cancer mortality rate estimation. Meanwhile, the crude method yields incomparable summary statistics because of th artifact introduced by varying age structure. I will then introduce a novel mean reference population method for a bias-artifact trade off, which removes the artifact, minimizes the bias, and largely improves the estimation accuracy. This is a joint work with Shuangge Ma, David Todem and Martina Fu.
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