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Length-Biased Sampling as a Unifying Concept in Population Studies
A single mathematical relationship, well known by mathematicians but little discussed in sociology and demography, structures phenomena that range from the intergenerational transmission of socioeconomic status to assessing the efficacy of cancer treatment; from criminal recidivism to lifespans and demographic frailty. I make the case that this relationship, "length-biased sampling," should be understood as a unifying concept in population studies -- particularly in contexts that switch perspectives between different levels of aggregation or that mix together cohort and period perspectives. Recognizing the length-biased structure underlying these problems can provide new intuitions for practical applications. I will also argue that three distinct mathematical forms for expressing length-biased relationships provide different insights, and so re-expressing substantive applications that seem most natural in one form in terms of the other form is a strategy for identifying new insights. To illustrate these ideas, I present new expressions for the average lifespan of the living in stationary and stable populations and explore their relationship to period and cohort measures. Substantive applications include interpreting the lifespan of a prevalent cohort in epidemiological studies and estimating the duration of incarceration for those currently in prison.
Elizabeth Wrigley-Field is an assistant professor in Sociology at the University of Minnesota, jointly appointed with the Minnesota Population Center. She works on problems that integrate social processes happening on multiple scales, from the micro (such as individuals' immunological development) to irreducibly macro population processes. Her work asks questions such as, how much inequality is hidden because we only measure the people who live long enough to be counted? and, how did cities, for the first time in human history, become the safest places to live beginning around 100 years ago?