Hi Yachen,
Maybe you find the paper
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.973.8418&rep=rep1&type=pdfuseful.
See formulae (7) and (8), and section 2 in particular.
Regards - Val Fedorov
Let me know if the link works. Otherwise, I can send you a pdf file.
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Valerii Fedorov
Vice President
ICONplc
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Original Message:
Sent: 02-05-2021 17:48
From: Yachen Zhu
Subject: How to understand the Berkson type measurement error?
Hi everyone,
I am a new researcher in environmental epidemiology. I heard people saying from time to time that "Berkson type measurement error will induce no/little bias on the risk estimates; especially in the linear regression model, where aggregation in the exposure/independent variable will yield no bias in the regression estimate." There are theoretical proof and many empirical papers on this topic. But personally I find it hard to understand, because when I simulate datasets myself, aggregating the independent variable by group and compare the linear regression effect estimate to that from the fully individual-level study, I would usually notice a bias. For example, in the case below:
(R packages 'dplyr' and 'broom' are loaded before running the code above)
It seems that the way that datasets are simulated does matter in the whether there is bias in regression estimate. But people usually use 'Berkson type error' to refer to the case where group mean is used for individual exposure assignment, and assert that there is no bias incurred by that. I wonder if that is always right, and I am eager to learn more about the Berkson type error model from professionals in statistics and epidemiology in the ASA community. Thank you, and I look forward to your insights on this problem.
Best,
Yachen
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Yachen Zhu
PhD Student
University of California-Irvine
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