September 2021 Assessing selection bias in regression coefficients estimated from nonprobability samples with applications to genetics and demographic surveys
Brady T. West, Roderick J. Little, Rebecca R. Andridge, Philip S. Boonstra, Erin B. Ware, Anita Pandit, Fernanda Alvarado-Leiton
Author Affiliations +
Ann. Appl. Stat. 15(3): 1556-1581 (September 2021). DOI: 10.1214/21-AOAS1453


Selection bias is a serious potential problem for inference about relationships of scientific interest based on samples without well-defined probability sampling mechanisms. Motivated by the potential for selection bias in: (a) estimated relationships of polygenic scores (PGSs) with phenotypes in genetic studies of volunteers and (b) estimated differences in subgroup means in surveys of smartphone users, we derive novel measures of selection bias for estimates of the coefficients in linear and probit regression models fitted to nonprobability samples, when aggregate-level auxiliary data are available for the selected sample and the target population. The measures arise from normal pattern-mixture models that allow analysts to examine the sensitivity of their inferences to assumptions about nonignorable selection in these samples. We examine the effectiveness of the proposed measures in a simulation study and then use them to quantify the selection bias in: (a) estimated PGS-phenotype relationships in a large study of volunteers recruited via Facebook and (b) estimated subgroup differences in mean past-year employment duration in a nonprobability sample of low-educated smartphone users. We evaluate the performance of the measures in these applications using benchmark estimates from large probability samples.

Funding Statement

This work was supported by grants from the National Institutes for Health (#1R21HD090366-01A1, #R01AG055406). The National Survey of Family Growth (NSFG) is conducted by the Centers for Disease Control and Prevention’s (CDC’s) National Center for Health Statistics (NCHS) under contract # 200-2010-33976 with University of Michigan’s Institute for Social Research with funding from several agencies of the U.S. Department of Health and Human Services, including CDC/NCHS, the National Institute of Child Health and Human Development (NICHD), the Office of Population Affairs (OPA) and others listed on the NSFG webpage (see The views expressed here do not represent those of NCHS nor the other funding agencies.


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Brady T. West. Roderick J. Little. Rebecca R. Andridge. Philip S. Boonstra. Erin B. Ware. Anita Pandit. Fernanda Alvarado-Leiton. "Assessing selection bias in regression coefficients estimated from nonprobability samples with applications to genetics and demographic surveys." Ann. Appl. Stat. 15 (3) 1556 - 1581, September 2021.


Received: 1 April 2020; Revised: 1 March 2021; Published: September 2021
First available in Project Euclid: 23 September 2021

MathSciNet: MR4316661
zbMATH: 1478.62345
Digital Object Identifier: 10.1214/21-AOAS1453

Keywords: Linear regression , National Survey of Family Growth , nonprobability samples , polygenic scores , probit regression , selection bias

Rights: Copyright © 2021 Institute of Mathematical Statistics


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Vol.15 • No. 3 • September 2021
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