Sample Size Guidelines When Using a Validation Study to Adjust for Measurement Error Bias in Linear Regression

• Activity Number: 512
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): John W. Rogers*+
• Companies: Westat Inc.
• Keywords: Regression calibration ; Multiple imputation

Abstract

From a set of N observations of Y and X, regression parameters predicting Y will be biased when X is measured with error. Unbiased slope estimates can be obtained if an estimated measurement error variance is available from a validation sample with paired measurements X and G, the "gold standard" for the quantity measured by X. Such situations often arise in environmental sampling, such as using a sampling badge as a surrogate for personal exposure monitoring or a pesticide use questionnaire as a surrogate for pesticide exposure. An internal validation sample may be collected as part of the N observations or an external estimate can be obtained from a separate study. The uncertainty in the measurement error variance contributes uncertainty to the bias corrected slope. That uncertainty needs to be included when determining sample sizes. This paper presents sample size guidelines for the size of the validation sample relative to the entire sample. The suggested sample sizes depend on the r-square(X,Y), r-square(Y,G), and the sample size that would be used if the gold standard was used for all cases. Guidelines are presented for both internal and external validation samples.