GfKl 2008 - Legos

On the power of corrected score functions to
adjust for measurement error
Thomas Augustin and Matthias Wallner
Department of Statistics, University of Munich (LMU)
augustin@stat.uni-muenchen.de
Abstract. Measurement error modeling, also called errors-in-variables-modeling,
is a generic term for all situations where additional uncertainty in the variables
has to be taken into account, in order to avoid severe bias in the statistical analysis.
The problem is omnipresent in technical statistics, when data from imperfect
measurement instruments are analyzed, as well as in biometrics, econometrics or
social science, where operationalizations (surrogates) are used instead of complex
theoretical constructs.
After a brief introduction to the area of measurement error modelling, the talk
discusses the power and some limitations of Nakamura’s general principle of corrected
score functions, mainly in the context of failure time data. Starting with classical
covariate measurement error in Cox’s PH model, it is shown how the Breslow
likelihood can be corrected, while according to results by Stefanski and Nakamura
himself no corrected score function for the partial likelihood can exist. We then turn
to parametric failure time models and extend consideration to additionally errorprone
lifetimes. Finally, some ideas for handling Berkson-type errors (as occurring,
e.g., in Radon studies) and rounded errors will be sketched.
Key words: Measurement error, error-in-variables, survival analysis, Cox model,
rounding
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