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Mark S Gilthorpe, Yu-Kang Tu, David Gunnell, A coda: oversimplification, implicit assumptions, and measurement error, International Journal of Epidemiology, Volume 33, Issue 6, December 2004, Pages 1402–1403, https://doi.org/10.1093/ije/dyh305
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This debate demonstrates the range of approaches, and their associated limitations, used to examine this deceptively complex issue. An understanding of the range of relationships of errors with each other and with the unobserved measures is crucial. We concur with all contributors that our pieces are an oversimplification, making various implicit assumptions that were omitted in the interests of simplicity and brevity; it is valuable to receive further comments and insights from other correspondents. We summarize what we feel are the main conclusions to draw from this debate.
The debate on underlying assumptions is probably more philosophical than statistical. There are differences in the adopted definitions of ‘true’ outcome and associated assessment errors. For instance, Ian White1 begins with the assumption that over-/under-reporting is present and therefore assessment errors are correlated with unobserved values for self-report whilst uncorrelated for measurement. Consequently, using Oldham's method to test for unequal variances is only valid if error variances of self-report and measurement are equal, which one cannot readily assess. In contrast, we made no assumptions about the correlation between assessment errors and unobserved values, as this is what we sought to test, though we assumed equal error variances. Oldham's method is then valid. The paradox of a method being valid/ invalid with different assumptions for the same problem further reflects the complexity of this issue!
