Abstract
The main points of in the letter by Kopylev and Dzierlenga can be summarized as: (1) if the difference of two parameter estimates is not statistically significant, then using either one can be considered a reasonable representation of a parameter for use in a meta-analysis, and (2) that we calculated the estimand in our simulation incorrectly. We address these two points in turn.
We welcome the comments in the letter by Kopylev and Dzierlenga [1] and the opportunity to reply. The main points of their letter can be summarized as: (1) if the difference of two parameter estimates is not statistically significant, then using either one can be considered a reasonable representation of a parameter for use in a meta-analysis, and (2) that we calculated the estimand in our simulation incorrectly. We address these two points in turn below. With respect to the first point, consider the following scenario. Assume that: (a) you have small, fixed budget with which to live, (b) your doctor has diagnosed you with a disease for which one apple per day will keep you alive and you want to live, and (c) the only place to buy apples is a fruit stand outside your apartment building. Furthermore, assume the fruit stand has two vendors who work on alternating days, and you know that one vendor sells apples at their true price of $1, and the other vendor charges variable prices, but those prices are, on average, $1.40. If a friend of yours, a statistician, tells you she has done a careful analysis of the prices that the two vendors charge, and that there is no statistically significant difference in the prices. Would this influence your decision about which vendor to buy from? Most would likely still opt to buy the apples at $1 regardless of the apparent lack of statistical difference. In epidemiology, subject-matter considerations can take precedence over the statistical stability of an estimate when making decisions on how to handle bias. A good example of this can be found in Rothman et al.’s third edition of Modern Epidemiology pp. 261–262 (2008) [2]. There they say, in essence, that if a bias is known to exist, whether it is statistically significant is irrelevant, and one chooses an approach that minimizes the bias. Applied to the re-expression case, this would mean using re-expression only when the expected bias would be below some amount felt to be ignorable, such as a < 10% difference. With respect to the second point, we note that Morris et al. (2018) [3] use the acronym ADEMP for the recommended elements of a report on a simulation, where A is for aims, D is for data generating mechanism, E is for estimand, M is for methods, and P is for performance. The section of their paper describing the estimand element is titled “Estimands and other targets”, and their Table 3 presents examples of what might constitute the estimand or target. In statistics, there is a difference between an estimand (population parameter) and a (point) estimate of the population parameter [4, 5]. Our report used the term estimand for consistency with the ADEMP acronym, but our target was an estimate. We were, in fact, trying to quantify the difference between an estimate and a re-expressed version of it. Our formula 5, for example, would have been better expressed by using “estimate” where we used “estimand”. While making sure the term estimand is used correctly is a good project, we regard Kopylev and Dzierlenga’s attention to this in our report a matter of semantics. With the improvement in labelling discussed here, we stand by our work, and do not agree with the re-interpretation proposed by Kopylev and Dzierlenga. In their letter, Kopylev and Dzierlenga suggest a new approach to evaluate methods of re-expression of estimates from one exposure scale to another (by “generating data with 
in un-logged space”). We look forward to reading a more detailed explication and an evaluation of the approach.
Authors’ contributions
M.P.L wrote the main manuscript text. All authors reviewed and edited the manuscript.
Funding
Support for this project came from 3 M to Ramboll. 3 M did not influence the research in any way and encouraged publication in a peer-reviewed journal.
Data availability
No datasets were generated or analysed during the current study.
Declarations
Ethics approval and consent to participate
Not applicable.
Competing interests
The authors declare no competing interests.
Footnotes
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References
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Associated Data
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Data Availability Statement
No datasets were generated or analysed during the current study.