The Authors Respond

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We are grateful for the interest in our article.1 We proposed an adjusted mortality statistic based on information for an outcome of primary interest and a negative control. In the appendix of our article,1 we provided a simple method to estimate this adjusted standardized mortality ratio (SMR) as a modest extension of the classical SMR. The approach involved using the negative control outcome and reference rates as an offset in a Poisson regression model for the outcome of primary interest. Hengelbrock and Becher2 correctly point out that the variance obtained from using offsets does not account for variability in the observed number of deaths due to the negative control, a component of the offset. They propose a variance estimate for the adjusted SMR which they note may be obtained under the assumption of no covariance between the outcome of interest and the negative control. As in many other settings, with negative control outcomes, there is a cost when addressing bias by calculating our proposed adjusted SMR that is expressed in terms of an increase in variance of the adjusted SMR relative to the standard SMR. Good general advice seems to be to choose a negative control outcome that is not rare compared with the outcome of interest, so that its contribution to the variance of the adjusted SMR is not large.
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