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Reply to: “Methodological issues regarding "Decline in ankle-brachial index is stronger in poorly than in well controlled diabetes: Results from the Heinz Nixdorf Recall cohort study"”

  • Bernd Kowall
    Correspondence
    Corresponding author.
    Affiliations
    Center of Clinical Epidemiology, Institute for Medical Informatics, Biometry and Epidemiology, Medical Faculty, University Duisburg-Essen, Essen, Germany
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  • Andreas Stang
    Affiliations
    Center of Clinical Epidemiology, Institute for Medical Informatics, Biometry and Epidemiology, Medical Faculty, University Duisburg-Essen, Essen, Germany
    School of Public Health, Department of Epidemiology Boston University, 715 Albany Street, Talbot Building, Boston, MA, 02118, USA
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      We are thankful to Dr. Yarandi et al. for their critical view on our manuscript [
      • Kowall B.
      • Erbel R.
      • Moebus S.
      • Lehmann N.
      • Kröger K.
      • Stang A.
      Decline in ankle-brachial index is stronger in poorly than in well controlled diabetes: results from the Heinz Nixdorf Recall Cohort Study.
      ]. They address several methodical issues, and we would like to give our position on these issues.
      • 1.
        We analyzed observational data from a cohort study with 5-year and 10-year follow-up. Yarandi et al. objected that we did not do a sample size calculation and, thus, cannot detect significant associations when the sample size is too small. Thus, in the view of Yarandi et al., finding statistically significant associations is the aim of statistical analyses. However, we stated in the Methods section that our aim was estimation and not significance testing. Significance testing has met a lot of criticism. The American Statistical Association, for example, advises against significance testing [
        • Wasserstein R.L.
        • Schirm A.L.
        • Lazar N.A.
        Moving to a world beyond „p < 0.05“.
        ], and Nature has recently published a comment titled “Retire Statistical Significance” [
        • Amrhein V.
        • Greenland S.
        • McShane B.
        Retire statistical significance.
        ].
      • 2.
        Yarandi et al. suppose that we used “enter mode” to select variables for our multivariable model. This is not the case, and we did not state this in the Methods section. Instead, we used a direct acyclic diagram (causal diagram) to identify a minimally sufficient adjustment set.
      • 3.
        Yarandi et al. advise us to have at least 10 events per variable included in the model. To have at least 10 events per variable (EPV) (or, to be more precise, per degree of freedom) is a rule of thumb for which there is some support in the literature. However, no consensus has been reached on this issue. Courvoisier et al. stated that problems may arise even if EPV is > 10 [
        • Courvoisier D.S.
        • Combescure C.
        • Agoritsas T.
        • Gayet-Ageron A.
        • Perneger T.V.
        Performance of logistic regression modeling: beyond the number of events per variable, the role of data structure.
        ]. Peduzzi et al. did a simulation study and suggested at least 10 EPVs [
        • Peduzzi P.
        • Concato J.
        • Kemper E.
        • Holford T.R.
        • Feinstein A.R.
        A simulation study of the number of events per variable in logistic regression analysis.
        ]. Vittinghoff and McCulloch, however, claimed that severe problems only arise for EPV <5 [
        • Vittinghoff E.
        • McCulloch C.E.
        Relaxing the rule of ten events per variable in logistic and Cox regression.
        ]. In our logistic regression models for 10-year follow-up, we included the exposure variable (HbA1c categories) plus 2 covariates in the first and plus 12 variables in the second model. There were 149 incident events of ABI <0.9, and, thus, the number of events per degree of freedom was 24.8 in the first, and 8.8 in the second model. So EPV is slightly smaller than 10 in model 2.
      • 4.
        Yarandi et al. criticize that the confidence intervals are rather wide in Table 3 [
        • Kowall B.
        • Erbel R.
        • Moebus S.
        • Lehmann N.
        • Kröger K.
        • Stang A.
        Decline in ankle-brachial index is stronger in poorly than in well controlled diabetes: results from the Heinz Nixdorf Recall Cohort Study.
        ]. This is true, and, of course, the estimates they picked out from the Table (0.6 (95% CI: 0.1–2.3) and 0.4 (95% CI: 0.1–1.7)) for newly detected diabetes are very imprecise and are compatible with an increase as well as a decrease of the odds to develop ABI < 0.9. The crucial information from Table 3 is the increased odds for poorly controlled diabetes compared to no diabetes (OR = 4.6 (95% CI: 2.2–9.7), and 3.1 (95% CI: 1.3–7.0), respectively). With regard to well controlled known diabetes, and newly detected diabetes, results from the linear regression models shown in Table 2 and results from the mixed linear models (cf. Results section) are more informative than the estimates from the logistic regression models [
        • Kowall B.
        • Erbel R.
        • Moebus S.
        • Lehmann N.
        • Kröger K.
        • Stang A.
        Decline in ankle-brachial index is stronger in poorly than in well controlled diabetes: results from the Heinz Nixdorf Recall Cohort Study.
        ].
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      References

        • Kowall B.
        • Erbel R.
        • Moebus S.
        • Lehmann N.
        • Kröger K.
        • Stang A.
        Decline in ankle-brachial index is stronger in poorly than in well controlled diabetes: results from the Heinz Nixdorf Recall Cohort Study.
        Atherosclerosis. 2019; 284: 37-43
        • Wasserstein R.L.
        • Schirm A.L.
        • Lazar N.A.
        Moving to a world beyond „p < 0.05“.
        Am. Stat. 2019;
        • Amrhein V.
        • Greenland S.
        • McShane B.
        Retire statistical significance.
        Nature. 2019; 567: 305-307
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        • Combescure C.
        • Agoritsas T.
        • Gayet-Ageron A.
        • Perneger T.V.
        Performance of logistic regression modeling: beyond the number of events per variable, the role of data structure.
        J. Clin. Epidemiol. 2011; 64: 993-1000
        • Peduzzi P.
        • Concato J.
        • Kemper E.
        • Holford T.R.
        • Feinstein A.R.
        A simulation study of the number of events per variable in logistic regression analysis.
        J. Clin. Epidemiol. 1996; 49: 1373-1379
        • Vittinghoff E.
        • McCulloch C.E.
        Relaxing the rule of ten events per variable in logistic and Cox regression.
        Am. J. Epidemiol. 2007; 165: 710-718

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