- Email: [email protected]
Frailty and influenza vaccine effectiveness
Vaccine 34 (2016) 4645–4646
Contents lists available at ScienceDirect
Vaccine journal homepage: www.elsevier.com/locate/vaccine
Letter to the Editor Frailty and influenza vaccine effectiveness
Dear Editor, We read with interest the recent paper by Talbot et al. which attempted to assess whether frailty confounds influenza vaccine effectiveness (VE) estimates in test-negative studies [1]. We do not think the authors’ analysis successfully rules out frailty as a confounder of VE estimates in their own study. We further believe that frailty should be expected to confound VE estimates because it meets the structural conditions of a confounder of having a causal effect on both the exposure and outcome [2]; i.e. the level of frailty influences both the decision to vaccinate and the risk of hospitalization and death from influenza [3]. The authors have attempted to measure confounding of VE by frailty by calculating a ratio of unadjusted (‘‘crude”) versus adjusted VE estimates. This kind of statistical approach to confounder identification has several problems. First, change-in-effect estimate criteria are justifiable when the underlying causal mechanisms are poorly understood and possible confounders are not established [4]. This is not the case for frailty. Second, when the outcome is a non-collapsible measure, such as the odds ratio, change-in-estimate criteria can be misleading [4]. Non-collapsibility means that the unadjusted effect is not a weighted average of stratum-specific effects [5,6]. Estimates derived from odds ratios for common outcomes like influenza are subject to non-collapsibility. Thus, the VE ratios reported by Talbot et al. may indicate confounding or noncollapsibility or both. Furthermore, it is also possible for the VE ratio to approach 1 if the confounding bias and non-collapsibility largely cancel each other out, leading to the erroneous conclusion that the VE estimate is not confounded by frailty [5]. Third, the degree of confounding in the reported estimates is difficult to discern because there were too few subjects in the not frail and frail groups, exposing the study to potential sparse data bias [7]. In the not-frail group, the number of test-positive unvaccinated people was just 4 and the number of test-positive vaccinated people was just 3. With the addition of 14 covariates to the model, the estimates will be affected by sparse-data bias [7]. The authors have attempted to mitigate the sparse-data bias by using penalized likelihood methods to shrink inflated covariate estimates. However, the lasso penalty deletes variables from the model when they fail to meet a certain datadriven threshold [8]. Inspection of Table 1 reveals that the VE point estimates for the not-frail and frail groups equal the VE from the crude odds ratios, suggesting that the lasso has dropped the 14 covariates from those models. If any of the deleted covariates are genuine confounders, the resulting VE estimate will remain confounded by them [4]. Similarly, if the lasso has dropped covariates from the ‘‘overall” model used in the VE ratios, the VE estimate will be biased and the VE ratios uninformative.
http://dx.doi.org/10.1016/j.vaccine.2016.08.003 0264-410X/Ó 2016 Elsevier Ltd. All rights reserved.
Given the limitations of this study, it is unwarranted to conclude that frailty does not confound estimates of VE. Estimates of confounding bias must account for other confounders in an unbiased fashion, which requires methods that do not delete confounders such as those based on quadratic rather than lasso penalties [7]. Thus better analyses as well as more data are needed before one can determine the extent of confounding by frailty in test-negative studies of influenza vaccination. Conflict of interest B.J.C. has received research funding from MedImmune Inc. and Sanofi Pasteur, and consults for Crucell NV. S.G. has received funding from Boehringer Ingelheim and Amgen. Acknowledgements The WHO Collaborating Centre for Reference and Research on Influenza is funded by the Australian Government Department of Health. References [1] Talbot HK, Nian H, Chen Q, Zhu Y, Edwards KM, Griffin MR. Evaluating the casepositive, control test-negative study design for influenza vaccine effectiveness for the frailty bias. Vaccine 2016;34(15):1806–9. [2] Pearce N, Greenland S. Confounding and interaction. In: Ahrens W, Pigeot I, editors. Handbook of epidemiology. New York: Springer; 2014. p. 659–84. [3] McGrath LJ, Cole SR, Kshirsagar AV, Weber DJ, Sturmer T, Brookhart MA. Hospitalization and skilled nursing care are predictors of influenza vaccination among patients on hemodialysis: evidence of confounding by frailty. Med Care 2013;51(12):1106–13. [4] Greenland S, Pearce N. Statistical foundations for model-based adjustments. Annu Rev Public Health 2015;36:89–108. [5] Pang M, Kaufman JS, Platt RW. Studying noncollapsibility of the odds ratio with marginal structural and logistic regression models. Stat Meth Med Res 2013. http://www.ncbi.nlm.nih.gov/pubmed/24108272. [6] Greenland S, Rothman KJ, Lash TL. Measures of effect and measures of association. In: Rothman KJ, Greenland S, Lash TL, editors. Modern epidemiology. Philadelphia: Lippincott, Williams & Wilkins; 2008. p. 51–70. [7] Greenland S, Mansournia MA, Altman DG. Sparse data bias: a problem hiding in plain sight. BMJ 2016;352:i1981. [8] Tibshirani R. Regression shrinkage and selection via the Lasso. J Roy Stat Soc B Met 1996;58(1):267–88.
⇑
Sheena G. Sullivan WHO Collaborating Centre for Reference and Research on Influenza, Peter Doherty Institute for Infection and Immunity, 792 Elizabeth St, Melbourne, VIC 3000, Australia Department of Epidemiology, Fielding School of Public Health, University of California, Los Angeles, USA ⇑ Address: Locked Bag 815, Carlton South, VIC 3053, Australia. E-mail address: [email protected]
4646
Letter to the Editor / Vaccine 34 (2016) 4645–4646
Benjamin J. Cowling WHO Collaborating Centre for Infectious Disease Epidemiology and Control, School of Public Health, Li Ka Shing Faculty of Medicine, The University of Hong Kong, Hong Kong Special Administrative Region Sander Greenland Department of Epidemiology, Fielding School of Public Health, University of California, Los Angeles, USA Department of Statistics, UCLA College of Letters and Science, University of California, Los Angeles, USA
Contents lists available at ScienceDirect
Vaccine journal homepage: www.elsevier.com/locate/vaccine
Letter to the Editor Frailty and influenza vaccine effectiveness
Dear Editor, We read with interest the recent paper by Talbot et al. which attempted to assess whether frailty confounds influenza vaccine effectiveness (VE) estimates in test-negative studies [1]. We do not think the authors’ analysis successfully rules out frailty as a confounder of VE estimates in their own study. We further believe that frailty should be expected to confound VE estimates because it meets the structural conditions of a confounder of having a causal effect on both the exposure and outcome [2]; i.e. the level of frailty influences both the decision to vaccinate and the risk of hospitalization and death from influenza [3]. The authors have attempted to measure confounding of VE by frailty by calculating a ratio of unadjusted (‘‘crude”) versus adjusted VE estimates. This kind of statistical approach to confounder identification has several problems. First, change-in-effect estimate criteria are justifiable when the underlying causal mechanisms are poorly understood and possible confounders are not established [4]. This is not the case for frailty. Second, when the outcome is a non-collapsible measure, such as the odds ratio, change-in-estimate criteria can be misleading [4]. Non-collapsibility means that the unadjusted effect is not a weighted average of stratum-specific effects [5,6]. Estimates derived from odds ratios for common outcomes like influenza are subject to non-collapsibility. Thus, the VE ratios reported by Talbot et al. may indicate confounding or noncollapsibility or both. Furthermore, it is also possible for the VE ratio to approach 1 if the confounding bias and non-collapsibility largely cancel each other out, leading to the erroneous conclusion that the VE estimate is not confounded by frailty [5]. Third, the degree of confounding in the reported estimates is difficult to discern because there were too few subjects in the not frail and frail groups, exposing the study to potential sparse data bias [7]. In the not-frail group, the number of test-positive unvaccinated people was just 4 and the number of test-positive vaccinated people was just 3. With the addition of 14 covariates to the model, the estimates will be affected by sparse-data bias [7]. The authors have attempted to mitigate the sparse-data bias by using penalized likelihood methods to shrink inflated covariate estimates. However, the lasso penalty deletes variables from the model when they fail to meet a certain datadriven threshold [8]. Inspection of Table 1 reveals that the VE point estimates for the not-frail and frail groups equal the VE from the crude odds ratios, suggesting that the lasso has dropped the 14 covariates from those models. If any of the deleted covariates are genuine confounders, the resulting VE estimate will remain confounded by them [4]. Similarly, if the lasso has dropped covariates from the ‘‘overall” model used in the VE ratios, the VE estimate will be biased and the VE ratios uninformative.
http://dx.doi.org/10.1016/j.vaccine.2016.08.003 0264-410X/Ó 2016 Elsevier Ltd. All rights reserved.
Given the limitations of this study, it is unwarranted to conclude that frailty does not confound estimates of VE. Estimates of confounding bias must account for other confounders in an unbiased fashion, which requires methods that do not delete confounders such as those based on quadratic rather than lasso penalties [7]. Thus better analyses as well as more data are needed before one can determine the extent of confounding by frailty in test-negative studies of influenza vaccination. Conflict of interest B.J.C. has received research funding from MedImmune Inc. and Sanofi Pasteur, and consults for Crucell NV. S.G. has received funding from Boehringer Ingelheim and Amgen. Acknowledgements The WHO Collaborating Centre for Reference and Research on Influenza is funded by the Australian Government Department of Health. References [1] Talbot HK, Nian H, Chen Q, Zhu Y, Edwards KM, Griffin MR. Evaluating the casepositive, control test-negative study design for influenza vaccine effectiveness for the frailty bias. Vaccine 2016;34(15):1806–9. [2] Pearce N, Greenland S. Confounding and interaction. In: Ahrens W, Pigeot I, editors. Handbook of epidemiology. New York: Springer; 2014. p. 659–84. [3] McGrath LJ, Cole SR, Kshirsagar AV, Weber DJ, Sturmer T, Brookhart MA. Hospitalization and skilled nursing care are predictors of influenza vaccination among patients on hemodialysis: evidence of confounding by frailty. Med Care 2013;51(12):1106–13. [4] Greenland S, Pearce N. Statistical foundations for model-based adjustments. Annu Rev Public Health 2015;36:89–108. [5] Pang M, Kaufman JS, Platt RW. Studying noncollapsibility of the odds ratio with marginal structural and logistic regression models. Stat Meth Med Res 2013. http://www.ncbi.nlm.nih.gov/pubmed/24108272. [6] Greenland S, Rothman KJ, Lash TL. Measures of effect and measures of association. In: Rothman KJ, Greenland S, Lash TL, editors. Modern epidemiology. Philadelphia: Lippincott, Williams & Wilkins; 2008. p. 51–70. [7] Greenland S, Mansournia MA, Altman DG. Sparse data bias: a problem hiding in plain sight. BMJ 2016;352:i1981. [8] Tibshirani R. Regression shrinkage and selection via the Lasso. J Roy Stat Soc B Met 1996;58(1):267–88.
⇑
Sheena G. Sullivan WHO Collaborating Centre for Reference and Research on Influenza, Peter Doherty Institute for Infection and Immunity, 792 Elizabeth St, Melbourne, VIC 3000, Australia Department of Epidemiology, Fielding School of Public Health, University of California, Los Angeles, USA ⇑ Address: Locked Bag 815, Carlton South, VIC 3053, Australia. E-mail address: [email protected]
4646
Letter to the Editor / Vaccine 34 (2016) 4645–4646
Benjamin J. Cowling WHO Collaborating Centre for Infectious Disease Epidemiology and Control, School of Public Health, Li Ka Shing Faculty of Medicine, The University of Hong Kong, Hong Kong Special Administrative Region Sander Greenland Department of Epidemiology, Fielding School of Public Health, University of California, Los Angeles, USA Department of Statistics, UCLA College of Letters and Science, University of California, Los Angeles, USA