BMJ Evidence-Based Medicine Month 2018 | volume 0 | number 0 | 1 ‘Depletion of the susceptibles’ taught through a story, a table and basic arithmetic Steven D Stovitz, 1 Hailey R Banack, 2 Jay S Kaufman 3 Letter 1 Family Medicine and Community Health, University of Minnesota System, Minneapolis, Minnesota, USA 2 Epidemiology and Environmental Health, University at Buffalo–The State University of New York, Buffalo, New York, USA 3 Epidemiology, Biostatistics and Occupational Health, McGill University, Montreal, Quebec, Canada Correspondence to: Dr Steven D Stovitz, Department of Family Medicine and Community Health, University of Minnesota, Minneapolis, MN 55455, USA; stovitz@umn. edu 10.1136/bmjebm-2018-110972 To cite: Stovitz SD, Banack HR, Kaufman JS. BMJ Evidence-Based Medicine Epub ahead of print: [please include Day Month Year]. doi:10.1136/ bmjebm-2018-110972 ‘Depletion of the susceptibles’ is a phrase occasion- ally used to describe a form of selection bias where harmful exposures can appear protective. 1 2 This bias, which affects evidence interpretation, may be diffcult for clinicians to recognise, because study participants may represent a random sample of people similar to a clinician’s patients. In this letter, we explain the bias through a story, a table and basic arithmetic to help those unfamiliar with other explanations using hazard ratios, 3 inverse probability weighting 4 or directed acyclic graphs conditioning on survival. 5 Imagine a town of 100 people (fgure 1) with genetic variation such that 20% have a short-life expectancy of only 60 years (S), 60% have a medi- um-life expectancy of 80 years (M) and 20% have a long-life expectancy of 100 years (L). Among the population, 30% engage in a harmful behaviour (H) that shortens lifespan by 10 years from expected. For simplicity, let the behaviour (H) be independent of the genetic make-up. Therefore: ► S+H (n=6) die at age 50 years. ► S without H (n=14) die at age 60 years. ► M+H (n=18) die at age 70 years. ► M without H (n=42) die at age 80 years. ► L+H die (n=6) at age 90 years. ► L without H (n=14) die at age 100 years. Study everyone and H appears harmful, as it should: ► Mean lifespan with H would be as follows: [(6x50)+(18x70)+(6x90)]/30=2100/30=70 years. ► Mean lifespan without H would be as follows: [(14x60)+(42x80)+(14x100)]/70=5600/70=80 years. However, if studying only those over the age of 70 years, then: ► Mean lifespan with Hwould be as follows: (6×90)/6=90 years. ► Mean lifespan without H would be as follows: [(42x80)+(14x100)]/56=4760/56=85 years. When studying only those over the age of 70 years, H appears protective, which it is not. In no person does H lead to a longer life. The bias occurs due to ‘depletion of the susceptibles’. Some may term this ‘collider strat- ifcation bias’ 5 (survival past 70 years is the ‘collider’), or ‘selection bias’ 4 due to conditioning on an effect, survival past 70 years, of both the exposure, H, and a cause of the outcome (genetic make-up). If clinicians understand the terminology in the previous sentence, then no need for a new pedagogical tool. If not, try this table and the basic arithmetic. Contributors All authors conceived the concept and contributed to the fnal manuscript. Competing interests None declared. Patient consent Not required. Provenance and peer review Not commissioned; internally peer reviewed. © Article author(s) (or their employer(s) unless otherwise stated in the text of the article) 2018. All rights reserved. No commercial use is permitted unless otherwise expressly granted. References 1. Moride Y, Abenhaim L, Yola M, et al. Evidence of the depletion of susceptibles effect in non-experimental pharmacoepidemiologic research. J Clin Epidemiol 1994;47:731–7. 2. Renoux C, Dell'Aniello S, Brenner B, et al. Bias from depletion of susceptibles: the example of hormone replacement therapy and the risk of venous thromboembolism. Pharmacoepidemiol Drug Saf 2017;26:554–60. 3. Hernán MA. The hazards of hazard ratios. Epidemiology 2010;21:13–15. 4. Hernán MA, Hernández-Díaz S, Robins JM. A structural approach to selection bias. Epidemiology 2004;15:615–25. 5. Cole SR, Platt RW, Schisterman EF, et al. Illustrating bias due to conditioning on a collider. Int J Epidemiol 2010;39:417–20. Figure 1 Hypothetical population of 100 people where genetic variation leads to either a short lifespan of 60 years (S), a medium lifespan of 80 years (M) or a long lifespan of 100 years (L). A harmful behaviour, H, shortens lifespan by 10 years and is independent of the genetic variation. on 10 July 2018 by guest. Protected by copyright. http://ebm.bmj.com/ BMJ EBM: first published as 10.1136/bmjebm-2018-110972 on 7 July 2018. Downloaded from