Response to Mindel C. Sheps: Counted, Dead or Alive

Abstract

It is true that when decision-making in medicine proceeds (e.g., drug A to prevent outcome Y), clinicians make use of research results that are reported in terms of estimated probabilities. Thus, Pr [Ya = 1 = 1] is the risk expected under the drug treatment whereas Pr [Ya = 0 = 1] is the estimated baseline risk under the control treatment. Thus for the particular baseline risk in the study (Pr [Ya = 0 = 1]) there is a relative risk (RR) given by RR = (Pr [Ya = 1 = 1])/(Pr [Ya = 0 = 1]). The problem with the common practice advocated to clinicians to combine the patient-specific baseline risk with the RR to estimate a patient’s risk under treatment is that the RR varies with prevalence of the outcome in the study data and hence with baseline risk and thus the estimated risk under treatment assuming a constant RR is not really that useful.1 As stated by Huitfeldt,2 statisticians tend to appreciate this more because RR models may lead to predictions outside the range of valid probabilities or different predictions depending on if the RR or its complement (cRR) are used (e.g., if RR = RRdead then cRR = RRalive). However, the latter are not the main limitations of the use of the RR in clinical practice, but rather the former is the critical issue and arguments about the implications of such variation dependence of the RR have led to heated discussions with Huitfeldt2 on Frank Harrell’s blog (https://www.fharrell.com/) and social media.