We appreciate the interest from Sarraf et al. in our recent clinical focus review of the drug titration paradox. Although their insights on anesthesiologists’ dosing strategies are appreciated, their control systems’ engineering-based interpretation might overlook the statistical and mathematical underpinnings of the paradox. This suggests a potential misunderstanding of the automaton-like behavior involved in titrating drug doses. The drug titration paradox is a form of Simpson’s paradox a statistical phenomenon that occurs when the relationship between two variables of interest (i.e., dose and effect in this case) is being confounded by another variable (i.e., different patient drug sensitivities here). We have previously demonstrated a mathematical proof that titration to effect associates lower doses with greater effect. 

We agree that clinical concerns related to over- or underdosing contribute to the observed negative correlation. However, we assert that the titration paradox arises whenever drug dose is titrated to achieve a specific effect, whether through manual titration or by closed-loop control. Indeed, the authors’ own simulation of closed-loop control exemplifies the titration paradox (fig. 1).

Fig. 1.
Redrawing of the closed-loop figures of Sarraf et al.1 (Top) Sensitive patient. (Middle) Resistant patient. The effect-site concentration (Ce) and effect values at 4 min (circles) and 10 min (squares) can be estimated from the two y-axes. (Bottom) Concentration effect curves for sensitive patient (blue) and resistant patient (red). The red and blue arrows represent titration occurring between 4 and 10 min. After closed-loop titration, the effects are the same (both squares lie on the same horizontal line at Bispectral Index [BIS] = 50). The average dose–effect relationship (diagonal arrow) associates lower doses with greater effect (this negative correlation is the titration paradox and not a property of the anesthesia team).

Redrawing of the closed-loop figures of Sarraf et al. (Top) Sensitive patient. (Middle) Resistant patient. The effect-site concentration (Ce) and effect values at 4 min (circles) and 10 min (squares) can be estimated from the two y-axes. (Bottom) Concentration effect curves for sensitive patient (blue) and resistant patient (red). The red and blue arrows represent titration occurring between 4 and 10 min. After closed-loop titration, the effects are the same (both squares lie on the same horizontal line at Bispectral Index [BIS] = 50). The average dose–effect relationship (diagonal arrow) associates lower doses with greater effect (this negative correlation is the titration paradox and not a property of the anesthesia team).

As we discussed in our review, confounding factors in the causal pathway (e.g., changing levels of surgical stimulus) could lead to the titration paradox within individual patient data.  We argue that anesthesiologists are not automatons; we vigilantly titrate drug doses while anticipating the impact of other confounding factors during surgery. Additionally, contrary to the authors’ claim of no a priori knowledge, anesthesiologists do possess prior knowledge about appropriate target concentrations and effects from the literature.