IN his famous autobiography “Surely You’re Joking, Mr. Feynman” the late Nobel laureate Richard Feynman describes with boyish enthusiasm how he picked the combinations of safes containing the blueprints for the atomic bomb at Los Alamos Laboratories.1Anesthesiologists are confronted with this same dilemma every day when selecting drugs for their patients: how to pick a safe combination. This is typically approached with some combination of experience, empiricism, and cookbook mentality. In this issue of Anesthesiology, Sveticic et al .2refine an ingenious mathematical approach to picking safe combinations that would make Dr. Feynman proud.

The fundamental problem with finding combinations is dimensionality. Let us assume that you want to find the right dose from four possible doses (e.g. , “big dose,”“high normal dose,”“low normal dose,” and “low dose”). Let us also assume that it takes six patients to reliably measure the effect. For two drugs in combination, there are 16 (42) possible “best” combinations, requiring a study with 96 subjects. For three drugs in combination, there are 64 (43) combinations, requiring a study with 384 subjects. For four drugs, there are 256 (44) combinations, requiring a study with 1536 subjects. The dimensionality problem has generally limited us to studies only looking at two drugs in combination. An exception is the study by Minto et al.  3for midazolam, propofol, and alfentanil. However, this is the exception that proves the rule: these authors needed 400 subjects to identify an optimum combination of three drugs for loss of consciousness. Scaling their model based approach to examine four drugs would, by extension, require 2900 patients:

The approach taken by Sveticic et al.  2is an extension of a previously published search routine,4,5the importance of which has previously been highlighted in the editorial pages of Anesthesiology.6In this approach, instead of trying to characterize the entire interaction surface in n-dimensional space (n = the number of drugs), the authors test approximately n2combinations (the exact number determined using simulations). For three drugs, this involves just eight combinations. Based on these tests, the authors identify a new region of the n-dimensional surface that may be interesting to explore. Like an n-dimensional amoeba crawling along the surface, this approach sends out sensing pseudopods and quickly converges on the optimum combination on the surface. The mathematical refinements in the present manuscript potentially accelerate an already efficient search algorithm.

Dixon brought about a revolution in characterizing drug potency with the introduction of the “up-down” method in 1965.7Dixon’s methodology enables investigators to efficiently zoom in on the effective dose of a single drug in clinical trials. The methodology of Sveticic et al.  is exactly analogous to the Dixon approach for multiple drugs in combination. Of course, the methodological details are quite different from Dixon’s, reflecting 40 yr of progress in modeling and regression since Dixon wrote his classic paper. And, like Dixon’s methodology, the search efficiency comes at the price of not knowing the steepness of the dose versus  relationship around the optimum combination.

Investigators in drug interactions should make every effort to become familiar with the methodology proposed by Sveticic et al.  It is far more efficient than response surface approaches for characterizing optimum drug combinations.8–11Clinicians looking for evidenced-based guidance for drug combinations can expect to see studies using these methodologies, which will hopefully replace empiricism and cookbook approaches to giving drugs in combination. And although Richard Feynman is no longer with us, it is wonderful to see talented scientists pursuing his avocation of picking safe combinations.

1.
Feynman RP; Surely you’re joking, Mr. Feynman. New York, W. W. Norton and Company, New York, 1985
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2.
Sveticic G, Gentilini A, Eichenberger U, Zanderigo E, Sartori V, Luginbühl M, Curatolo M: Combinations of bupivacaine, fentanyl, and clonidine for lumbar epidural postoperative analgesia: a novel optimization procedure. Anesthesiology 2004; 101:1381–93
3.
Minto CF, Schnider TW, Short TG, Gregg KM, Gentilini A, Shafer SL: Response surface model for anesthetic drug interactions. Anesthesiology 2000; 92:1603–16
4.
Curatolo M, Schnider TW, Petersen-Felix S, Weiss S, Signer C, Scaramozzino P, Zbinden AM: A direct search procedure to optimize combinations of epidural bupivacaine, fentanyl, and clonidine for postoperative analgesia. Anesthesiology 2000; 92:325–37
5.
Sveticic G, Gentilini A, Eichenberger U, Luginbuhl M, Curatolo M: Combinations of morphine with ketamine for patient-controlled analgesia: A new optimization method. Anesthesiology 2003; 98:1195–205
6.
Fisher DM: The direct search procedure: a new approach to evaluating clinical regimens. Anesthesiology 2000; 92:301–3
7.
Dixon WJ: The up-and-down method for small samples. Am Stat Assoc J 1965; 60:967–78
8.
Nieuwenhuijs DJ, Olofsen E, Romberg RR, Sarton E, Ward D, Engbers F, Vuyk J, Mooren R, Teppema LJ, Dahan A: Response surface modeling of remifentanil-propofol interaction on cardiorespiratory control and bispectral index. Anesthesiology 2003; 98:312–22
9.
Mertens MJ, Olofsen E, Engbers FH, Burm AG, Bovill JG, Vuyk J: Propofol reduces perioperative remifentanil requirements in a synergistic manner: response surface modeling of perioperative remifentanil-propofol interactions. Anesthesiology 2003; 99:347–59
10.
Bouillon TW, Bruhn J, Radulescu L, Andresen C, Shafer TJ, Cohane C, Shafer SL: Pharmacodynamic interaction between propofol and remifentanil regarding hypnosis, tolerance of laryngoscopy, bispectral index, and electroencephalographic approximate entropy. Anesthesiology 2004; 100:1353–72
11.
Kern SE, Xie G, White JL, Egan TD: A response surface analysis of propofol-remifentanil pharmacodynamic interaction in volunteers. Anesthesiology 2004; 100:1373–81