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Editorial Views  |   December 2003
MAC Attack?
Author Affiliations & Notes
  • Omeed Sani, M.D.
    *
  • Steven L. Shafer, M.D.
  • *University of Szeged, Szeged, Hungary. † Pala Alto Veterans Administartion Health Care System, Palo Alto, California.
Article Information
Editorial Views
Editorial Views   |   December 2003
MAC Attack?
Anesthesiology 12 2003, Vol.99, 1249-1250. doi:
Anesthesiology 12 2003, Vol.99, 1249-1250. doi:
IN this issue of the Journal, Lu et al.  explore the arcane subject of modeling binary data using population analysis, a technique that determines the response of the typical individual, as well as inter- and intraindividual variability. 1 They demonstrate that when there are small numbers of observations per individual, the population approach to data analysis results in a hugely biased estimate of the Hill coefficient in logistic regression. The article mentions minimum alveolar concentration (MAC) only in passing, but their findings raise the question, Is MAC fundamentally flawed?
MAC is among the most useful concepts in anesthetic pharmacology. MAC establishes a common measure of potency for inhaled anesthetic drugs: the partial pressure at steady state associated with 50% probability of movement to noxious stimulation (e.g.  , incision). We use the concept of MAC to provide uniformity to our dosage of inhaled anesthetic drugs, establish the relative amounts of drug for different endpoints (e.g.  , MACawake, MACBAR, MACthe knife), characterize drug interactions (e.g.  , MAC-reduction), and guide our search for mechanisms of anesthetic action (the concentration responsible for biologic effects must be similar to MAC).
One of the great mysteries of anesthetic action is that MAC is so consistent. The inhaled anesthetic drugs are unique in pharmacology in their incredibly small amount of pharmacodynamic variability. Within a population, MAC varies by not more than 10–15% among individuals. 2,3 MAC varies from species to species by approximately the same amount as it does from individual to individual. 4 Someday, when we understand the mechanism of inhaled anesthetic action, we will look back on this low variability in MAC and think “it was so obvious that the mechanism had to be X, because only that could have accounted for the low variability.”
Lu et al.  demonstrate that the type of study used to determine MAC in humans might produce highly biased underestimates of variability. By definition, MAC in humans is the concentration associated with 50% probability of response to initial incision. It is limited to initial incision to provide a uniform experimental design. However, because there is only one initial incision in a patient, you only get one lousy bit of information per patient: response or no response. There is no room for partial responses—either the patient responded or didn't. It takes eight patients to make a single byte of data.
This Editorial View accompanies the following article: Lu W, Ramsay JG, Bailey JM: Reliability of pharmacodynamic analysis by logistic regression: Mixed-effects modeling. Anesthesiology 2003; 99:1255-62.
A consequence of the minimal data in each observation is that estimates of MAC and its variability are vulnerable to bias. Paul and Fisher observed that the classic “up–down” experimental design to determine MAC could be expected to produce errors in MAC of 10%, and that variability in MAC was systematically underestimated. 5 In a previous manuscript, Lu and Bailey demonstrated that when patient-to-patient differences are ignored, and the data are treated as arising from one giant rat (called the naïve pooled data  approach), the steepness of the concentration versus  response curve is grossly under  estimated. 6 Figure 1shows the probability versus  response relationship in many individuals (thin lines  ) and the apparent curve that would result from treating the data as though arising from one individual (thick line  ).
Fig. 1. Individual concentration versus  probability of no response curves (thin lines  ) which (in theory) can be estimated using population modeling, and an overall concentration versus  probability of no response curve (thick line  ), which results when interindividual differences are ignored (the naïve pooled data approach).
Fig. 1. Individual concentration versus 
	probability of no response curves (thin lines 
	) which (in theory) can be estimated using population modeling, and an overall concentration versus 
	probability of no response curve (thick line 
	), which results when interindividual differences are ignored (the naïve pooled data approach).
Fig. 1. Individual concentration versus  probability of no response curves (thin lines  ) which (in theory) can be estimated using population modeling, and an overall concentration versus  probability of no response curve (thick line  ), which results when interindividual differences are ignored (the naïve pooled data approach).
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In the current article, the authors ask the question, Could population analysis describe representative individuals (fig. 1, thin lines  ) and thus correct the “error” of the thick line  in figure 1? Their results are quite disconcerting. They demonstrate that it takes at least 10 observations per subject to get an unbiased estimate of the Hill coefficient with the population approach. To understand the reason for this, consider a study with only two observations per patient. With two observations, there are four possibilities for the concentration versus  response relationship as shown in figure 2. The thin curve  has a very large Hill coefficient. This curve perfectly predicts the observations in 2A–C but provides a perfectly terrible fit of the observations in 2D. The thick curve provides OK fits of all the data points (similar to the thick curve  in fig. 1). However, if A, B, C, and D were all individuals in the same study, a population approach would average the nearly infinite Hill coefficients of A, B, and C (thin lines  ), with something more modest to fit D. The average of three near-infinities and something less than infinity still yields an enormous value for the Hill coefficient. Because the Hill coefficient is directly related to the SD of MAC, 7 could the low variability in MAC be an artifact of the data analysis?
Fig. 2. Four possible alignments of two data points. In graphs A, B  , and C  , the perfect fit for individuals would have an infinite Hill coefficient. In graph D  , the infinite Hill coefficient results in a very poor fit. The naïve pooled data approach to all of the data results in a fairly shallow curve (thick line  ) and thus a small Hill coefficient. Were these data from four separate individuals, the average of the infinite slope from individuals A, B, and C, with the shallow slope for individual D would still yield a very high value for the Hill coefficient.
Fig. 2. Four possible alignments of two data points. In graphs A, B 
	, and C 
	, the perfect fit for individuals would have an infinite Hill coefficient. In graph D 
	, the infinite Hill coefficient results in a very poor fit. The naïve pooled data approach to all of the data results in a fairly shallow curve (thick line 
	) and thus a small Hill coefficient. Were these data from four separate individuals, the average of the infinite slope from individuals A, B, and C, with the shallow slope for individual D would still yield a very high value for the Hill coefficient.
Fig. 2. Four possible alignments of two data points. In graphs A, B  , and C  , the perfect fit for individuals would have an infinite Hill coefficient. In graph D  , the infinite Hill coefficient results in a very poor fit. The naïve pooled data approach to all of the data results in a fairly shallow curve (thick line  ) and thus a small Hill coefficient. Were these data from four separate individuals, the average of the infinite slope from individuals A, B, and C, with the shallow slope for individual D would still yield a very high value for the Hill coefficient.
×
Fortunately, the early MAC studies preceded modern population analysis techniques and simply used the giant rat analysis technique. 8–10 More recent studies continue to use the giant rat analyses technique. 11–13 As a result, virtually all MAC studies estimate the response shown by the thick line  in figure 1and do not attempt to estimate the response in individuals (fig. 1, thin lines  ). This is a good thing. First, clinicians want to set their doses at concentrations at which the majority of individuals are anesthetized, which is the dose determined using the giant rat analysis technique. Second, the probability of response versus  concentration curve is by definition steeper in each individual than in the population as a whole. Because the population as a whole shows variability of just 10% or less, in each individual the curve must be almost vertical, with individuals moving from 100% chance of responding to zero chance of responding, with very small increments in concentration. This agrees with clinical practice.
Although the observations of Lu et al.  thus do not invalidate the conclusions of MAC studies to date, they convincingly demonstrate that studies with only a single observation per subject will never establish the concentration versus  response curve in individuals, at least not by using population analysis techniques. More important, the article by Lu et al.  reinforces the previous message of Paul and Fisher: In human MAC studies, each individual literally contributes one bit of data. As a result, modest differences in MAC values between two groups in a study, or when compared with historical controls, may be an artifact unless very careful statistical measures are used to compare the groups.
References
Lu W, Ramsay JG, Bailey JM: Reliability of pharmacodynamic analysis by logistic regression: Mixed-effects modeling. A nesthesiology 2003; 99: 1255–62Lu, W Ramsay, JG Bailey, JM
de Jong RH, Eger EI II: MAC expanded: AD50 and AD95 values of common inhalation anesthetics in man. A nesthesiology 1975; 42: 384–9de Jong, RH Eger, EI
Eger EI II, Fisher DM, Dilger JP, Sonner JM, Evers A, Franks NP, Harris RA, Kendig JJ, Lieb WR, Yamakura T: Relevant concentrations of inhaled anesthetics for in vitro studies of anesthetic mechanisms. A nesthesiology 2001; 94: 915–21Eger, EI Fisher, DM Dilger, JP Sonner, JM Evers, A Franks, NP Harris, RA Kendig, JJ Lieb, WR Yamakura, T
Eger EI II: Anesthetic Uptake and Action. Baltimore, Williams & Wilkins, 1974, p 5
Paul M, Fisher DM: Are estimates of MAC reliable? A nesthesiology 2001; 95: 1362–70Paul, M Fisher, DM
Lu W, Bailey JM: Reliability of pharmacodynamic analysis by logistic regression: A computer simulation study. A nesthesiology 2000; 92: 985–92Lu, W Bailey, JM
Sonner JM: Issues in the design and interpretation of minimum alveolar anesthetic concentration (MAC) studies. Anesth Analg 2002; 95: 609–14Sonner, JM
Saidman LJ, Eger EI II: Effect of nitrous oxide and of narcotic premedication on the alveolar concentration of halothane required for anesthesia. A nesthesiology 1964; 25: 302–6Saidman, LJ Eger, EI
Eger EI II, Saidman LJ, Brandstater B: Minimum alveolar anesthetic concentration: A standard of anesthetic potency. A nesthesiology 1965; 26: 256–63Eger, EI Saidman, LJ Brandstater, B
Torri G, Damia G, Fabiani ML: Effect on nitrous oxide on the anaesthetic requirement of enflurane. Br J Anaesth 1974; 46: 468–72Torri, G Damia, G Fabiani, ML
McEwan AI, Smith C, Dyar O, Goodman D, Smith LR, Glass PS: Isoflurane minimum alveolar concentration reduction by fentanyl. A nesthesiology 1993; 78: 864–9McEwan, AI Smith, C Dyar, O Goodman, D Smith, LR Glass, PS
Lang E, Kapila A, Shlugman D, Hoke JF, Sebel PS, Glass PS: Reduction of isoflurane minimal alveolar concentration by remifentanil. A nesthesiology 1996; 85: 721–8Lang, E Kapila, A Shlugman, D Hoke, JF Sebel, PS Glass, PS
Johansen JW, Schneider G, Windsor AM, Sebel PS: Esmolol potentiates reduction of minimum alveolar isoflurane concentration by alfentanil. Anesth Analg 1998; 87: 671–6Johansen, JW Schneider, G Windsor, AM Sebel, PS
Fig. 1. Individual concentration versus  probability of no response curves (thin lines  ) which (in theory) can be estimated using population modeling, and an overall concentration versus  probability of no response curve (thick line  ), which results when interindividual differences are ignored (the naïve pooled data approach).
Fig. 1. Individual concentration versus 
	probability of no response curves (thin lines 
	) which (in theory) can be estimated using population modeling, and an overall concentration versus 
	probability of no response curve (thick line 
	), which results when interindividual differences are ignored (the naïve pooled data approach).
Fig. 1. Individual concentration versus  probability of no response curves (thin lines  ) which (in theory) can be estimated using population modeling, and an overall concentration versus  probability of no response curve (thick line  ), which results when interindividual differences are ignored (the naïve pooled data approach).
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Fig. 2. Four possible alignments of two data points. In graphs A, B  , and C  , the perfect fit for individuals would have an infinite Hill coefficient. In graph D  , the infinite Hill coefficient results in a very poor fit. The naïve pooled data approach to all of the data results in a fairly shallow curve (thick line  ) and thus a small Hill coefficient. Were these data from four separate individuals, the average of the infinite slope from individuals A, B, and C, with the shallow slope for individual D would still yield a very high value for the Hill coefficient.
Fig. 2. Four possible alignments of two data points. In graphs A, B 
	, and C 
	, the perfect fit for individuals would have an infinite Hill coefficient. In graph D 
	, the infinite Hill coefficient results in a very poor fit. The naïve pooled data approach to all of the data results in a fairly shallow curve (thick line 
	) and thus a small Hill coefficient. Were these data from four separate individuals, the average of the infinite slope from individuals A, B, and C, with the shallow slope for individual D would still yield a very high value for the Hill coefficient.
Fig. 2. Four possible alignments of two data points. In graphs A, B  , and C  , the perfect fit for individuals would have an infinite Hill coefficient. In graph D  , the infinite Hill coefficient results in a very poor fit. The naïve pooled data approach to all of the data results in a fairly shallow curve (thick line  ) and thus a small Hill coefficient. Were these data from four separate individuals, the average of the infinite slope from individuals A, B, and C, with the shallow slope for individual D would still yield a very high value for the Hill coefficient.
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