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Predicting the Best Fit: A Comparison of Response Surface Models for Midazolam and Alfentanil Sedation in Procedures With Varying Stimulation

Liou, Jing-Yang MD; Ting, Chien-Kun MD, PhD; Mandell, M. Susan MD, PhD; Chang, Kuang-Yi MD, PhD; Teng, Wei-Nung MD; Huang, Yu-Yin MD; Tsou, Mei-Yung MD, PhD

doi: 10.1213/ANE.0000000000001299
Ambulatory Anesthesiology: Original Clinical Research Report

BACKGROUND: Selecting an effective dose of sedative drugs in combined upper and lower gastrointestinal endoscopy is complicated by varying degrees of pain stimulation. We tested the ability of 5 response surface models to predict depth of sedation after administration of midazolam and alfentanil in this complex model. The procedure was divided into 3 phases: esophagogastroduodenoscopy (EGD), colonoscopy, and the time interval between the 2 (intersession).

METHODS: The depth of sedation in 33 adult patients was monitored by Observer Assessment of Alertness/Scores. A total of 218 combinations of midazolam and alfentanil effect-site concentrations derived from pharmacokinetic models were used to test 5 response surface models in each of the 3 phases of endoscopy. Model fit was evaluated with objective function value, corrected Akaike Information Criterion (AICc), and Spearman ranked correlation. A model was arbitrarily defined as accurate if the predicted probability is <0.5 from the observed response.

RESULTS: The effect-site concentrations tested ranged from 1 to 76 ng/mL and from 5 to 80 ng/mL for midazolam and alfentanil, respectively. Midazolam and alfentanil had synergistic effects in colonoscopy and EGD, but additivity was observed in the intersession group. Adequate prediction rates were 84% to 85% in the intersession group, 84% to 88% during colonoscopy, and 82% to 87% during EGD. The reduced Greco and Fixed alfentanil concentration required for 50% of the patients to achieve targeted response Hierarchy models performed better with comparable predictive strength. The reduced Greco model had the lowest AICc with strong correlation in all 3 phases of endoscopy. Dynamic, rather than fixed, γ and γalf in the Hierarchy model improved model fit.

CONCLUSIONS: The reduced Greco model had the lowest objective function value and AICc and thus the best fit. This model was reliable with acceptable predictive ability based on adequate clinical correlation. We suggest that this model has practical clinical value for patients undergoing procedures with varying degrees of stimulation.

Published ahead of print May 17, 2016

From the *Department of Anesthesiology, Taipei Veterans General Hospital and National Yang-Ming University, Taipei, Taiwan; Department of Anesthesiology, University of Colorado Hospital, Aurora, Colorado; and Department of Anesthesiology, Cheng Hsin General Hospital, Taipei City, Taiwan.

Accepted for publication January 31, 2016.

Published ahead of print May 17, 2016

Funding: Taiwan National Science Council, Taipei City, Taiwan: National Science Council Grant NSC 102-2314-B-075-078 and NSC 103-2314-B-075-030.

The authors declare no conflicts of interest.

Jing-Yang Liou and Chien-Kun Ting contributed equally to this work.

Reprints will not be available from the authors.

Address correspondence to Mei-Yung Tsou, MD, PhD, Department of Anesthesiology, Taipei Veterans General Hospital and National Yang-Ming University, No. 201, Sec. 2, Shipai Rd, Beitou District, Taipei, Taiwan 11217, People’s Republic of China. Address e-mail to mytsou8095@gmail.com.

Response surface pharmacodynamic models have been used to guide drug administration. Models use topographical layout plots that describe drug interactions.1–4 Data from these models guide drug dosing by presenting the desired drug effects for a specific clinical target such as depth of sedation and time to awakening.5,6

There are models for predicting depth of anesthesia or sedation in a single-staged procedure for hypnotic-hypnotic,1,2 opioid-hypnotic,3,6,7 or analgesic-analgesic8 drug pairs. However, there are no response surface models for predicting benzodiazepine-opioid interactions in procedures with distinct phases associated with differing degrees of stimulation.

Upper and lower endoscopy is often performed under deep sedation in a single session.9–11 There are 3 distinct phases, including esophagogastroduodenoscopy (EGD), colonoscopy, and the time lapse between the 2 procedures. The varying levels of stimuli can lead to inadequate analgesia or oversedation, resulting in discomfort or respiratory depression.12–16 Synergistic and additive effects of drug combinations can increase the risk of oversedation.

We reasoned that objective models to guide drug dosing during upper and lower endoscopy will improve patient satisfaction and safety. Therefore, the aim of this study was to identify which model and associated parameters best predicted the sedative effect for each of the 3 procedural phases of combined endoscopy. Five response surface constructs were tested for accuracy. Validation and performance were assessed by comparing observed and reported patient responses with model predictions.

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METHODS

Patient Selection and Management

Study Group

Requirements for written informed consent were waived after obtaining IRB approval (IRB 2014-12-001BC) from the Taipei Veterans General Hospital. Patients younger than 65 years scheduled for combined EGD and colonoscopy were candidates for the study. Patients were excluded if they had documented impairment in verbal communication or a history of sedative, opioid, or chronic alcohol use.

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Anesthesia Management

Analgesic drugs were given through a dedicated 22-gauge IV catheter placed in a distal extremity. Patients were monitored using standard noninvasive equipment: electrocardiography, pulse oximetry, and noninvasive blood pressure. Supplemental oxygen was administered by nasal cannula to maintain oxygen saturation at ≥90%. The health care provider administered bolus IV doses of midazolam and alfentanil. The initial dosage of midazolam and alfentanil was 0.03 to 0.04 mg/kg and 6 to 9 ng/kg, respectively.

Table 1

Table 1

The Observer Assessment of Alertness/Score (OAA/S)17 was used to measure arousal by clinical observation on a 1 to 5 scale (Table 1). Endoscopy began when there was no response to mild prodding or shaking (OAA/S <2). Additional alfentanil was given if the patient appeared uncomfortable and midazolam if the patient’s OAA/S was >4 with or without pain. Additional drugs were given in increments of approximately half the initial dose. After each bolus, the medication was flushed with 3 mL normal saline. Two health care providers, trained in OAA/S, scored depth of sedation every 2 minutes for each study patient. Loss of response was defined as OAA/S <4 during the intersession phase18 and OAA/S <2 during EGD and colonoscopy.

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Response Surface Models

Pharmacokinetic Modeling

Pharmacokinetic profiles for effect-site drug concentrations (Ce) were calculated using a simulation program (TIVA trainer-Version 9.1, Build 5, European Society for Intravenous Anaesthesia). The Maitre model19 was used for the alfentanil and Zomorodi model20 for midazolam. The t1/2 keo values in the program were from electroencephalogram analyses by Scott et al21 for alfentanil and Bührer et al22 for midazolam. Models for endoscopy (EGD and colonoscopy) and the time between both procedures (intersession) were constructed by fitting binary data from OAA/S scores into 5 response surface constructs: Full Greco, Reduced Greco, Minto, Scaled C50 Hierarchy, and Fixed C50 Hierarchy models.23–27

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Greco Model

The full Greco model is shown in Equation 1.

CV

CV

E is the drug effect with values measured using OAA/S scoring. We used a cutpoint of ≥4 (sedated versus awake) for the intersession to create dichotomous classifications. An OAA/S cutpoint of <2 (responds after mild prodding or shaking) was used for EGD and colonoscopy. This produced binary data for analysis. The Emax is the maximal drug effect and was fixed at 1. Calf and Cmid were Ce values in nanograms per milliliter. C50alf and C50mid were Ce values at which 50% of people experienced the independent maximal clinical effect for alfentanil and midazolam, respectively. The parameter α was a measure of the interaction between alfentanil and midazolam for the 2 OAA/S cutpoints used in our study, and γ was the steepness of the concentration-effect relationship.

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Reduced Greco Model

The full Greco model assumed each drugs could independently reach an OAA/S <4 for intersession and OAA/S <2 for EGD and colonoscopy. Opioids produce unreliable hypnotic activity and had a C50alf magnitude greater than C50mid after regression. The full Greco model was therefore rewritten, omitting opioid effect alone (Calf/C50alf) and combining C50alf and α into a new parameter, α’. We therefore did not estimate C50alf (Equation 2).

CV

CV

This can be further simplified into Equation 3.

CV

CV

In reduced form, the Greco model had 3 parameters (C50mid, α’, and γ).

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Minto Model

The Minto model incorporated interaction function (Equation 4):

CV

CV

E was the drug effect. The Emax was the maximal drug effect (1), whereas E0 was the baseline effect with no drug present (0). U was the normalized potency of the drug defined in Equation 5.

CV

CV

The model introduced a central concept, θ a new drug as a ratio of alfentanil (UAlf) and midazolam (Umid) (Equation 6).

CV

CV

The sigmoidicity factor, γ, determined the steepness of the effect. U50 (θ) was new drug potency at ratio θ that yielded half maximal response calculated using Equation 7.

CV

CV

CV

CV

was an interaction parameter. A value of 0 indicated an additive effect, whereas a value >0 or <0 a synergistic or antagonistic interaction, respectively.

CV

CV

Steepness (γ) was a function of θ, as shown in Equation 8. In summary, the Minto model required 6 parameters (C50alf, C50mid,

CV

CV

, γmid, γalf, and βγ).

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C50 Hierarchy Model

This model analyzed 2 drugs in separate components of the construct. The model assumed the sequence that drugs were introduced into the model affects the results. This was distinct from other models. The model defined C50alf as the concentration required for a 50% attenuation of stimuli/pain. It defined C50mid as the concentration required to produce hypnosis in 50% of the patients after opioid administration. Equations 9 and 10 show the original form of the model.

CV

CV

CV

CV

PreOI was the preopioid stimulus intensity, whereas PostOI was the postopioid intensity. The PostOI was eliminated by assuming the following:

CV

CV

The final form of the hierarchy model for a specific stimulus is shown in Equation 11.

CV

CV

Equation 11 was similar to the reduced Greco model and should have produced identical results if γalf was assumed to be 1. When used to fit multiple stimuli, the model was overparameterized. Placing constraints on C50alf and/or C50mid resolved this issue and the results became a Scaled or Fixed Hierarchy model. The Scaled Hierarchy model assumed the change in C50mid and C50alf was a factor of the initial C50 for different stimuli.

CV

CV

CV

CV

The change in C50mid for different stimuli was dependent on the initial C50mid, hence the name Fixed Hierarchy model.

CV

CV

CV

CV

Parameters requiring approximation were identical in both Hierarchy models (C50alf, C50mid, γ, and γalf).

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Patient Response Modeling

The model was designed to fit 3 phases of the combined endoscopic procedure response: EGD, colonoscopy, and intersession. Model parameters were estimated with MATLAB software (R2013a; The MathWorks, Inc, Natick, MA) for pharmacodynamic analysis. MATLAB’s built-in function, fmincon, was selected, and an iterative process using the bootstrap method was used to find the minimal value of −2 times the logarithm of the maximal likelihood (−2LL) in Equation 12.

CV

CV

where K was the pooled observations, R the response to stimuli measured by OAA/S cutpoints, and P the probability for loss of response to stimuli. Objective function value (OFV) was chosen to represent −2LL and used to select the better model. Coefficient of variance (CV) was calculated using the SD (σ) and mean (μ) in Equation 13:

CV

CV

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Model Fit Assessment

Model Fit Selection

The OFV difference between model pairs was calculated and used as our primary endpoint. Assuming a χ2 distribution with 1 degree of freedom and P = 0.05 (OFV critical difference of 3.84), the model with an OFV difference <3.84 was considered significantly better. The corrected Akaike Information Criterion (AICc) was used to help find the best model resulting from the relatively small number of observations. AIC was calculated using −2LL + 2p, where p was the number of parameters in a model. AICc was calculated using

CV

CV

, where n was the number of observations.

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Model Correlation Strength

The calculated model parameters for each of the 3 endoscopy phases were assessed to predict observed clinical patient responses. We used the Spearman rank correlation (ρ) in both MATLAB and SigmaPlot 12.5 (Systat Software, Inc, San Jose, CA) to compare clinical responses and model predictions. A 2-tailed unpaired t test was used with a null hypothesis that assumed new models did not correlate with clinical observations.

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Model Accuracy

A model was arbitrarily defined as accurate if there was a value of <0.5 from the observed response. For example, if a predicted chance of unresponsiveness was 0.7 and the clinical observed effect 1 (unresponsive), the difference would be 0.3. This gave an objective measure of predictive accuracy.

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RESULTS

Study Group

Forty patients, age 48.3 ± 9.6 years, were enrolled and 7 excluded, 5 for inadequate records and 2 for neurologic disorders. All patients were ASA physical status I or II. There were 18 males (54.55%). Body mass index ranged from 20 to 28 kg/m2 (21.77 ± 2.21). The EGD averaged 3.0 ± 1.5 minutes, colonoscopy averaged 6.5 ± 2.6 minutes, and intersession averaged 2.7 ± 1.4 minutes.

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Effect-Site Concentration and Clinical Effect

A total of 218 effect-site concentration sets were analyzed. There were 68, 75, and 75 concentration sets for EGD, colonoscopy, and the intersession groups, respectively. All sets were categorized using OAA/S scores for binary data analysis. The average cumulative dose of midazolam was 0.048 ± 0.016 mg/kg and 0.013 ± 0.005 mg/kg for alfentanil. The effect-site concentrations ranged from 1 to 76 ng/mL and from 5 to 80 ng/mL for midazolam and alfentanil, respectively.

Patient movement occurred in 6 (18.2%) and 1 (3%) of our 33 patients (OAA/S ≥2) during EGD and colonoscopy insertion, respectively. Eight (24.2%) and 22 (66.67%) were OAA/S >2 and showed signs of discomfort during EGD and colonoscopy examination. This suggested the most stimulating part of EGD was endoscope insertion. In contrast, most discomfort during colonoscopy occurred during the examination rather than insertion. These identified parts of the procedure that may require additional models for optimal drug concentrations. One patient developed hypoxia approximately 2 minutes after induction and the pulse oximetry remained between 80% and 90% for approximately 2 minutes. This was successfully managed by increasing oxygen flow through the nasal cannula and using the chin-lift maneuver. The Ce at the time of initial desaturation was 48 ng/mL for midazolam and 45 ng/mL for alfentanil. Peak Ce was 59 ng/mL for both drugs during the period of desaturation.

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Drug Effect and Interactions

Results for the calculated response surface model parameters and model fit are shown in Tables 2 to 4. The full Greco model had large C50alf in all 3 phases of endoscopy. The OFVs were more favorable in the reduced compared with the full Greco model in all 3 phases. The EGD group in the reduced model reached statistical significance with an OFV difference of 4.4.

Table 2

Table 2

Table 3

Table 3

Table 4

Table 4

CV

CV

in the Minto model ranged from 1.3 to 1.4, and synergism was identified between midazolam and alfentanil in both EGD and colonoscopy groups. An additive relationship during intersession was observed between alfentanil and midazolam with a very small

CV

CV

(0.124) and α (0.393) in the Minto and full Greco model. The reduced Greco α’ parameter only ranged from 0.028 to 0.04, which was also close to additivity.

The Scaled and Fixed Hierarchy models were identical in the intersession group. C50mid in the Fixed Hierarchy was higher than the Scaled Hierarchy model because constraints on C50alf were different. PreOI differed between Scaled Hierarchy and Fixed Hierarchy models for EGD (1.37 and 1.5) and colonoscopy (1.52 and 1.93). There was a greater PreOI for colonoscopy than for EGD. CVs for C50mid and C50alf were derived from the CV in PreOI. Results shown in Tables 2 to 4 were modified using PreOI constraints. Findings from a previous study26 fixed the γ and γalf values for different stimuli. However, we found better model fit (lower OFV and higher ρ) if the γ and γalf were dynamic. OFV decreased from 63.46 to 48.78 for colonoscopy and from 48.14 to 37.86 for EGD in the Scaled Hierarchy model. OFV decreased from 62.6 to 46.03 for colonoscopy and from 48.14 to 37.93 for EGD in the Fixed Hierarchy model.

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Model Fit and Selection

Table 5

Table 5

Adequate prediction rates were 84% to 85% in the intersession group, 84% to 88% during colonoscopy, and 82% to 87% during EGD. A strong correlation was identified from Spearman ρ (0.68 to 0.77, P < 0.001). The Minto model had the highest OFV and AICc as a result of increased parameters. OFV (139.64; Table 5) was lowest in the reduced Greco model, which was insignificantly lower than the Fixed C50alf Hierarchy model but significantly lower than the rest of the models. AICc was lowest in the reduced Greco model.

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Response Surfaces and Isoboles

The 50% isoboles are shown in Figure 1. Both Hierarchy models were identical in the intersession group and only 4 isoboles were visible. Full and reduced Greco and Minto models had weak drug synergy in the intersession phase.

Figure 1

Figure 1

Figure 2

Figure 2

Figure 3

Figure 3

Figure 4

Figure 4

Figure 5

Figure 5

Figure 6

Figure 6

The 5%, 50%, and 95% isoboles for the 3 phases are shown for better fitting models (reduced Greco and Fixed C50alf Hierarchy) in Figures 2 and 3. The response surfaces for better fitting models are also shown in Figures 4 and 5. Circles size (representing concentration pairs) varied by deviance from the surface with better accuracy in smaller circles. Figure 6 shows the 95% isoboles for all models and groups.

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DISCUSSION

This is the first response surface model analysis for midazolam-alfentanil interactions during endoscopy with 3 distinct levels of stimulation. A comparison of 5 models showed the Fixed C50alf Hierarchy and reduced Greco models equally predicted patient responses and were better than the remaining models. The data confirmed a strong synergism for sedation between drugs during EGD and colonoscopy but additive during the intersession. Translation of the data into isoboles produced a practical tool to guide administration of medications during sedation.

We adopted Ce, instead of plasma concentration28 or dosage by weight,29,30 to construct models and predict our clinical target points (OAA/S <4 or <2). There were few comparable studies. A single case report described awake laryngoscopy using a combination of midazolam and remifentanil.31 However, drug concentrations fell in the extreme end (high opioid/low midazolam), and we could not use the findings as a reference to evaluate the validity of our findings. The AICc was chosen instead of AIC because the number of observations was not greater than the square of the number of the parameters. More model parameters produced higher AIC and AICc values. This limited predictive accuracy and discouraged overfitting.

The full Greco and Minto models assume each drug can independently achieve maximal target response. However, opioids do not fit this assumption because they do not produce reliable hypnosis as a single agent.32,33 This explains the large C50alf in the full Greco and Minto model, findings similar to previous studies.26,34 A simulated single bolus exceeding normal dosing for sedation (2 mg) of alfentanil would be required for plasma concentration >250 ng/mL and a corresponding Ce of 160 ng/mL in a 70-kg male patient. The C50alf in the full Greco and Minto models produced similar findings and highlighted the failure of opioids to induce hypnosis adequately. The Minto model had a significantly higher OFV and AICc in all 3 phases.

Other studies used fixed parameters for γ and γalf26,27 that assumed the drug interaction was similar for different stimuli. These assumptions worked poorly in our models, in which the amount of stimulation varied according to the phase of endoscopy. The AICc values were consistently greater and correlations weaker for colonoscopy and EGD. By allowing both parameters to be dynamic, AICc and correlation improved dramatically. We analyzed parameters for the Hierarchy model without constraints on C50alf and C50mid. The OFV results were not significantly better than the current Scaled Hierarchy and Fixed Hierarchy models.

Isoboles were constructed to provide a practical tool of drug interaction for clinical use. Overlapping isobolograms showed good agreement between models for colonoscopy and EGD phases but varied for intersession. Intersession displayed an additive rather than a synergistic interaction in the full and reduced Greco and Minto models. Opioids and benzodiazepines have previously been shown to be synergistic. Our findings from upper and lower endoscopy concur with these observations.35,36 However, the intersession group in our study was a nonpainful phase of the combined procedure. The additive interaction between drugs is an interesting finding and suggests that the type of interaction between drug classes could be influenced by the degree of painful stimulation. Additive interactions observed in our study require additional testing during steady-state conditions where there is minimal pain to ensure that this observation is reliable. The additive effects may be related to endpoint observations in our study.

We used an OAA/S ≥4 to identify light sedation.37 Without painful or strong verbal stimuli, drug interactions can be weakly synergistic, even approaching an additive effect. Choosing OAA/S ≥4 better reflects actual clinical practice. Patients need to be fully awake before they can leave the recovery room. The Hierarchy model did not capture the additive interaction very well; there was a rapid transformation from a concave to sigmoid-shaped isobole with increasing γalf. The Hierarchy models showed synergism between midazolam and alfentanil in the intersession group. In the latter model, we were unable to capture an additive effect by using multiple values from 0.7 to 2.0 to fix γalf. The resulting OFVs were significantly worse than the current parameters.

Metabolism of both midazolam and alfentanil is influenced by age, genetic, racial, and gender38 factors. We suggest that drug compartmental redistribution plays a much more important role than metabolism in our study setting. It is unlikely the administered drugs underwent significant metabolism during the short procedure duration. Onset and offset of the drug effects were probably attributable to redistribution. Only 1 patient experienced arterial desaturation. Oxygen saturation remained between 80% and 90% for 2 minutes and was treated by increasing the nasal cannula oxygen flow and using the chin lift. The patient received a higher total dose (1200 μg) of alfentanil but the effect-site concentration was not higher. This was probably the result of a longer examination time and thus higher cumulative drug dose.

There are several limitations to the study. First, all models have inherent limitations39 to predict biological outcomes in diverse patient groups. The findings need additional testing with larger and more demographically diverse patients. It must be kept in mind that different models have different strengths and applications. Choosing a model will be highly dependent on the original data and endpoints investigated. Second, the data set variability is limited. Crisscross design was not plausible because we enrolled patients rather than volunteers and collected our data during an actual examination. The drug concentrations land only in a limited range and extreme concentrations at both ends of the response surface were not available. Therefore, we cannot draw conclusions regarding these areas of the response surface. Hierarchy and Reduced Greco models assumed drug interactions were the same across the surface. The very extreme concentrations are inferred mathematically, but these drug concentrations are not used during routine practice. We did not test the extreme ranges because our main goal was to develop a practical model that could be easily used in a clinical setting.

Third, the study does not reflect steady-state conditions. The tissue-brain concentration equilibrium constant is longer with midazolam with a t1/2ke0 of 2.6 to 4.2 minutes.40 The average times for each phase (EGD 3.0 ± 1.5 minutes, colonoscopy 6.5 ± 2.6 minutes, and intersession 2.7 ± 1.4 minutes) preclude steady-state conditions. This is compounded by administering multiple boluses. The bootstrap method was therefore used to improve model stability. Fourth, accuracy deviation of <50% was used for this study.6 We are uncertain whether a more strict definition would improve model parameters, and the effects on correlation are unknown. Implementing stricter definitions of accuracy into a study population with low variation in patient data would have made model development more difficult.

Fourth, the inability of sedation scores to measure pain intensity may have influenced our findings. Drugs administered from multiple classes improve patient comfort during endoscopic procedures. Common combinations are analgesics and anxiolytic-sedative agents. This produces a state of sedation in which the clinical contribution of analgesia cannot be distinguished from anxiolysis or impaired consciousness. Thus, sedation scores measure cumulative effects of all drugs given. These scoring systems are limited for detailed analysis of drug effect but are a useful tool for clinical practice.

Pain varies during combined endoscopy, usually greater during upper endoscopy compared with colonoscopy. There should be no pain during intersession. The changes in pain intensity may have influenced our analysis of drug interactions. The additive and synergistic effects of opioids and anxiolytics observed in our study, therefore, require further testing in other clinical scenarios where there is less variation in pain intensity.

In summary, we modified response surface models to estimate drug combination dosing for sedation during a surgical procedure with 3 distinct phases that produced differing levels of stimulation. The reduced Greco and fixed C50alf Hierarchy models performed the best. Wakeup time and optimal drug concentrations that provide the quickest awakening time and optimal examination conditions can be estimated from our pharmacodynamic study findings. The results from these findings can be used to construct simple visual tools to aid clinical decision-making.

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DISCLOSURES

Name: Jing-Yang Liou, MD.

Contribution: This author helped design the study, conduct the study, analyze the data, and write the manuscript.

Name: Chien-Kun Ting, MD, PhD.

Contribution: This author helped design the study, conduct the study, analyze the data, and write the manuscript.

Name: M. Susan Mandell, MD, PhD.

Contribution: This author helped design the study, conduct the study, analyze the data, and write the manuscript.

Name: Kuang-Yi Chang, MD, PhD.

Contribution: This author helped design the study, conduct the study, and analyze the data.

Name: Wei-Nung Teng, MD.

Contribution: This author helped design the study, conduct the study, and write the manuscript.

Name: Yu-Yin Huang, MD.

Contribution: This author helped design the study and analyze the data.

Name: Mei-Yung Tsou, MD, PhD.

Contribution: This author helped design the study, conduct the study, analyze the data, and write the manuscript.

This manuscript was handled by: Tong J. Gan, MD, MHS, FRCA.

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ACKNOWLEDGMENTS

The authors thank Professor Ken B. Johnson, MD, PhD (Department of Anesthesiology and Department of Bioengineering, University of Utah, Salt Lake City, Utah) and Professor Dwayne R. Westenskow, PhD (Department of Anesthesiology, and Department of Bioengineering, University of Utah, Salt Lake City, Utah), for providing technical and consultation support.

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