Response Surface Analysis of Propofol-Remifentanil using the Curve-Fitting Toolbox

Contents

The aim of this demo is to characterize the "complete spectrum of interaction" between opiods and hypnotics, using propofol and remifentanil as drug class prototypes [1]. 4 different surrogate drug effects measures for analgesia and hypnosis were used to understand the analgesic and sedative effects combined drug action – these are tibial pressure algometry, electrical tetany, response to laryngoscopy and an alertness/sedation score. The effects were modelled using the following drug interaction model.

References: [1] Kern SE, Xie G, White JL, Egan TD. Opioid-hypnotic synergy. Anesthesiology 2004; 100: 1373–81.

close all, clear all, clc

Import response data

ResponseData.xls contains measures of surrogate drug effects at various concentration combinations of propofol and reminfentanil. Import the data as a dataset object.

data = dataset('xlsfile', 'ResponseData.xls');

Characterize the response surfaces for 4 surrogate effects

Use the drug interaction model published in [1] to characterize the response surface for each of the 4 measured effects - Algometry, Tetany, Sedation and Laryingoscopy.

EffectName = {'Algometry'    'Tetany'    'Sedation'    'Laryingoscopy'};

for i = 1:length(EffectName)

    [fitresults(i), gof(i)] = myCreateSurfaceFit(data.Propofol, data.Remifentanil, data.(EffectName{i}), EffectName{i}) ;  %#ok<SAGROW>
    disp([' Model for ', EffectName{i}, '  is '])
    disp(fitresults{i})
    disp('... and GOF is ')
    disp(gof(i))

end
 Model for Algometry  is 

     General model:
       ans(x,y) = combinedEffect(x,y, IC50A, IC50B, alpha, n)
     Coefficients (with 95% confidence bounds):
       IC50A =       4.148  (4.123, 4.173)
       IC50B =       9.042  (8.969, 9.116)
       alpha =       8.499  (8.313, 8.684)
       n =       8.293  (8.136, 8.451)

... and GOF is 
           sse: 0.0842
       rsquare: 0.9991
           dfe: 393
    adjrsquare: 0.9991
          rmse: 0.0146

 Model for Tetany  is 

     General model:
       ans(x,y) = combinedEffect(x,y, IC50A, IC50B, alpha, n)
     Coefficients (with 95% confidence bounds):
       IC50A =       4.544  (4.522, 4.567)
       IC50B =       21.22  (21.04, 21.4)
       alpha =       14.94  (14.67, 15.21)
       n =       6.132  (6.055, 6.209)

... and GOF is 
           sse: 0.0537
       rsquare: 0.9993
           dfe: 393
    adjrsquare: 0.9993
          rmse: 0.0117

 Model for Sedation  is 

     General model:
       ans(x,y) = combinedEffect(x,y, IC50A, IC50B, alpha, n)
     Coefficients (with 95% confidence bounds):
       IC50A =       1.843  (1.838, 1.847)
       IC50B =        13.7  (13.67, 13.74)
       alpha =       1.986  (1.957, 2.015)
       n =       44.27  (42.56, 45.98)

... and GOF is 
           sse: 0.0574
       rsquare: 0.9994
           dfe: 393
    adjrsquare: 0.9994
          rmse: 0.0121

 Model for Laryingoscopy  is 

     General model:
       ans(x,y) = combinedEffect(x,y, IC50A, IC50B, alpha, n)
     Coefficients (with 95% confidence bounds):
       IC50A =       5.192  (5.177, 5.207)
       IC50B =       37.77  (37.58, 37.97)
       alpha =       19.67  (19.48, 19.86)
       n =          37  (35.12, 38.87)

... and GOF is 
           sse: 0.1555
       rsquare: 0.9982
           dfe: 393
    adjrsquare: 0.9982
          rmse: 0.0199

Assessment of model predictions

Evaluate the surface fit at certain characteristic drug-combination to verify that the model prediction are sensible.

valData = dataset('xlsfile', 'ValidationData.xls');

% Evaluate surface at concentration in validation data
valData.Algometry       = fitresults{1}(valData.Propofol, valData.Remifentanil) ;
valData.Tetany          = fitresults{2}(valData.Propofol, valData.Remifentanil) ;
valData.Sedation        = fitresults{3}(valData.Propofol, valData.Remifentanil) ;
valData.Laryingoscopy   = fitresults{4}(valData.Propofol, valData.Remifentanil) ;

valData
valData = 

    Propofol    Remifentanil    Algometry      Tetany         Sedation       Laryingoscopy
     0          0                         0              0              0              0  
     2          0                 0.0023506      0.0064789        0.97402    4.6985e-016  
     5          0                    0.8247        0.64245              1        0.19851  
    10          0                   0.99932        0.99213              1              1  
     0          1               1.1725e-008    7.3143e-009    4.6611e-051    4.4779e-059  
     0          2               3.6786e-006    5.1298e-007    9.8995e-038    6.1345e-048  
     0          4                 0.0011528    3.5977e-005    2.1025e-024    8.4039e-037  
     2          2                   0.98106        0.70638              1      0.0015253  
     5          2                   0.99998        0.99795              1              1  
    10          2                         1        0.99997              1              1