具有生物制药数据的自定义方程式的表面拟合

打开实时脚本

此示例显示了如何使用曲线拟合工具箱™将响应表面拟合到一些麻醉数据以分析药物相互作用效果。响应表面模型提供了一种理解药物组合的药效学相互作用行为的好方法。

This data is based on the results in this paper: Kern SE, Xie G, White JL, Egan TD. Opioid-hypnotic synergy: A response surface analysis of propofol-remifentanil pharmacodynamic interaction in volunteers. Anesthesiology 2004; 100: 1373-81.

Anesthesia is typically at least a two-drug process, consisting of an opioid and a sedative hypnotic. This example uses Propofol and Reminfentanil as drug class prototypes. Their interaction is measured by four different measures of the analgesic and sedative response to the drug combination. Algometry, Tetany, Sedation, and Laryingoscopy comprise the four measures of surrogate drug effects at various concentration combinations of Propofol and Reminfentanil.

The following code, using Curve Fitting Toolbox methods, reproduces the interactive surface building with the Curve Fitting Tool described inSurface Fitting to Biopharmaceutical Data.

Load Data

Load the data from file.

data = importdata（'apioidhypnoticsynergy.txt'）；propofol = data.data（：，1）;Remifentanil = data.data（：，2）;算法= data.data（：，3）;tetany = data.data（：，4）;镇静= data.data（：，5）;喉镜= data.data（：，6）;

创建模型拟合类型

You can use theFittype从纸上定义模型的功能，其中CA和CBare the drug concentrations, andIC50A,IC50B,alpha，和nare the coefficients to be estimated. Create the model fit type.

ft = fittype（'Emax*( CA/IC50A + CB/IC50B + alpha*( CA/IC50A ) * ( CB/IC50B ) )^n /(( CA/IC50A + CB/IC50B + alpha*( CA/IC50A ) * ( CB/IC50B ) )^n + 1 )',...'independent'，{'CA','CB'}，，'dependent','Z','problem','emax')

ft =常规模型：ft（IC50A，IC50B，Alpha，N，Emax，CA，CB）= EMAX*（CA/IC50A + CB/IC50B + Alpha*（CA/IC50A）*（CB/IC50B）*（CB/IC50B）^n//（（CA/IC50A + CB/IC50B + Alpha *（CA/IC50A） *（CB/IC50B））^n + 1）

认为emax = 1because the effect output is normalized.

emax = 1;

Set Fit Options

设置适合拟合，界限和起点的拟合选项。

opts = fitoptions( ft ); opts.Lower = [0, 0, -5, -0]; opts.Robust ='LAR';opts.startpoint = [0.0089，0.706，1.0，0.746];

Fit and Plot a Surface for Algometry

[f，gof] = fit（[propofol，Remifentanil]，算法，ft，...opts,'problem', Emax )

Success, but fitting stopped because change in residuals less than tolerance (TolFun).

一般模型：F（CA，CB）= EMAX*（CA/IC50A + CB/IC50B + Alpha*（CA/IC50A）*（CB/IC50B））^n/（（CA/IC50A + CB/IC50B + Alpha*）( CA/IC50A ) * ( CB/IC50B ) )^n + 1 ) Coefficients (with 95% confidence bounds): IC50A = 4.149 (4.123, 4.174) IC50B = 9.044 (8.971, 9.118) alpha = 8.502 (8.316, 8.687) n = 8.289 (8.131, 8.446) Problem parameters: Emax = 1

gof =struct with fields:sse: 0.0842 rsquare: 0.9991 dfe: 393 adjrsquare: 0.9991 rmse: 0.0146

plot( f, [Propofol, Remifentanil], Algometry );

Figure contains an axes object. The axes object contains 2 objects of type surface, line.

Fit a Surface to Tetany

Reuse the sameFittypeto create a response surface for tetany.

(f, gof) = ([Propofol, Remifentanil], Tetany, ft, opts,'problem', Emax )

一般模型：F（CA，CB）= EMAX*（CA/IC50A + CB/IC50B + Alpha*（CA/IC50A）*（CB/IC50B））^n/（（CA/IC50A + CB/IC50B + Alpha*）( CA/IC50A ) * ( CB/IC50B ) )^n + 1 ) 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) Problem parameters: Emax = 1

gof =struct with fields:sse: 0.0537 rsquare: 0.9993 dfe: 393 adjrsquare: 0.9993 rmse: 0.0117

情节（F，[丙泊酚，瑞芬太尼]，Tetany）;

Figure contains an axes object. The axes object contains 2 objects of type surface, line.

适合表面镇静

[f，gof] = fit（[丙泊酚，雷利芬太尼]，镇静，ft，opts，'problem', Emax )

一般模型：F（CA，CB）= EMAX*（CA/IC50A + CB/IC50B + Alpha*（CA/IC50A）*（CB/IC50B））^n/（（CA/IC50A + CB/IC50B + Alpha*）（CA/IC50A） *（CB/IC50B））^n + 1）系数（具有95％的置信边界）：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）问题参数：emax = 1

gof =struct with fields:sse: 0.0574 rsquare: 0.9994 dfe: 393 adjrsquare: 0.9994 rmse: 0.0121

plot( f, [Propofol, Remifentanil], Sedation );

Figure contains an axes object. The axes object contains 2 objects of type surface, line.

Fit a Surface to Laryingoscopy

[f，gof] = fit（[丙泊酚，瑞芬太尼]，喉镜检查，ft，opts，'problem', Emax )

一般模型：F（CA，CB）= EMAX*（CA/IC50A + CB/IC50B + Alpha*（CA/IC50A）*（CB/IC50B））^n/（（CA/IC50A + CB/IC50B + Alpha*）( CA/IC50A ) * ( CB/IC50B ) )^n + 1 ) 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) Problem parameters: Emax = 1

gof =struct with fields:sse: 0.1555 rsquare: 0.9982 dfe: 393 adjrsquare: 0.9982 rmse: 0.0199

图（f，[丙泊酚，雷列芬太尼]，喉镜检查）；

Figure contains an axes object. The axes object contains 2 objects of type surface, line.