Tools on R for Dose- Response curves analysis Chantal THORIN 2009 - - PowerPoint PPT Presentation

Tools on R for Dose- Response curves analysis

Chantal THORIN

UPSP 5304 : Physiopathologie Animale et Pharmacologie Fonctionnelle ENV Nantes France

2009 July 8th

• 2009 July 8th

Background: experimental pharmacology

Drug - receptor interactions studies commonly establish

Dose – response curves Applied agonist concentrations on isolated tissues Physiological effect observed

Design : repeated measurements with cumulative

concentrations

• 2009 July 8th

Background : data analysis

Data analysis of Dose – Response experiments should model:

Experimental design of repeated measurements Physiological response : Empirical equations commonly used :

Hill equation Richards function Gompertz model Hill modified equation Mixed effects models : the best way to analyse such data sets

• 2009 July 8th

DRC data analysis with R by nlme models

Statistical modeling

Choice of predictive function Est.Pop function

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• 2009 July 8th

Estimation of parameters

Summary(Est.Pop) CI.par function provides the 95% Confidence interval for each parameter:

Diagnosis curves

DRC data analysis with R by nlme models

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DRC data analysis with R

Model comparison

Comp.Mod function

More additionnal graph

Graph.Curves display fixed and individual curves Observed Curves

Est.Boot function

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• 2009 July 8th

Full Script :

DRC data analysis with R

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An example: Analysis of Cumulative Concentration Response Curves

• 9
• 8
• 7
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• 5

20 40 60 80 100

Observed CCRC

Log C Response (%)

Experiment on β-adrenoceptors-mediated blood vessels relaxation

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• 2009 July 8th

An example : CCRC data analysis

Model Comparison

Comp.Mod(EstH.Pop(Iso),EstR.Pop(Iso)) Model df AIC BIC logLik Test L.Ratio p-value Mod1 1 12 332.75 356.62

• 154.3766

Mod2 2 17 334.51 368.33

• 150.2595 1 vs 2

8.234197 0.1438 Approximate 95% confidence intervals Fixed effects: lower est. upper Em 87.90 94.803 101.701 n 1.059 1.207 1.354 d -7.383

• 7.167
• 6.951

Random Effects: Level: Identity lower est. upper sd(Em) 2.9020 6.9413 16.6025 sd(d) 0.1351 0.2508 0.465 sd(n) 0.0098 0.0957 0.934 cor(Em,d)

• 0.7318

0.0212 0.751 cor(Em,n)

• 0.999

0.7562 0.999 cor(d,n)

• 0.9735
• 0.3189

0.904 Correlation structure: lower est. upper Phi

• 0.142

0.466 0.818 Variance function: lower est. upper power 0.1621966 0.2988498 0.4355029

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Graphes

LogC Response

20 40 60 80 100

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1 2

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• 5

3 4 5

20 40 60 80 100

6

20 40 60 80 100

7 fixed Individu

• 2
• 1

1 2

• 10
• 5

5 10

Normal Q-Q Plot

Theoretical Quantiles Sample Quantiles

Fitted values Standardized residuals

• 2
• 1

1 2 20 40 60 80 100

Scatter Plot Matrix Em

95 100 95 100 85 90 85 90

n

1.20 1.25 1.30 1.20 1.25 1.30 1.10 1.15 1.20 1.10 1.15 1.20

D

• 7.2
• 7.0
• 7.2
• 7.0
• 7.4
• 7.2
• 7.4
• 7.2

An example : CCRC data analysis

• 2009 July 8th

DRC data analysis with R : Limits and conditions

Complete curves : no missing data DataSet organised in a specific way Script « closed » : no interactivity to choose and modify one

function component

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DRC data analysis with R : Conclusion

Script easy to use for non informatician and non statistician

scientists

Evolution in a more interactive form

• 2009 July 8th

Thank you for your attention !