Dose-response evaluation using a combined parametric/non-parametric - - PowerPoint PPT Presentation

Dose-response evaluation using a combined parametric/non-parametric approach

John-Philip Lawo Baxter Innovations GmbH, Vienna, Austria

2008-09-25 John-Philip Lawo, Baxter 2

A Safety Issue: Thrombogenicity

Thrombogenicity is a safety aspect for plasma derived VonWillebrand products intended to treat haemophilia (EMEA Guideline CPMP/BPWG/220/02) ‘Wessler score’:

• Used to measure thrombogenicity
• Based on 7-part ordinal scale (0, 0.5, 1, 2, 3, 3.5, 4),

where 0 = no thrombus formation, 4 = high thrombus formation

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Essential Part of Drug Development: Dose-response

• ICH E4: „Assessment of dose-response should be an

integral component of drug development with studies designed to assess dose-response an inherent part of establishing the safety and effectiveness of the drug.“

• The estimated dose to cause 50% effect (ED50) is one

characteristic of dose-response relation

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Fitting Shapes to Data: The Emax-Model

i = subject Ri = response of subject i Di = dose level of subject i h = slope factor E0 = effect at zero-dose Emax = maximum effect attributable to the drug

h h i h i i

ED D E D E R

50 max

+ ⋅ + =

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A Simulation Study

Frequencies of Wessler scores by dose group were generated using the multinomial distribution Parameters used:

• Wessler scores: 0, 0.5, 1, 2, 3, 3.5, 4
• Dose groups: 0, 300, 600, 900, 1200
• Samples per dose group: 3, 6, 10, 100
• True doses of ED50: 100, 300, 600, 1200, 1500

five different shapes were investigated, 104 simulation runs were performed

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Investigated Dose-response Shapes

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Linear Left skewed Sigmoid Right skewed Heavy right skewed 1500 1200 600 300 100 True ED50 n 0.16%

(1502.6)

1.83%

(1527.5)

3.58%

(1553.7)

8.65%

(1629.7)

0.03%

(1200.3)

• 0.07%

(599.6)

• 0.7%

(297.9)

0%

(100.0)

100 0.43%

(1205.2)

• 0.33%

(598.0)

0.63%

(301.9)

0.1%

(100.1)

10 0.77%

(1209.2)

• 0.55%

(596.7)

5.17%

(315.5)

0.2%

(100.2)

6 1.89%

(1222.6)

• 0.93%

(594.4)

16.5%

(349.5)

0.3%

(100.3)

3 Shape

Results: Estimation of ED50

% mean bias (mean estimated value)

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Accuracy of ED50: Confidence Intervals

Calculation of 95% CI for ED50 according to

• Bootstrap-percentile
• Bootstrap-t (using SE from non-linear model)
• Normal approximation

using 103 bootstrap resamples Coverage of intervals evaluated by 104 simulation runs

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Results: Coverage of 95% CI for ED50

1500 1200 600 300 100 True ED50 0.9473 0.9461 0.9494 100 0.9043 0.8952 0.9216 10 0.8695 0.8672 0.8538 6 0.6695 0.7840 0.6471 3 Linear 0.9458 0.9463 0.9474 100 0.9198 0.9341 0.8633 10 0.8918 0.8869 0.8677 6 0.9373 0.9310 0.8573 3 Heavy left skewed 0.9478 0.9192 0.9514 100 0.8952 0.8916 0.9207 10 0.8670 0.8488 0.8935 6 0.7125 0.6899 0.7323 3 Sigmoid 0.9396 0.9370 0.9466 100 0.7937 0.7660 0.9551 10 0.7460 0.7186 0.9316 6 0.6810 0.5762 0.8067 3 Right skewed 0.9454 0.9451 0.9421 100 0.9308 0.9306 0.9069 10 0.9243 0.9023 0.8940 6 0.9149 0.8831 0.8788 3 Heavy right skewed Normal approximation Bootstrap-t Bootstrap percentile n Shape

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Results: Width of 95% CI for ED50

100 10 6 3 100 10 6 3 100 10 6 3 100 10 6 3 100 10 6 3 n 214.6 213.1 215.1 808.7 808.7 808.7 1263.2 1020.2 1211.0 2504.0 1747.2 2347.6 1500 Linear 55.4 55.4 55.6 169.3 176.5 174.1 225.1 207.7 215.2 340.9 344.5 341.2 1200 Heavy left skewed 42.1 40.0 42.3 121.9 120.8 121.1 150.5 32837.1 147.0 186.7 456.4 184.5 600 Sigmoid 150.9 150.2 151.2 360.6 383.4 348.8 398.8 450.5 381.3 414.9 547.4 364.9 300 Right skewed 7.3 7.3 7.3 20.8 20.8 20.8 25.3 25.4 25.0 32.0 32.2 30.7 100 Heavy right skewed Normal approximation Bootstrap-t Bootstrap percentile True ED50 Shape

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Recommendations Based on Combined Coverage and Width

Shape Bootstrap-t Bootstrap-t Bootstrap-t Linear Bootstrap-t Bootstrap-t Bootstrap-t Left skewed Normal approximation Bootstrap percentile Normal approximation Heavy right skewed Bootstrap percentile Bootstrap percentile Bootstrap percentile Sigmoid Bootstrap percentile Bootstrap percentile Bootstrap percentile Right skewed Best coverage Recommendation Smallest width

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Pitfalls

• Estimation of ED50 may fail change starting values
• Heavy right skewed data were only estimable with a

fixed prespecified slope of 1

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Summary

• The Emax-model can be used for robust estimation of

ED50

• Confidence intervals for ED50 can be estimated using

resampling methods in most cases

• Approach can be extended for comparisons of dose-

response shapes

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References

• Davison, A. C. & Hinkley, D. V. (1997) Bootstrap Methods and Their
• Applications. Cambridge University Press, Cambridge
• Ting, N. (Eds.) (2006). Dose Finding in Drug Development. Springer

Verlag, 127-145

• Hereen, T. & D’Agustino, R. (1987) Robustness of the two independent

sample t-test when applied to ordinal scale data. Statistics in Medicine, 6, 79-90

• Wessler S., Reimer S. M., Steps M. C. (1959): Biologic assay of a

thrombosis-inducing activity in human serum. J. Appl. Physiol. 14, 943- 946

• CPMP/BPWG/220/02: Guideline on the clinical investigation of human

plasma derived von Willebrand factor products

• CPMP/ICH/378/95: Note for guidance on dose response information to

support drug registration