exemplifi plified ed for r a proje ject ct to determi ermine - PowerPoint PPT Presentation

Scientifi ntific c collaborati oration on wi with African ican stud udents ents in mathemati hematics, cs, exemplifi plified ed for r a proje ject ct to determi ermine ne the assuran rance ce durin ing project ct planning of clinical al developm pment ent program rams A. R Ring 1,2 ,2 , , D. Habima imana na 3 , G. T Tumusab musabe 3 , , W. Nakiy kiying ingi 3 1 University of the Free State, South Africa 2 medac GmbH, Germany 3 AIMS Rwanda, Germany

Overview 2

AIMS in Websites • https://nexteinstein.org/ und https://nef.org/ • https://www.aims.ac.rw • A day at AIMS Rwanda https://youtu.be/wtqVTiK5L1w • RSS-Initiative https://docs.google.com/forms/d/e/1FAIpQLSc4DwjDjY06BJohRNc9SnpeFhd9O9zBV95F3pKILbZ4o3t2pQ/viewform • http://www.lancaster.ac.uk/staff/giorgi/AIMS_syllabus.pdf https://de.wikipedia.org/wiki/African_Institute_for_Mathematical_Sciences • https://www.nexteinstein.org/research/researchchairprogram • 3

Objective • Understanding of the parameters that determine the power • Exploring the assurance concept for a quantitative endpoint • Based on Chuang-Stein 2006 • Extending the concept to optimize the sample size of two subsequent trials 4

Implementation of Chuang-Stein paper • Exploring statistical power 5

Implementation of Chuang-Stein paper • The illustration of the method • Uncertainty of delta • Estimated from Phase II trial 𝛿 𝑜, 𝑥 𝜄 0 , 𝜏 0 = න 𝜌 𝑜, 𝜄, 𝜏 0 𝑥 𝜄 0 𝜄 𝑒𝜄 6

Implementation of Chuang-Stein paper • The illustration of the method (uncertainty of delta) 7

Extension to planning optimal sample sizes 8

Extension to planning optimal sample sizes Optimum sample size of the old trial for desired assurance, so that total sample size of both trials is minimal, assuming the true 𝜄 0 is known (before old trial is performed) 𝑜 𝑝𝑚𝑒 | (𝑜 𝑝𝑚𝑒 + 𝑜 𝑜𝑓𝑥 ) is minimal ∧ 𝛿 𝑜 𝑜𝑓𝑥 , 𝑥 𝜄 0 , 𝑜 𝑝𝑚𝑒 , 𝜏 0 = 𝛿 0 𝑜 𝑝𝑚𝑒 𝛿 0 , 𝑥 𝜄 0 , 𝜏 0 = 9

Extension to planning optimal sample sizes 10 10

ሷ ሷ Future plans • Comparison of assurance with approaches in Whitehead paper • Extension to uncertainty of expected treatment effect in pilot trial 𝛿 𝑜 𝑜𝑓𝑥 , 𝑥 𝜄 0 ,𝜏 𝑣 , 𝑜 𝑝𝑚𝑒 , 𝜏 0 = න න 𝜌 𝑜 𝑜𝑓𝑥 , 𝜄, 𝜏 0 𝑥 𝜐 𝜄 𝑒𝜄 𝑥 𝜄 0 ,𝜏 𝑣 𝜐 𝑒𝜐 𝑥 𝜄 0 ,𝜏 𝑣 = 𝑂 𝜄 0 , 𝜏 𝑣 𝑥 𝜐 = 𝑂(𝜐, 𝜏 0 / 𝑜 𝑝𝑚𝑒 ) • Derivation of optimal sample size of pilot trial 𝑜 𝑝𝑚𝑒 𝛿 0 , 𝑥 𝜄 0 , 𝜏 0 = 𝑜 𝑝𝑚𝑒 | (𝑜 𝑝𝑚𝑒 + 𝑜 𝑜𝑓𝑥 ) is minimal ∧ 𝛿 𝑜, 𝑥 𝜄 0 ,𝜏 𝑣 , 𝑜 𝑝𝑚𝑒 , 𝜏 0 = 𝛿 0 11 11

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