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Lost Opportunities for Design Theory in Drug Development

(C)Stephen Senn. 2. Basic Thesis. Design theory has great potential in drug developmentBut this potential is unrealisedThose working in so-called optimal design are so ignorant of application realities that where their influence is not zero it is harmfulOn the other hand the understanding of design theory by biostatisticians is pitifully inadequateWe must cooperate properly to cure this parlous state of affairs.

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Lost Opportunities for Design Theory in Drug Development

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    1. (C)Stephen Senn 1 Lost Opportunities for Design Theory in Drug Development Stephen Senn

    2. (C)Stephen Senn 2 Basic Thesis Design theory has great potential in drug development But this potential is unrealised Those working in so-called optimal design are so ignorant of application realities that where their influence is not zero it is harmful On the other hand the understanding of design theory by biostatisticians is pitifully inadequate We must cooperate properly to cure this parlous state of affairs

    3. (C)Stephen Senn 3 Outline Quick tutorial on cross-over trials I shall then give two introductory examples of nonsense By leading design theoreticians By leading biostatisticians I shall then consider ‘design nonsense’ further Some conclusions After lunch a case-study

    4. (C)Stephen Senn 4 Warning I am a biostatistician We are used to thinking of data matrices with rows as subjects and columns as measurements That means that we write sequences for designs with rows representing subjects and columns representing periods

    5. (C)Stephen Senn 5

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    7. (C)Stephen Senn 7

    8. (C)Stephen Senn 8

    9. (C)Stephen Senn 9 Simple Carry-over Carry-over lasts for exactly one period It depends only on the engendering treatment and is unmodified by the perturbed treatment There is a huge literature proposing ‘optimal’ designs for this model There is no empirical evidence that any of this has been useful

    10. (C)Stephen Senn 10 Three Period Bioequivalence Designs Three formulation designs in six sequences common. Subjects randomised in equal numbers to six possible sequences. For example, 18 subjects, three on each of the sequences ABC, ACB, BAC, BCA, CAB, CBA. A = test formulation under fasting conditions, B = test formulation under fed conditions C = reference formulation under fed conditions.

    11. (C)Stephen Senn 11

    12. (C)Stephen Senn 12 Properties of these weights Sum 0 in any column, eliminates the period effect. Sum 0 in any row eliminates patient effect Sum 0 over cells labelled A A has no part in definition of contrast Sum to 1 over the cells labelled B and to -1 over the cells labelled C Estimate contrast B-C

    13. (C)Stephen Senn 13

    14. (C)Stephen Senn 14

    15. (C)Stephen Senn 15 Properties of These Weights As before Estimates B-C contrast Eliminates, period and patient effect Eliminates A Sum to zero over cells labelled a,b, and c Eliminate simple carry-over

    16. (C)Stephen Senn 16 Have We Got Something for Nothing? Sum of squares weights of first scheme is 1/3 (or 4/12) Sum of squares of weights of second scheme is 5/12 Given independent homoscedastic within- patient errors, there is thus a 25% increase in variance Penalty for adjusting is loss of efficiency

    17. (C)Stephen Senn 17 First Example Some Design Theory Nonsense

    18. (C)Stephen Senn 18 What’s wrong here?

    19. (C)Stephen Senn 19

    20. (C)Stephen Senn 20

    21. (C)Stephen Senn 21 Multi-Story

    22. (C)Stephen Senn 22 Conclusion Multi-dose trials real scope for design theory. These will employ active wash-out Design problem is trade-off between exploiting correlation and eliminating carry-over. Short vs long active wash-out periods

    23. (C)Stephen Senn 23 Second Example Some Biostatistics Nonsense

    24. (C)Stephen Senn 24 Second Example Some Biostatistics Nonsense

    25. (C)Stephen Senn 25 What is wrong 1. It’s not correct design theory As any design expert knows residual degrees of freedom are (nearly) irrelevant to efficiency It is the impact of adjustment on the degree of orthogonality of the design matrix that is important

    26. (C)Stephen Senn 26 What is wrong 2. It’s not realistic biostatistics In fact as any biostatistician who has had to think about it will know from a practical point of view far from being optimal Balaam’s design is simply inadmissible The reasons is that only half of the resources are devoted to actually measuring the treatment The rest are devoted to providing an adjustment for a form of carry-over that is itself implausible

    27. (C)Stephen Senn 27 Allocation of patients for two designs

    28. (C)Stephen Senn 28 Investigation of the real efficiency of Balaam’s design

    29. (C)Stephen Senn 29

    30. (C)Stephen Senn 30

    31. (C)Stephen Senn 31 Dose Response: The Statistician’s Version

    32. (C)Stephen Senn 32 The Models Which use Simple Carry-over are Inconsistent

    33. (C)Stephen Senn 33

    34. (C)Stephen Senn 34 The Rhinoceros

    35. (C)Stephen Senn 35 The Phoenix Bioequivalence Trials Analysed by D’Angelo & Potvin 20 drug classes 1989-1999 12 or more subjects 96 three period designs 324 two period designs

    36. (C)Stephen Senn 36

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    39. (C)Stephen Senn 39 Conclusions Distribution of P-values uniform no evidence of carry-over Carry-over a priori implausible presence testable by assay No point is testing for it leads to bias Or adjusting for it increased variance

    40. (C)Stephen Senn 40 Do Bayesians do Better? In principle the Bayesian approach ought to allow us to be more flexible about nuisance parameters such as carry-over However, the Bayesian track record is not impressive here Realistic models have not been employed

    41. (C)Stephen Senn 41 Classic analysis ignoring carry-over Accumulated analysis of variance Change d.f. s.s. m.s. v.r. F pr. + Patient 28 600.897 21.461 3.99 <.001 + Period 1 18.776 18.776 3.49 0.073 + Treatment 1 58.364 58.364 10.84 0.003 Residual 27 145.360 5.384 Total 57 823.397 14.446 Estimates and confidence limits for treatment 2.037 0.768 3.306 Analysis of first period values only Two sample t Standard Standard error Sample Size Mean Variance deviation of mean Drug 17 8.118 14.74 3.839 0.9310 Placebo 12 7.667 8.97 2.995 0.8646 Difference of means: 0.451 Standard error of difference: 1.327 95% confidence interval for difference in means: (-2.272, 3.174) Classic analysis ignoring carry-over Accumulated analysis of variance Change d.f. s.s. m.s. v.r. F pr. + Patient 28 600.897 21.461 3.99 <.001 + Period 1 18.776 18.776 3.49 0.073 + Treatment 1 58.364 58.364 10.84 0.003 Residual 27 145.360 5.384 Total 57 823.397 14.446 Estimates and confidence limits for treatment 2.037 0.768 3.306 Analysis of first period values only Two sample t Standard Standard error Sample Size Mean Variance deviation of mean Drug 17 8.118 14.74 3.839 0.9310 Placebo 12 7.667 8.97 2.995 0.8646 Difference of means: 0.451 Standard error of difference: 1.327 95% confidence interval for difference in means: (-2.272, 3.174)

    42. (C)Stephen Senn 42 This is a re-analysis of the Hills and Armitage data by 1. Teather, D, Morrey, GH. Bayesian methods in cross-over trials, Byocybernetics and Biomedical Engineering 1995; 15: 41-52. This is a re-analysis of the Hills and Armitage data by 1. Teather, D, Morrey, GH. Bayesian methods in cross-over trials, Byocybernetics and Biomedical Engineering 1995; 15: 41-52.

    43. (C)Stephen Senn 43 Identical Priors for Treatment and Carryover? Patients treated repeatedly during trial Fourteen day treatment period Average time to last treatment plausibly 4 hours Average time to previous treatment seven days Saying that it is just as likely that carry-over could be greater than treatment is not coherent In any case the two cannot be independent Is negative carry-over as likely as positive carry-over? Large values of carry-over seem implausible if the treatment effect is small. This implies that the prior distributions cannot be independent. Negative carry-over would imply that the residual effect of a treatment had an opposite effect to the direct effect of that treatment.Large values of carry-over seem implausible if the treatment effect is small. This implies that the prior distributions cannot be independent. Negative carry-over would imply that the residual effect of a treatment had an opposite effect to the direct effect of that treatment.

    44. (C)Stephen Senn 44 So What are Acceptable Models for Carry-over? Ignoring carry-over altogether (not allowing for it because one believes one has taken adequate steps to eliminate it) This is always a reasonable strategy Using an integrated pharmacokinetic pharmacodynamic model (Sheiner et al, 1991) This may work for dose-finding trials Very difficult to implement where more than one molecule is involved

    45. (C)Stephen Senn 45 The Sheiner model

    46. (C)Stephen Senn 46

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    50. (C)Stephen Senn 50 Advice for Design-Theoreticians Resist the temptation to give advice if you are unfamiliar with the application area Seek collaborators Ground your models in pharmacology Remember that the goal is good medicine not elegant mathematics Don’t defend the indefensible

    51. (C)Stephen Senn 51 Advice for biostatisticians Remember that design theoreticians have many powerful results It’s just conceivable that some of them may even be useful

    52. (C)Stephen Senn 52

    53. (C)Stephen Senn 53 References

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