Ferring Pharmaceuticals

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Ferring Pharmaceuticals

• The extended Williams trend test - Background
  and practical example
• Anders Malmberg
• DSBS Generalforsamling
• May 26th, 2011

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Outline

• BPH
• Degarelix in BPH
• Williams trend test
• Conclusion

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Prevalence of BPH with age
Berry SJ et al. J Urol 1984 132 4749
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Guidelines for Management

• Watchful waiting
• Medical management
• If medical therapy fails surgery

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Normal bladder and prostate

• BPH is the most common benign condition in man
• The cause of BPH is multifactorial but there are
  two essential pre-requisites the presence of
  testes and ageing

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Benign prostatic enlargement

• The median lobe projects into the base of the
  bladder
• The prostatic urethra narrows
• The bladder shows thickening of the wall

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Symptoms of BPH

• Storage symptoms
• Frequency
• Nocturia
• Urgency

• Voiding symptoms
• Weak stream
• Intermittency
• Incomplete emptying
• Straining

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Symptom Score - IPSS

• Each one of the symptoms is rated on a 0 5
  scale (0 not bothersome 5 very bothersome)
• Total IPSS sum of the symptom scores
• Mild patients score 0 7
• Moderate patients score 8 19
• Severe patients score 20 35
• Primary objective of BPH trials is to reduce IPSS
  score

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Outline

• Benign Prostate Hyperplasia
• Degarelix in BPH
• Williams trend test
• Conclusion

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Degarelix in BPH

• Prostate cancer
• Degarelix is marketed for the treatment of
  prostate cancer in the U.S.A. and EU
• Patients are castrated and growth of prostate is
  arrested
• BPH
• In an earlier phase IIa study, it was found that
  degarelix can induce a marked but transient
  testosterone suppression resulting in sustained
  symptom relief in patients with BPH
• Primary objective of the study was to find a
  dosing regimen that provides a clinical effect
  defined as reduction in IPSS at Month 3

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Trial design
Primary endpoint Reduction in IPSS at Month 3
End at Month 12
Screening
Follow-up Period

Dose
A Placebo, mannitol
B 10 mg degarelix
C 20 mg degarelix
D 30 mg degarelix
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Trial design
Primary endpoint Reduction in IPSS at Month 3
Interim analysis at Month 6
End of Phase II meeting...
Screening
Follow-up Period
Dose
A Placebo, mannitol
B 10 mg degarelix
C 20 mg degarelix
D 30 mg degarelix
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Power calculation (1)

• Expected mean differences in reduction from
  baseline in IPSS vs placebo at Month 3 is assumed
  to be 1, 3, and 3 points for the 10, 20 and 30 mg
  dose group
• Between-subject standard deviation of change
  from baseline 6 points
• Type I error 5 (two-sided)
• Power of 90 to declare mean IPSS response in
  both 20 and 30 mg to be significantly different
  from placebo...

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Power calculation Multiple testing

• Dunnetts Type-I error correction for many to
  one comparison
• Step-down (30 mg vs placebo then 20 mg vs
  placebo)
• t-test
• Williams test

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Power calculation (2)

• Expected mean differences in reduction from
  baseline in IPSS vs placebo at Month 3 is assumed
  to be 1, 3, and 3 points for the 10, 20 and 30 mg
  dose group
• Between-subject standard deviation of change
  from baseline 6 points
• Type I error 5 (two-sided)
• Power of 90 to declare mean IPSS response in
  both 20 and 30 mg to be significantly different
  from placebo
• The number of patients saved using Williams
  trend instead if t-test is about 36 patients (8
  )
• For our phase II b study this translated to
  1.000.000 EUR

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Outline

• Benign Prostate Hyperplasia
• Degarelix in BPH
• Williams trend test
• Conclusion

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Williams trend test background (1)

• Useful when an overall dose related trend is to
  be expected
• An estimate of target dose is of interest
• Null hypotesis all means are equal
• µ0 µ1 µ2 µ3
• Restrictive alternative hypothesis
• µ0lt µ1lt µ2lt µ3, µ0lt µ3

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Williams trend test background (2)

• Bartholomew (1961) used the following test
  statistic
• van Eeden (1958) derived method for computing
  mean effect levels under restrictive alternative
  hypothesis
• Williams (1971) tested highest dose versus
  control

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How to find mean effect level of highest dose
group under the restricted alternative...

• Click to continue...

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X1
X2
X3
X0
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X1
X0ltX1 ?
X2
X3
X0
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X1ltX2 ?
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M1 M2ltX3 ?
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M1 M2 M3
26

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Williams trend test background (4)

• Williams (1971) tested highest dose versus
  control
• In SAS probmc("williams",W3,.,3(n-1),3)
• For step 2 the procedure is repeated with W2

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Wheres the gain? (1)

• Assuming mean differences versus placebo of 1, 3,
  3
• N95 per arm and SD6
• power using Williams test 90 power with
  t-test 88

Conditional power, given the estimated shape under the isotonic restriction Relative frequency Williams power power of t-test
M0 lt M1 lt M2 lt M3 50 87 88
M0 lt M1 lt M2 M3 49 94 87
M0 lt M1 M2 M3 1 79 79
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Wheres the gain? (2)

• Assuming mean differences versus placebo of 1,
  2.5, 3
• N130 per arm and SD6
• power using Williams test 90 power with
  t-test 90

Conditional power, given the estimated shape under the isotonic restriction Relative frequency Williams power power of t-test
M0 lt M1 lt M2 lt M3 74 88 89
M0 lt M1 lt M2 M3 25 97 94
M0 lt M1 M2 M3 1 89 79
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... but

• Williams test works only for balanced one-way
  layouts
• Instead, use the extended Williams test (Bretz,
  2006)
• General unbalanced linear models
• Accurate computation of p-values using
  multivariate t-distribution

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How Williams test is extended

• Numerator of W3 can be written as
• Which gives three studentized variables
• Where the extended test statistic W3 max(T1,
  T2, T3)

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Linear fixed effects model

• Interested in differences between the adjusted
  means
• Use the following standardized quantities

• Where Tj j1,..., 3 are multivariate t with
  known correlation matrix

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Extensions that Bretz made

• Wrote the solution using matrices
• Considered the multivariate t-disribution of
  (T1, T2, T3)
• Remember
• Prob(max (T1, T2, T3) lt W3) Prob(T1ltW3,
  T1ltW3, T1ltW3)
• Used numerical integrations of Genz and Bretz
  (2002) to calculate the p-value
• SAS code for computing p-values is available for
  downloading from Bretz homepage

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Outline

• Benign Prostate Hyperplasia
• Degarelix in BPH
• Williams trend test
• Conclusion

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Conclusions

• Consider to use the extended Williams trend
  test if an overall dose related trend is expected
• The modified version (smoothing also the control
  grop) is more powerful in concave cases (but will
  increase p-value since number of dimensions in
  joint test statistic will increase)
• To think of
• Algorithm to estimate target dose
• Confidence interval estimation is not available

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References

• Bartholomew, D.J., 1961, A test of homogeneity
  of means under restriced alternatives J. R.
  Statisti. Soc. B 23, 239-281
• Barry, M. J., et al., 1995, Benign prostatic
  hyperplasia specific health status measures in
  clinical research How much change in the
  American Urological Association Symptom index and
  the Benign prostatic hyperplasia impact index is
  perceptible to patients? J. Urol., 154, 1770-1774
• Berry S. J., et al., 1984, The Development of
  human benign prostatic hyperplasia with age J.
  Urol., 132, 4749
• Bretz, F., 2006, An extention of the Williams
  trend test to general unbalanced linear models
  Comp. Stat. Data Ana. 50, 1735-1748
• Genz, A., Bretz, F., 2002, Methods for the
  computation of multivariate t-probabilities J.
  Comp. Graph. Statist. 11, 950-971
• Marcus, R. 1976, The power of some tests of the
  equality of normal means against an ordered
  alternative, Biometrika 63, 177-183
• Williams, D.A., 1971, A test for differences
  between treatment means when several dose levels
  are compared with a zero dose control Biometrics
  27, 103-117