Evaluation of surrogate markers when surrogate and true endpoints are survival times

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Evaluation of surrogate markers when surrogate
and true endpoints are survival times
Martina Mittlböck Core Unit for Medical
Statistics and Informatics Medical University of
Vienna Michael Gnant (Department of Surgery,
Vienna) Richard Greil (Medical Department,
Salzburg) Michael Fridrik (Department
of Internal Medicine, Linz) Peter
Wohlmuth (ABCSG, Vienna)
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• Is there a causal relationship between surrogate
  and clinical endpoint?
• change in the marker ? corresponding change in
  the clinical endpoint?
• Statistical criteria to provide indirect evidence

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• Prentices Criteria (Prentice, 1989)
• Operational criteria to check if a triplet
  (T,S,Z) fulfills the definition for surrogate
  validation
• (1) treatment has a sig. impact on the true
  entpoint (TZ) ? (T)
• (2) treatment has a sig. impact on the surrogate
  endpoint (SZ) ? (S)
• (3) the surrogate endpoint has a sig. impact on
  the true endpoint (TS) ? (T)
• (4) the full effect of treatment upon the true
  endpoint is captured by the surrogate (TS,Z)
  (TS)

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• Problem with Prentice criteria
• If (TS,Z) (TS) lacks significance due to
  low power
• useful to reject a poor surrogate
• but inadequate to validate a good surrogate
  endpoint
• large numbers of observations may be needed
  for the validation of surrogate endpoints
• no quantification of the impact of the
  surrogate on the analysis of the true
  endpoint

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other Methods for quantification Proportion
Explained (PE) that is the proportion of
treatment effect explained by a Surrogate
(Freedman, Graubard and Schatzkin, 1992)
ß - estimate of the effect of Z on T without
adjustment for S ßs - estimate of the effect of Z
on T with adjustment for S
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other Methods for quantification Proportion
Explained (PE)
Buyse and Molenberghs (1998) decomposed the
proportion explained (PE) further into the
relative effect (RE) and adjusted association
(?Z) (? is a nuisance parameter)
ß - estimate of the effect of Z on T ? - estimate
of the effect of Z on S
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other Methods for quantification Relative Effect
(RE)
RE1 ? the effects of Z on T and on S are of
identical magnitude ? perfect at the
population level RElt1 ? the true endpoint is
more difficult to affect than the
surrogate endpoint
Adjusted Association (?Z)
association between S and T after adjustment for
the treatment Z
?Z1 ? a deterministic relationship between S
and T ? perfect at the individual level
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• Critisism
• assumption that the validation of a surrogate is
  based on data from a single randomized
  clinical trial
• problems with untestable assumptions (e.g.
  multiplicative effect of RE) and too low
  statistical power
• Solution of Albert et al. (1998)
  combination of information from several groups of
  patients (multi-center trials or
  meta-analyses)

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Two Failure Time Endpoints for the meta-analytic
approach Burzykowsky et al. (2001) proposed a
meta-analytic approach 1st stage estimate a
copula model (C?), i.e. a bivariate joint
survival function FSij and FTij denote
marginal survival functions (do not depend on the
choice of the copula function)
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Two Failure Time Endpoints The following two
copulas were considered 1. Clayton copula
(shared gamma frailty model) ?gt1 positive
association ??1 independence 2. Hougaard
copula (shared frailty model with positive stable
distribution) induces positive association
among the failure-times??1 independence ?
Kendalls ? can easily be calculated from ?
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Two Failure Time Endpoints - 2nd
stage Burzykowski et al. (2001) proposed to use
the model where the second term on the right
hand side is assumed to follow a zero-mean normal
distribution with dispersion matrix The quality
of surrogate S at the trial level is assessed
based on the coefficient of determination
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Recommendation values of R2trial(r) around 0.9
have been judged as sufficiently close to 1,
values of R2trial(r) around 0.5 as not close
to 1
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Study 8
Prospective, multicenter, randomised and
open-label studyPostmenopausal women ? 80 years
with endocrine responsive tumours and either G1
and G2 ductal carcinoma or Gx lobular
tumours Therapies2 years after surgery patients
received either Tamoxifen or Anastrozol
3297 randomized and eligible patients with 265
events 114 deaths alone 106 recurrences
alone (local, contralateral and distant)
45 recurrencesdeaths (local, contralateral
and/or distant recurrence and death)
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Study 8
1.0
Anastrozole
Anastrozole
Anastrozole
Tamoxifen
Tamoxifen
Tamoxifen
Disease-free surival (DFS)local, distant and,
contralateral events
Overall Survival (OS)all deaths
0.5
Distant disease free survival (DDFS)distant
metastases
0.0
0
100
20
40
60
80
0
100
20
40
60
80
0
100
20
40
60
80
months
months
months
3297 patients 91 distant metastases HR1.51
(0.99-2.29) p0.056
3297 patients 151 recurrences HR1.51
(1.09-2.08) p0.013
3297 patients 159 deaths HR1.24
(0.91-1.70) p0.176
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Study 8
No interaction between DFS and treatment
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Study 8
No interaction between DFS and treatment
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Study 8
only centers with 10 patients and at least one
death and one recurrence were included
treatment effects on OS
treatment effects on DFS
treatment effects on DFS
Two separate models are estimated for OS and
DFS r0.21 R2trial 0.04
bivariate model with Clayton copula r0.42
R2trial 0.18?0.78
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Study 8
LN neg
1.0
LN neg
LN neg
LN pos
LN pos
LN pos
0.5
Overall Survival (OS)all deaths
Disease-free surival (DFS)local, distant and,
contralateral events
Distant disease free survival (DDFS)distant
metastases
0.0
0
100
20
40
60
80
0
100
20
40
60
80
0
100
20
40
60
80
months
months
months
3297 patients 91 distant metastases HR3.86
(2.55-5.85) plt0.0001
3297 patients 151 recurrences HR2.37
(1.72-3.27) plt0.0001
3297 patients 159 deaths HR1.85
(1.35-2.55) p0.0002
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Study 8
No interaction between DFS and LN
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Study 8
No interaction between DFS and LN
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Study 8
only centers with 10 patients and at least one
death and one recurrence were included
LN effects on OS
LN effects on DDFS
LN effects on DDFS
Two separate models are estimated for OS and
DDFS r0.21 R2trial 0.05
bivariate model with Clayton copula r0.29
R2trial 0.08?0.72
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Study 6
Prospective, multicenter, randomised and
open-label studyPostmenopausal women ? 80 years
with endocrine responsive tumours TreatmentsTa
moxifen (Nolvadex)Tamoxifen (Nolvadex) and
Aminoglutethimid (Orimeten)
1980 patients with 723 events 298 deaths
alone 154 recurrences alone (local, distant)
271 deathsrecurrences (local, distant
recurrences and deaths)
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Study 6
1.0
Tam. Aminogl.
Tam. Aminogl.
Tam. Aminogl.
Tamoxifen
Tamoxifen
Tamoxifen
0.5
Disease-free surival (DFS)local, distant and,
contralateral events
Overall Survival (OS)all deaths
Distant disease free survival (DDFS)distant
metastases
0.0
0
200
50
100
175
0
200
50
100
175
0
200
50
100
175
months
months
months
1980 patients 354 distant metastases HR1.03
(0.834-1.265) P0.8041
1980 patients 425 recurrences HR1.05
(0.87-1.28) P0.5821
1980 patients 569 deaths HR1.05
(0.89-1.24) P0.5450
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Study 6
No interaction between DFS and treatment
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Study 6
No interaction between DFS and treatment
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Study 6
only centers with 40 patients and at least one
death and one recurrence were included
treatment effects on OS
treatment effects on DFS
treatment effects on DFS
treatment effects on DFS
Two separate models are estimated for OS and
DFS r0.83 R2trial 0.69
bivariate model with Claytons copula r0.92
R2trial 0.85?0.717
bivariate model with Hougaards copula r0.87
R2trial 0.75?0.47
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Discussion
results of the meta-analytic approach may differ
from Prentice criteria Further research has to
be done!!