estimating the dose-toxicity curve from completed phase i studies
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Estimating the dose-toxicity curve from completed Phase I studies. Alexia Iasonos, Irina Ostrovnaya Department of Biostatistics Memorial Sloan Kettering Cancer Center CRM Workshop, October 2009. Motivation. - PowerPoint PPT PresentationTRANSCRIPT
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Estimating the dose-toxicity curve from completed Phase I studies
Alexia Iasonos, Irina Ostrovnaya
Department of BiostatisticsMemorial Sloan Kettering Cancer Center
CRM Workshop, October 2009
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Motivation
1. Retrospective analysis of completed Phase I studies in order to recommend, possibly, a new MTD
โข among existing/visited dose levels,โข between dose levels
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Exampleโข When tested levels are too low (safe), ie no
activityโข Example for Extrapolation:
โข Example for Interpolation
Dose level 30 mg/m2 60 mg/m2 120 mg/m2 200 mg/m2
DLT/ # patients
0/3 0/3 1/6 1/6
Dose level 30 mg/m2
60 mg/m2
120 mg/m2
240mg/m2
DLT/ # patients
0/3 0/3 1/6 3/3 or 2/2
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Motivation Cont.
2. Switching from 3+3 to adaptive design, how can we use toxicity data up to this point to add additional levels?
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Statistical Question of Interest
โข If we can fit a curve to the existing trial/data then this curve can be used to interpolate or possibly extrapolate.
โข Dose-toxicity curve?
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Available statistical methods for estimating the dose-response curve
โข Parametric: probit or logit (Prentice
1976; He, 2006) sigmoid (Schmoyer 1984)
โข Non-parametric: isotonic regression (Stylianou, 2003)
โข Semi-parametric: splines or kernels (Kong 2006; Staniswalis 1988)
x
ph
at
15 30 60 120 240 4800
.00
50
.20
.60
.8
PROBLEM: small sample size, 0 tox. at many dose levels; model assumptions; change point from concave to convex
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Literature Review
โข Can we use the Continual Reassessment Method (CRM) retrospectively?
โข CRM uses toxicity data accumulated on all pts and updates a model that assigns the next patient to a dose that is closest to the target toxicity rate
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CRM and
retrospective CRM (retro-CRM)
are not the same.
Design (CRM)vs
Analysis (retro-CRM)
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Can we use CRM retrospectively?
Oโ Quigley (2005) NOโข You had already followed another design so
you canโt analyze the data assuming they were collected under the CRM scheme.
โข Solution: if you weight the information obtained from toxicities at each dose, then you can use the retro-CRM methodology that accounts for the fact that CRM would have allocated pts/doses differently.
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The weights are obtained by simulations and correspond to the percentage of patients CRM would have assigned to dose i . A large number of CRM trials of size are simulated using as the true toxicity rates, where are the observed toxicity rates from the existing trial.
Weights depend on which CRM you use (cohorts or not)
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Message:โข The trials followed a modified 3+3 design;
MTD not based on the 3+3 algorithm
โข The two methods result in the same MTD but different patient/doses allocation ratio
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Objective
โข To estimate the dose-toxicity curve based on available data from a completed trial
โข To evaluate the proposed method in 3+3 simulated trials, and compare it to retro-CRM
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Constrained Maximum Likelihood Estimation (CMLE)
There is no restriction on the toxicity rate at the first dose, p1.
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Constrained Maximum LikelihoodCMLE
โข Use available data based on numerator and denominator separately , ie:
2/2, 3/3, or 6/6 has different implications โข We will have constraints as of how much can this
curve increase between adjacent dose levels:โ MIN= it has to increase by at least MIN value (useful at
doses where we obtain no DLTs)โ MAX= it cannot increase by more than MAX value (this
downplays the 100% observed at last dose - often out of 1-2 pts , e.g. 1/1 or 2/2)
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Challenge: how to select MIN, MAX ? 5 levels, MIN=target rate at MTD/5=0.25/5=0.05
MAX=1/4=0.25
1 2 3 4 5
0.0
0.2
0.4
0.6
0.8
1.0
Levels
Pro
b. T
oxi
city
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Constrained MLEโข Small values of MIN_value lead to a conservative estimation by favoring a
flatter curve, while larger values of MIN impose larger jumps when the existing dose levels are low.
โข Similarly, MAX_value controls toxic dose levels by constraining the curve from increasing radically when high toxicity rates are observed.
โข The curve is between these bounds but the shape is not restricted by a model; only the observed toxicities at each dose, i.e. both the numerator and denominator count for the structure of the curve.
โข Robust to the choice of MIN, MAXโข Fewer toxicities or pts then constrains matterโข Otherwise if available data are rich, constraints matter less
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Simulations
โข Simulated 1000 trials followed 3+3 design, testing 6, 5, 4 dose levels, target tox. rate=0.25
Compared MTD by:1. Standard Method (SM)2. CRM- not weighted (LCRM โ Oโ Quigley, Shen
1996)3. Retrospective CRM (CRM-w; Oโ Quigley 2005)4. CMLE (with various MIN/MAX)
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Level 0 1 2 3 4 5 6
True .01 .05 .1 .15 .2 .25
SM <1 3 10 17 22 21 26
CRM <1 3 14 27 31 22
CRM_w
1 2 14 28 29 22
New <1 3 14 27 30 26
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Level 0 1 2 3 4 5 6
True .05 .1 .25 .35 .55 .7
SM 3 9 41 30 15 3
CRM <1 4 22 45 25 4
CRM_w
1 5 21 44 27 3
New <1 4 23 45 25 4
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0 1 2 3 4 5 NF
True 0.05 0.10 0.15 0.20 0.30
SM 3 9 21 21 24 22
CRM <1 4 13 25 34 21 3
CRM_w
1 5 11 25 33 22 3
New <1 4 13 24 35 25
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0 1 2 3 4 5 NF
True .15 .25 .3 .4 .5
SM 15 34 25 14 6 1 6
CRM 9 22 36 24 8 1
CRM_w
11 24 32 23 9 1 <1
New 14 23 30 23 9 1
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0 1 2 3 4 NF
True 0.15 .25 .3 .4
SM 15 34 26 14 6 6
CRM 9 22 36 23 10 <1
CRM_w
10 24 32 23 10 <1
New 9 20 37 27 7
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Additional Simulations (not shown)
โข Under true toxicity rates that violate the constraints in increments between adjacent dose levels
โข Under modified 3+3 trials that expanded accrual at MTD. If โค 3 toxicities were observed out of 10, then the MTD remained the same. Otherwise, the method de-escalated and followed the 3+3 scheme by expanding a cohort to 6 patients until โฅ 2 DLTs out of 6 patients were observed.
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99-083: pralatrexate in combination with paclitaxel or docetaxel in adv solid tumors, doses 80P+35D,100/35,120/35 (2,16),120/35 (1,15), 120/35 (1,8,15), 140/35 ,
MTD dose 4= 120 (1,15)other methods suggest dose 5, one level above MTD of the trial
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01-021 Phase I study of an oral histone deacetylase inhibitor, suberoylanilidehydroxamic acid, in patients with advanced cancer.
Oral SAHA, 200, 400, 600 mg qd or 400 mg bid after amend 200, 300 mg bid for solid tumors; Methods suggest 600, trial suggests 400
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Phase I trial of the cyclin-dependent kinase inhibitor and protein kinase Cinhibitor 7-hydroxystaurosporine in combination with Fluorouracil in patientswith advanced solid tumors.Trial recommended 2600 which is the last doseCMLE recommends dose=7, retro-CRM recommends 4th level, not weighted CRM recommends 5th level
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๐ข๐:Prแบ๐๐โฒ โค ๐ก๐แป= ฮฑ/2, where ๐๐โฒ~๐ต๐๐๐๐๐๐๐(๐ข๐,๐๐)
๐ข๐ : (๐ก๐ ๐๐)ฮค โ๐ข๐เถฅ๐ข๐แบ1โ๐ข๐แป๐๐ = zฮฑ/2
Morris (Biometrics, 1988) showed that a weighted sum ๐ ๐ = ฯ ๐ค๐๐ก๐๐๐=๐ , as well as any function of
๐ก๐,..,๐ก๐ that is non-increasing in each argument, can be used to obtain an exact or conservative
แบ1โ ๐ผแป100% upper confidence limit ๐ข๐, for ๐๐, in the following way:
๐ข๐ =upper limit of ๐๐ in the constrained space, if ๐ก๐ = ๐๐ for all ๐= ๐,โฆ,๐,
or otherwise
๐ข๐: Pr (ฯ ๐ค๐๐๐โฒ โค ๐ ๐) = ๐ผ๐๐=๐ , where ๐๐โฒ~๐ต๐๐๐๐๐๐๐(๐ข๐,๐๐).
Confidence Intervals Estimation
Wilson CI (Agresti, 1998): upper confidence limit ui for probability of toxicity pi
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An obvious selection of ๐ค๐, ๐> ๐, is ๐ค๐ = ๐๐ ๐๐ฮค , since it satisfies ๐ธ(๐ก๐) = ๐ธ(๐ค๐๐ก๐). Assume
๐ค๐ = 1. As the true probabilities are unknown, the weights can be approximated using the
constrained model (shown in the appendix), and they are equal to:
๐ค๐ โ 1โ ๐โ๐๐ .
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Average Width of 95% CI across dose levels
Scenario Wilson CI CMLE with Equal weights CI
CMLE with Weighted CI
6.1 0.55 0.46 0.44 6.2 0.56 0.51 0.48 6.3 0.56 0.57 0.54 5.1 0.56 0.50 0.48 5.2 0.57 0.60 0.56 4.1 0.55 0.50 0.48 4.2 0.57 0.59 0.55
All 95% CIs are conservative and have 99-100% coverage (across all dose levels) for all scenarios.
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Confidence Intervals
200 300 400 500 600 700 800
0.0
0.2
0.4
0.6
0.8
1.0
Scher 01-021(b) trial
Dose units
Ob
se
rve
d T
oxic
itie
s
6/0 9/0 10/4 6/3
CMLE 1/k-1CMLE 1/k
- -
-
-
- --
--
-
-
-
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Dose spacing โ use of actual units
Dose
p
15 120 240 480 560 630
1e
-04
0.2
0.3
0.5
0.6
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Quality assessment of Phase I dose-finding cancer trials โ
checklist (Zohar, Clinical Trials 2008)
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Conclusion
โข Rogatko (JCO 2007) : phase I rarely follow the 3+3. They follow a 3+3 scheme with โdeviationsโ
โข Since you deviate from the 3+3 you canโt assume that the statistical properties of 3+3 hold anymore.
โข Not efficient use of data even if they followed 3+3โข The proposed analysis method can estimate a
retrospective MTD by analyzing the data that you obtained from this deviated scheme/design.
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Acknowledgements
Thank you to:โข Elyn Riedel โ data collectionโข Dr. Spriggs and other PIs of studies