Two-Stage%20Treatment%20Strategies%20Based%20On%20Sequential%20Failure%20Times

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Two-Stage Treatment Strategies Based On
Sequential Failure Times
Peter F. Thall Biostatistics Department Univ. of
Texas, M.D. Anderson Cancer Center
Designed Experiments Recent Advances in Methods
and Applications Cambridge, England August 2008
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• Joint work with
• Leiko Wooten, PhD
• Chris Logothetis, MD
• Randy Millikan, MD
• Nizar Tannir, MD
• The basis for a multi-center trial comparing
• 2-stage strategies for Metastatic Renal Cell
  Cancer

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A Metastatic Renal Cancer Trial

• Entry Criteria Patients with Metastatic Renal
  Cell Cancer (MRCC) who have not had previous
  systemic therapy
• Standard treatments are ineffective, with
  median(DFS) approximately 8 months
• ? Three targeted treatments will be studied in
  240 MRCC patients, using a two-stage
  within-patient Dynamic Treatment Regime

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Outcome Example
Disease Worsening ? Cancer Progression Psychotic Episode ? Alcoholic Relapse
Discontinuation of Therapy ? Death ? SAE precluding further therapy ? Physician stops rx due to futility ? Dropout
Treatment Failure Disease Worsening or Discontinuation of Therapy
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A Within-Patient Two-Stage Treatment Assignment
Algorithm (Dynamic Treatment Regime)

• Stage1
• At entry, randomize the patient among the stage 1
  treatment pool A1,,Ak
• Stage 2
• If the 1st failure is disease worsening
• (progression of MRCC) not discontinuation,
• re-randomize the patient among a set of
  treatments B1,,Bn not received initially
• Switch-Away From a Loser

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Frontline
Salvage
Strategy
A B C
B (A, B) C (A,
C) A (B, A) C (B,
C) A (C, A) B (C, B)
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Selection Trials Screening New Treatments

• - Randomize patients among experimental treatment
  regimes E1,, Ek
• - Evaluate each patients outcome(s)
• - Select the best treatment Ek that maximizes
  a summary statistic quantifying treatment benefit
  
• A selection design does not test hypotheses ?
• It does not detect a given improvement over a
  null value with given test size and power
• E.g. with k3, in the null case where q1 q2
  q3 each Ej is selected with probability .33
• (not .05 or some smaller value)

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Goal of the Renal Cancer Trial

• Select the two-stage strategy having the largest
  average time to second treatment failure
  (overall failure time)
• With 6 strategies
• In the null case where all strategies give the
  same overall failure time, each strategy is
  selected with probability
• 1/6 .166

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Higher Mathematics

• Stage1 treatment pool A1,,Ak
• Stage 2 treatment pool B1,,Bn
• ?
• kxn possible 2-stage strategies
• N/k effective sample size to estimate each
  frontline rx effect
• N/(kn) effective sample size to estimate each
  two-stage strategy effect

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Higher Mathematics

• Example If k3, n3 with switch-away within
  patient rule, and N240 ?
• 2x3 6 possible 2-stage strategies
• 240/3 80 effective sample size to estimate
  each frontline rx effect
• 240/6 40 effective sample size to estimate
  each two-stage strategy effect

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(No Transcript)
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Outcomes
TD time of discontinuation S1 time from
start of stage 1 of therapy of 1st disease
worsening S2 time from start of stage 2 of
therapy to 2nd treatment failure d delay
between 1st progression and start of 2nd stage
of treatment
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Outcomes
T1 Time to 1st treatment failure T2
Time from 1st disease worsening to 2nd
treatment failure T1 T2 Time of 2nd
treatment failure (provided that the 1st
failure was not a discontinuation)
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Unavoidable Complications

• Because disease is evaluated repeatedly (MRI,
  PET), either T1 or T1 T2 may be interval
  censored
• There may be a delay between 1st failure and
  start of stage 2 therapy
• T1 may affect T2
• The failure rates may change over time (they
  increase for MRC)

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Delay before start of 2nd stage rx
Discontinuation
Start of stage 2 rx
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T2,1 Time from 1st progression to 2nd
treatment failure if it occurs during the delay
interval before stage 2 therapy is begun T2,2
Time from 1st progression to 2nd treatment
failure if it occurs after stage 2 therapy has
begun
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A Simple Parametric Model
Weib(a,x) Weibull distribution with mean m(a,x)
ea G(1e-x), for real-valued a and x T1 A
Weib(aA,xA) T2,1 A,B, T1 Exp gAbA
log(T1) T2,2 A,B, T1 Weib( gA,BbA
log(T1), xA,B)
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Mean Overall Failure Time
T T1 Y1,W T2 ? mA,B(q) E T
(A,B) E(T1) Pr(Y1,W 1) E(T2)
Mean time to 1st failure
Pr(1st failure is a Disease Worsening)
Mean time to 2nd failure
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Criteria for Choosing a Best Strategy

• Mean mA,B(q) data B-Weib-Mean
• 2. Median mA,B(q) data B-Weib-Median
• 3. MLE of mA,B(q) under simple Exponential
• F-Exp-MLE
• 4. MLE of mA,B(q) under full Weibull
• F-Weib-MLE

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A Tale of Four Designs
Design 1 (February 21, 2006) N240, accrual rate
a 12/month ? 20 month accrual 18 mos addtl
FU Stage 1 pool A,B,C,D ? 12 strategies
(A,B), (A,C), (A,D), (B,A), (B,C), (B,D),
(C,A), (C,B), (C,D), (D,A), (D,B),
(D,C) Drop-out rate .20 between stages ?
(240/12) x .80 16 patients per strategy
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A Tale of Four Designs
Design 2 (April 17, 2006) Following advice
from CTEP, NCI N 240, a 9/month (more
realistic) Stage 1 pool A,B (C, D not
allowed as frontline) Stage 2 pool A,B,C,D
? 6 strategies (A,B), (A,C), (A,D), (B,A),
(B,C), (B,D) (240/6) x .80 32 patients per
strategy
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A Tale of Four Designs
An Interesting Property of Design 2 Stage 1 may
be thought of as a conventional phase III trial
comparing A vs B with size .05 and power .80 to
detect a 50 increase in median(T1), from 8 to 12
months, embedded in the two-stage design However,
the design does not aim to test hypotheses. It
is a selection design.
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A Tale of Four Designs
Design 3 (January 3, 2007) CTEP was no longer
interested, but several Pharmas now VERY
interested N 360, a 12/month, 3 new
treatments Stage 1 rx pool Stage 2 rx pool
a,s,t ? 6 strategies (different from Design 2)
(a,s), (a,t), (s,a), (s,t), (t,a), (t,s)
(360/6) x .80 48 patients per strategy
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A Tale of Four Designs
Design 4 (May 15, 2007) Question Should a
futility stopping rule be included, in case the
accrual rate turns out to be lower than planned?
Answer Yes!! Weeding Rule When 120 pats.
are fully evaluated, stop accrual to strategy
(a,b) if Pr m(a,b) lt m(best) 3 mos data gt
.90
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A Tale of Four Designs
Applying the Weeding Rule when 120 patients have
been fully evaluated ?
Accrual Rate ( Patients per month) Expected Future Patients Affected by the Rule
12 24
9 78
6 132
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Establishing Priors

• q has 28 elements, but the 6 subvectors are
• qA,B (n1,A, n2,A,B , aA , xA, gA, bA , aA,B ,
  xA,B )
• Pr(Dis. Worsening) Reg. of T2 on T1
• Weib pars of T1 Weib pars of
  T2
• The qA,Bs are exchangeable across the 6
  strategies, so they have the same priors

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Establishing Priors

• ? n1,A , n2,A,B iid beta(0.80, 0.20) based on
  clinical experience
• ? aA , xA, gA, bA , aA,B , xA,B indep. normal
  priors
• Prior means We elicited percentiles of T1 and
• T2 T1 8 mos, applied the Thall-Cook
  (2004) least squares method to determine means
• Prior variances We set
• varexp(aA) varexp(xA) varexp(xA,B)
  100
• Assuming Pr(Disc. During delay period) .02 ?
• E(mA,B) 7.0 mos sd(mA,B ) 12.9

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Computer Simulations

• Simulation Scenarios specified in terms of z1(A)
  median (T1 A) and
• z2(A,B) median T2,2 T1 8, (A,B)
• Null values z1 8 and z2 3
• z1 12 ? Good frontline
• z2 6 ? Good salvage
• z2 9 ? Very good salvage

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Simulations No Weeding Rule
In terms of the probabilities of correctly
selecting superior strategies, F-Weib-MLE
B-Weib-Median gt B-Weib-Mean
gtgt F-Exp-MLE
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Simulations B-Weib-Median, No weeding rule
Strategy Strategy Strategy Strategy Strategy Strategy
(a, s) (a, t) (s, a) (s, t) (t, a) (t, s)
1 m 15.7 15.7 15.7 15.7 15.7 15.7
select 15 17 17 18 17 16

2 m 19.4 19.4 15.7 15.7 15.7 15.7
select 52 48 0 0 0 0

3 m 15.7 18.8 15.7 18.8 15.7 15.7
select 0 49 0 51 0 0
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Simulations B-Weib-Median, No weeding rule
Strategy Strategy Strategy Strategy Strategy Strategy
(a, s) (a, t) (s, a) (s, t) (t, a) (t, s)
4 m 19.4 23.3 15.7 15.7 15.7 15.7
select 0 100 0 0 0 0

5 m 15.7 18.8 15.7 22.0 15.7 15.7
select 0 3 0 97 0 0

6 m 12.5 12.5 15.7 15.7 15.7 15.7
select 0 0 28 25 25 23
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Sims With Weeding Rule

1. Correct selection probabilities are affected only
   very slightly
2. There is a shift of patients from inferior
   strategies to superior strategies but this only
   becomes substantial with lower accrual rates

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Sims With Weeding Rule (Scenario 5)
Acc rate (a, s) (a, t) (s, a) (s, t) (t, a) (t, s)
Acc rate m 15.7 18.8 15.7 22.0 15.7 15.7
12 PET .68 .24 .78 .01 .69 .70
pats 45 51 44 59 45 44

9 PET .68 .25 .81 .01 .67 .71
pats 41 55 39 72 42 40

6 PET .68 .22 .82 0 .68 .69
pats 37 59 34 84 37 36
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Future Research / Extensions

1. Distinguish between drop-out and other types of
   discontinuation and conduct Informative
   Drop-Out analysis
2. Account for patient heterogeneity
3. Correct for selection bias when computing final
   estimates
4. Accommodate more than two stages