two-stage treatment strategies based on sequential failure times
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Two-Stage Treatment Strategies Based On Sequential Failure Times
Peter F. ThallBiostatistics Department
Univ. of Texas, M.D. Anderson Cancer Center
Designed Experiments: Recent Advances in Methods and Applications
Cambridge, EnglandAugust 2008
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
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
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
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”
B = (A, B)
C = (A, C)
A = (B, A)
C = (B, C)
A = (C, A)
B = (C, B)
Frontline Salvage Strategy
A
B
C
- Randomize patients among experimental treatment regimes E1,…, Ek
- Evaluate each patient’s outcome(s)
- Select the “best” treatment E[k] 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 k=3, in the “null” case where 1 = 2 = 3 each Ej is selected with probability .33 (not .05 or some smaller value)
Selection Trials: Screening New Treatments
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
Goal of the Renal Cancer Trial
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
Higher Mathematics
Example : If k=3, n=3 with “switch-away” within patient rule, and N=240
2x3 = 6 = # possible 2-stage strategies240/3 = 80 = effective sample size to
estimate each frontline rx effect
240/6 = 40 = effective sample size to estimate each two-stage strategy effect
Higher Mathematics
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
= delay between 1st progression and
start of 2nd stage of treatment
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)
Unavoidable Complications
1)Because disease is evaluated repeatedly (MRI, PET), either T1 or T1 + T2 may be interval censored
2)There may be a delay between 1st failure and start of stage 2 therapy
3)T1 may affect T2
4)The failure rates may change over time (they increase for MRC)
Discontinuation
Delay before start of 2nd stage rx
Start of stage 2 rx
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
A Simple Parametric Model
Weib() = Weibull distribution with mean () = e(1+e), for real-valued and
[ T1 | A ] ~ Weib(AA)
[ T2,1 | A,B, T1] ~ Exp{ AA log(T1) }
[ T2,2 | A,B, T1] ~ Weib( A,BA log(T1), A,B)
Mean Overall Failure Time
T = T1 + Y1,W T2
A,B() = E{ T | (A,B)}
= E(T1) + Pr(Y1,W =1) E(T2)
Pr(1st failure is a
Disease Worsening)
Mean time
to 2nd failure
Mean time
to 1st failure
Criteria for Choosing a Best Strategy
1. Mean{ A,B() | data }: B-Weib-Mean
2. Median{ A,B() | data }: B-Weib-Median
3. MLE of A,B() under simple Exponential:
F-Exp-MLE
4. MLE of A,B() under full Weibull:
F-Weib-MLE
A Tale of Four Designs
Design 1 (February 21, 2006)
N=240, accrual rate a = 12/month
20 month accrual + 18 mos addt’l 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
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
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.
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
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{ (a,b) < (best) – 3 mos | data} > .90
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
has 28 elements, but the 6 subvectors are
A,B = (1,A, 2,A,B , A , A, A, A , A,B , A,B )
Pr(Dis. Worsening) Reg. of T2 on T1
Weib pars of T1 Weib pars of T2
The A,B’s are exchangeable across the 6 strategies, so they have the same priors
Establishing Priors
1,A , 2,A,B ~ iid beta(0.80, 0.20) based on clinical experience
A , A, A, A , A,B , A,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
var{exp(A)} = var{exp(A)} = var{exp(A,B)} = 100
Assuming Pr(Disc. During delay period) = .02 E(A,B) = 7.0 mos & sd(A,B ) = 12.9
Establishing Priors
Simulation Scenarios specified in terms of 1(A) = median (T1 | A) and
2(A,B) = median { T2,2 | T1 = 8, (A,B) }
Null values 1 = 8 and 2 = 3
1 = 12 Good frontline
2 = 6 Good salvage
2 = 9 Very good salvage
Computer Simulations
Simulations: No Weeding Rule
In terms of the probabilities of correctly selecting superior strategies,
F-Weib-MLE ~ B-Weib-Median
>
B-Weib-Mean
>>
F-Exp-MLE
Simulations: B-Weib-Median, No weeding rule
Strategy
(a, s) (a, t) (s, a) (s, t) (t, a) (t, s)
1 15.7 15.7 15.7 15.7 15.7 15.7
% select 15 17 17 18 17 16
2 19.4 19.4 15.7 15.7 15.7 15.7
% select 52 48 0 0 0 0
3 15.7 18.8 15.7 18.8 15.7 15.7
% select 0 49 0 51 0 0
Strategy
(a, s) (a, t) (s, a) (s, t) (t, a) (t, s)
4 19.4 23.3 15.7 15.7 15.7 15.7
% select 0 100 0 0 0 0
5 15.7 18.8 15.7 22.0 15.7 15.7
% select 0 3 0 97 0 0
6 12.5 12.5 15.7 15.7 15.7 15.7
% select 0 0 28 25 25 23
Simulations: B-Weib-Median, No weeding rule
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
Acc rate
(a, s) (a, t) (s, a) (s, t) (t, a) (t, s)
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
Sims With Weeding Rule (Scenario 5)
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
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