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Two-Stage Treatment Strategies Based On Sequential Failure Times

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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

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

- Entry Criteria: Patients withMetastatic 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

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”

Frontline

Salvage

Strategy

A B C

- B= (A, B)
- C= (A, C)
- A= (B, A)
- C= (B, C)
- A = (C, A)
- B= (C, B)

- 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 q1 = q2 = q3 each Ej is selected with probability .33

(not .05 or some smaller value)

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

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

Example : If k=3, n=3 with “switch-away” within patient rule, and N=240

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

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

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)

Because disease is evaluated repeatedly (MRI, PET),either T1 or T1 + T2may 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)

Delay before start of 2nd stage rx

Discontinuation

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

Weib(a,x) = Weibull distribution with meanm(a,x) = ea G(1+e-x), for real-valued a and x

[ T1 | A ] ~ Weib(aA,xA)

[ T2,1 | A,B, T1] ~ Exp{ gA+bA log(T1) }

[ T2,2 | A,B, T1] ~ Weib( gA,B+bA log(T1), xA,B)

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

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

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

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

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.

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

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) < m(best) – 3 mos | data} > .90

Applying the Weeding Rule when 120 patients have been fully evaluated

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,B’s are exchangeable across the 6 strategies, so they have the same 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

var{exp(aA)} = var{exp(xA)} = var{exp(xA,B)} = 100

Assuming Pr(Disc. During delay period) = .02

E(mA,B) = 7.0 mos & sd(mA,B) = 12.9

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

In terms of the probabilities of correctly selecting superior strategies,

F-Weib-MLE ~ B-Weib-Median

>

B-Weib-Mean

>>

F-Exp-MLE

Sims With Weeding Rule

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

Sims With Weeding Rule(Scenario 5)

Distinguish betweendrop-out and other types of discontinuation and conduct “Informative Drop-Out” analysis

Account forpatient heterogeneity

Correct forselection biaswhen computing final estimates

Accommodatemore than two stages