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