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

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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

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


Two stage treatment strategies based on sequential failure times

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

A Metastatic Renal Cancer Trial

  • 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


A within patient two stage treatment assignment algorithm dynamic treatment regime

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”


Two stage treatment strategies based on sequential failure times

Frontline

Salvage

Strategy

A B C

  • B= (A, B)

    • C= (A, C)

    • A= (B, A)

    • C= (B, C)

    • A = (C, A)

    • B= (C, B)


Selection trials screening new treatments

Selection Trials: Screening New Treatments

- 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)


Goal of the renal cancer trial

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


Higher mathematics

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


Higher mathematics1

Higher Mathematics

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


Outcomes

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


Outcomes1

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

Unavoidable Complications

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)


Two stage treatment strategies based on sequential failure times

Delay before start of 2nd stage rx

Discontinuation

Start of stage 2 rx


Two stage treatment strategies based on sequential failure times

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

A Simple Parametric Model

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)


Mean overall failure time

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


Criteria for choosing a best strategy

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


A tale of four designs

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 designs1

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 designs2

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 designs3

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 designs4

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) < m(best) – 3 mos | data} > .90


A tale of four designs5

A Tale of Four Designs

Applying the Weeding Rule when 120 patients have been fully evaluated 


Establishing priors

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


Establishing priors1

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

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


Computer simulations

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


Simulations no weeding rule

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

Simulations: B-Weib-Median,No weeding rule


Simulations b weib median no weeding rule1

Simulations: B-Weib-Median,No weeding rule


Two stage treatment strategies based on sequential failure times

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


Two stage treatment strategies based on sequential failure times

Sims With Weeding Rule(Scenario 5)


Future research extensions

Future Research / Extensions

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


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