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An update from the JSM 2006 - Seattle

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An update from the JSM 2006 - Seattle

Ryan Woods – January 8, 2007

- Adaptive Designs and Randomizations in clinical trials
- Statistical Methods for studies of Bioequivalence
- Some models for competing risks in cancer research

“Adaptive” has two common meanings in the design of clinical trials literature:

- A trial in which the design changes in some fashion after the study has commenced (e.g. # of interim looks)
- A trial in which the randomization probabilities change throughout the study in some fashion

Review of Sequential Hypothesis Testing:

- We choose a number of interim looks
- Select desired power for study, sample size, overall Type I error rate
- Select a spending function for Type I error that reflects how much “alpha” we want to spend at each look
- The spending function determines our rejection boundaries for test statistics computed at each analysis → example…

- Suppose we choose two interim looks + final analysis
- Sample size of 600 with interim looks at n=200, 400
- Overall Type I error = 0.05
- Want fairly conservative boundaries early, with some alpha left for final analysis…
process looks like…

Reject Ho

At an interim look we may want to:

- Increase in sample size
- Increase number of looks
- Change the shape of the spending function for remaining looks
- Change inclusion criteria
BUT: can we do this without inflating Type I error? Can we estimate the Rx effect at the end?

- If at some look L in a K-look trial, we want to make a design change, we need to consider ε:

- This is referred to as the conditionalrejectionprobability.
- Zj, bj are values of test statistic and boundary at look J.
- Any change to the trial at look L must preserve ε for the modified trial (Muller & Schafer)

Reject Ho

Conditional Rejection Probability at N=400 → 0.255

Reject Ho

Such changes are fine, provided ε=0.255 for modified trial

- These conditional rejection probabilities can be calculated conveniently under various adaptations using EaSt (Cytel Software)
- At present our license expired and we are updating it!
- I promise an example delivered to you when our license is upgraded
…Example to come!!!

Interval Estimation for the treatment difference δ is explained in Mehta’s slides

In summary, the concept is an extension of Jennison and Turnbull’s Repeated Confidence Interval Method from sequential trials (1989)

Mehta adapts this method by applying the results of Muller & Schafer to allow for the adaptive design change

- Designs in which allocation probabilities change over the course of the study
- Why?
1) Ensure more patients receive better treatment

2) Ensure balance between allocations

- Examples include: Play the Winner Rule, Randomized Play the Winner Rule, Drop the Loser rule, Efron’s biased coin design, etc
…more to come on these….

1) Connor (1994, NEJM) report a trial of AZT to reduce rate of mother to child HIV transmission; coin toss randomization used with results:

AZT: 20/239 transmissions

Placebo: 60/238 transmissions

So transmission in control group was 3 times rate in treated group.

2) Bartlett (1985, Pediatrics) report study of ECMO in infants; Play The Winner rule used with results:

ECMO: 0/11 deaths

Control: 1/1 deaths → study stopped

- Follow-up study proceeded with very high death rate in control group (40% versus 3% in ECMO)

- See debate in Statistical Science over this! (Nov.1989, Vol 4, No. 4, p298)

- Simple Play the Winner Rule
- First patient is randomized by a coin toss
- If patient is Rx success, next patient gets same Rx; if Rx failure, next patient gets other Rx (Zelen, 1969)
Pros/Cons:

- Should put more patients on better Rx
- Need current patient’s outcome before next patient allocated
- Not a randomized design

2) Randomized Play the Winner Rule [RPW(Δ,μ,β)]

- Start with an urn with Δ red balls, Δ blue balls inside (one colour per Rx group)
- Patient randomized by taking a ball from urn; ball is then replaced
- When patient outcome is obtained, the urn changes in the following way:
i) If Rx success: we add μ balls of current Rx to urn and β balls of other Rx

ii) If Rx fails: we add β balls of current Rx to urn and μ balls of other Rx

where μ ≥ β ≥ 0

2) RPW(Δ,μ,β) continued…

- Commonly discussed design is RPW(0,1,0) [See Wei and Durham: JASA, 1978]
Pros/Cons:

- Can lead to selection bias issues even in a blinded scenario if investigator enrolls selectively
- Should put more patients on better Rx
- Does not require instantaneous outcome
- Implementation can be difficult
- What about the analysis of such data?

3) Drop the Loser Rule [DL(k)]

- An urn contains K+1 types of balls, 1 for each Rx 1, .., K, plus an “immigration” ball
- Initially, there are Z0,K balls of type K in the urn
- After M draws, the urn composition is equal to ZM = (ZM,0,ZM,1,…, ZM,K)
- To allocate patient, draw a ball; if it is type K, give patient Rx K – ball is not replaced!
- Response is observed on patient; if successful, replace ball in urn (thus ZM= ZM+1). If failure, do not replace ball (thus ZM+1,K= ZM,K-1 for Rx K).
…more…

3) Drop the Loser Rule continued…

- If immigration ball drawn, replace the ball, and add to the urn one of each of the Rx balls
Pros/Cons:

- Can accommodate several Rx groups
- Also should put patients on the better Rx
- Can also be extended to delayed response
- Again, what about analysis of data?
- Implementation is also not easy

- Extensive discussion in the literature about how these various methods for allocation behave in simulation
- Some issues include:
1) how these methods perform when multiple Rx’s exist and variation in efficacy of Rx’s is high

2) how to balance discrimination of efficacy of Rx’s with minimizing number of patients allocated to poorer Rx’s

- Many, many, many generalizations of these methods to improve the “undesirables” of previous incarnations
- Interim analyses versus adaptive randomization

- Re-sampling methods for Adaptive Designs
- Issues associated with non-inferiority and superiority trials and adaptive designs
- Dynamic Rx Allocation and regulatory issues (EMEA’s request for analysis)
- General commentary on risks and benefits of adaptive methods in clinical trials
In general, a very active area right now!

- Also Feifang Hu gave a recent talk at UBC!

I will attempt to cover (briefly):

- Purpose of a bioequivalence study
- Type of data typically collected
- Common methods of data analysis and hypothesis testing/estimation
- Additional comments

- Bioequivalence (BE) studies are performed to demonstrate that different formulations or regimens of drug product are similar in terms of efficacy and safety
- BE Studies are done even when formulations are identical between new and old drugs, but type of delivery differ (capsule vs. tablet); could also be generic versus previously patented drug
- Even small changes to formulation can affect bioavailability/absorption/etc so BE studies can reassure regulators new formulation is good WITHOUT repeating entire drug development program (e.g. several phase III trials with clinical endpoints)

- Typically, BE studies are done as cross-over trials in healthy volunteer subjects
- Each individual will be administered two formulations (Reference and Test) in one of two sequences (e.g. RT and TR)

* Wash-out is period of time where patient takes neither of the formulations

- In Clinical Pharmacology (CP) and BE studies, the central outcomes are pharmacokinetic (PK) summaries
- These PK measures have more to do with what the body does with the drug, than what the drug does to the body
- Many of the outcomes of interest are taken from the drug concentration time curve and include: AUC(0-t), AUC(0-∞), Tmax, Cmax, T1/2
….more to come on these…

CMAX

AUC

TMAX

- FDA defines BE as: “the absence of a significant difference in the rate and extent to which the active ingredient becomes available at site of drug action”
- AUC is taken as the measure of extent of exposure; Cmax as the rate of exposure
- In general, these two outcomes are assumed to be log-normally distributed
- A small increase/decrease of Cmax can result in a safety issue → T and R cannot differ “too much”

- The chosen hypothesis testing procedure by regulatory agencies has been called TOST (two one-sided tests)
- For each PK parameter, we apply a set of two one-sided hypothesis tests to determine if the formulations are bioequivalent
- One of the hypotheses is that the data in the new formulation are “too low” (H01) relative to the reference; another hypothesis is that they are “too high” (H02)
…mathematically we have…

The two tests can be written:

H01: μT - μR≤ -Δ

versus

H11: μT - μR ≥ -Δ

And then…

H02: μT - μR ≥ Δ

versus

H12: μT - μR≤Δ

- The testing parameter Δ was chosen by the FDA to be Δ=log(1.25)
- Both of the two tests are carried out with a 5% level of significance
- Thus, there is a maximum 5% chance of declaring two products bioequivalent when in fact they are not
- TOST has some drawbacks: drugs which small changes in dose → BIG change in clin. response, test limit too narrow for high variability products, doesn’t address individual BE (“Can I safely switch my patient’s formulation?”)

- They suggest modeling data from the two period, two Rx cross-over via a linear mixed model:
- Let Yijk be the (log-transformed) response obtained from Subject k, in period j, in sequence i, taking formulation l
- If we assume no carry-over effects the model resembles:
Yijk= μi + λj + πl + βk + εijkl

where μi, λj, andπlare fixed; βk, εijkl are random

So to estimate πT –πR we are supposed to take:

½ [(Y21-Y22)-(Y11-Y12)] which in expectation is equal to the treatment difference

Yij is the sample mean from the i,j’th cell above

* μparameters could likely be dropped

- Guidelines from the FDA on methodology are very specific in this field (e.g. numerical method for AUC, “goal posts” for determining BE, distributional assumptions, etc)
- Interesting history of how these regulations came about/evolved:
- 75/75 rule (70’s): 75% of subjects’ individual ratios of T to R must be≥ 0.75 to prove BE

- 80/20 rule (80’s): set up H0 such that the two formulations are equal. If the test is NOT rejected, and a difference of 20% not shown, then the formulations are BE

Some mixing of UNIX commands and SAS:

%SYSEXEC %str(mkdir MYNEWDATA; cd MYNEWDATA; mkdir Output; cd ..;);%let value=%sysget(PWD);%put &VALUE;libname data "MYNEWDATA";data data.junk; variable="ONE VARIABLE";run;ods rtf file="MYNEWDATA/Output/file.rtf";proc print; title "&VALUE.";

run;

Competing risks models in the monogenic cancer susceptibility syndromes

Philip S. Rosenberg, Ph.D.

Bingshu E. Chen, Ph.D.

Biostatistics Branch

Division of Cancer Epidemiology and Genetics

National Cancer Institute

7 Aug 2006, JSM 2006 Session #99

Acknowledgements

Monogenic cancer susceptibility syndromes

Fanconi Anemia (FA)

Severe Congenital Neutropenia (SCN)

Hereditary Breast and Ovary Cancer (HBOC)

Cause-specific hazard functions for competing risks

B-Spline

Individualized Risks

Covariates

Cumulative Incidence versus Actuarial Risk

Conclusions

Cancer Syndromes

- Single gene defects predisposes to more than one event type (pleitropy).
- Occurrence of one event type censors or alters the natural history of other event types.
- Heterogeneity.
- Competing risks theory provides a unifying framework.

Breast Cancer

SepsisDeath

HBOC

SCN

MDS/AML

Competing Risks

Fanconi

Anemia (FA)

Severe

Congenital

Neutropenia (SCN)

Hereditary

Breast and Ovary

Cancer (HBOC)

Death

BMT

FA

AML

Death

Solid

Tumor

GENES:FANCA, FANCB FANCC, FANCD1/BRCA2, FANCD2, FANCE, FANCF, FANCG, (FANCI), FANCJ, FANCL, FANCM

ELA2, other genes

BRCA1, BRCA2, other genes

Modeling the Natural History

- Cause-specific hazards:
- Cumulative Incidence
- (In the presence of other causes):
- Actuarial Risk (“Removes” other causes):

B-Spline Models of Cause-Specific Hazards:

Linear combination

- For each cause k separately:

- Knot selection by Akaike Information Criterion (AIC).
- Variance calculations via Bootstrap (because of constraint).

Rosenberg P.S. Biometrics 1995;51:874-887

Fanconi Anemia (n=145)

Natural History

Rosenberg P.S. et al. Blood 2003;101:2136

Same modeling approach identifies

distinct hazard curves.

Severe Congenital Neutropenia (n=374)

Natural History

Rosenberg, P. S. et al. Blood 2006;107:4628-4635

HBOC – BRCA1 (n=98)

Natural History

Individualized Risks

- Covariates:
- A covariate may affect one endpoint or multiple endpoints.
- (Different endpoints may be affected by different covariates.)

- Analysis:
- Cox regression models for each endpoint.
- Define a summary categorical risk variable.
- Estimate hazards and Cumulative Incidence for each level.

Covariate: No Congenital Abnormalities

Covariate: Specific Congenital Abnormalities

- Abnormalities are associated only with hazard of BMF.
- BMF curve goes up, other curves go down.

Rosenberg, P. S. et al. Blood 2004;104:350-355

Years on Rx

Years on Rx

Covariate: Low Response

Covariate: Good Response

SCN: Impact of Hypo-Responsiveness to Rx

- Low Response is associated with hazard of both endpoints.
- Both curves go up or down together.

Rosenberg, P. S. et al. Blood 2006;107:4628-4635

Actuarial Risk vs.

Cumulative Incidence

- Actuarial Risk:
- “Removes” other causes.
- Estimate using 1 – KM curve.

- Impact of each cause in real-world setting.
- Estimate using
- non-parametric MLE or
- spline-smoothed hazards.

Example: Fanconi Anemia

1-KM vs. Cumulative Incidence

- If you removed other causes, risk of Solid Tumor by age 50 would increase from ~25% to ~75%.

Rosenberg, P. S. et al. Blood 2003;101:822-826

Extrapolating 1 – KM: A Cautionary Tale

**Kramer, J. L. et al. JCO 2005; 23: 8629-8635

Conclusions

- B-spline models of cause-specific hazards elucidate the natural history.
- Physicians understand Cumulative Incidence (our experience).
- Stand-alone software will be available from us.
- Much room for methodological refinements.