Transcript An update from the JSM 2006

An update from the JSM 2006 - Seattle
Ryan Woods – January 8, 2007
Topics for this presentation…
• Adaptive Designs and
Randomizations in clinical trials
• Statistical Methods for studies of
Bioequivalence
• Some models for competing risks
in cancer research
Part 1: Adaptive Designs in Clinical Trials…
“Adaptive” has two common meanings
in the design of clinical trials literature:
1) A trial in which the design changes in
some fashion after the study has
commenced (e.g. # of interim looks)
2) A trial in which the randomization
probabilities change throughout the
study in some fashion
Case 1: Change in Trial Design…
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…
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…
Three-look Sequential Boundary for Rejection of Ho
3.5
Standardized Test Statistic
3.0
Reject Ho
2.5
2.0
1.5
1.0
0.5
0.0
0
200
400
C umulativ e Sample Siz e
600
What if we want to make a change?
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?
We Want Change!
• 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 conditional rejection
probability.
•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)
Three-look Sequential Boundary for Rejection of Ho
3.5
Original D es ign Boundaries
Ac c umulated D ata
Standardized Test Statistic
3.0
Reject Ho
2.5
2.0
1.5
1.0
0.5
Conditional
Rejection
Probability atat
N=400
= 0.255
Conditional
Rejection
Probability
N=400
→ 0.255
0.0
0
200
400
C umulativ e Sample Siz e
600
Modified Design to Four-look Larger Study (N=800)
Original D es ign Boundaries
Ac c umulated D ata
Modified Study Boundaries
4.0
Standardized Test Statistic
3.5
3.0
Reject Ho
2.5
2.0
1.5
1.0
0.5
Such changes are fine, provided ε=0.255 for modified trial
0.0
0
200
400
C umulativ e Sample Siz e
600
800
How to calculate these ε’s?
• 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!!!
What about Estimation?
• 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
Case 2: Adaptive Randomizations
• 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….
Some serious examples…
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.
Some serious examples…
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)
Some allocation methods…
1) 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
Some allocation methods…
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
Some allocation methods…
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?
Some allocation methods…
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…
-
Some allocation methods…
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
For all of these methods…
•
•
•
•
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
At the JSM some talks included…
•
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!
Bioequivalence Studies
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
What is bioequivalence?
•
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)
Typical Study Design
•
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)
Sequence
Rx 1 Wash-out
Rx 2 # subjects
1 (RT)
R
---
T
n/2
2 (TR)
T
---
R
n/2
* Wash-out is period of time where patient takes neither of the formulations
Typical Outcomes
•
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…
Plasma Concentration (mg/L) versus T ime (hours)
CMAX
100
Drug Concentration - mg/L
80
60
40
AUC
20
TMAX
0
0
12
24
Time (hours )
36
44
More on these outcomes…
•
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”
Testing what is ”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…
Testing what is ”too much”…
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
Testing what is ”too much”…
•
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?”)
Models for the outcomes…
•
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, and πl are fixed; βk, εijkl are random
Models for the outcomes…
Group
Period 1
Period 2
1 (RT)
μ1 + λ1 + πR
μ1 + λ2 + πT
2 (TR)
μ2 + λ1 + πT
μ2 + λ2 + πR
* μ parameters could likely be dropped
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
Some general comments…
•
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
SAS tricks!!!
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
Statistics
Bingshu E Chen
SCN
David C Dale
Blanche P Alter
Severe Chronic
Neutropenia International
Registry
FA
Blanche P Alter
Wolfram Ebell
Eliane Gluckman
Gerard Socié
HBOC
Mark H Greene
Joan L Kramer
Outline
I.
Monogenic cancer susceptibility syndromes
a)
b)
c)
Fanconi Anemia (FA)
Severe Congenital Neutropenia (SCN)
Hereditary Breast and Ovary Cancer (HBOC)
II. Cause-specific hazard functions for
competing risks
•
B-Spline
III. Individualized Risks
•
Covariates
IV. Cumulative Incidence versus Actuarial Risk
V. 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.
Competing Risks
Fanconi
Anemia (FA)
Severe
Congenital
Neutropenia (SCN)
Hereditary
Breast and Ovary
Cancer (HBOC)
Death
Sepsis
Death
BMT
SCN
FA
AML
Breast
Cancer
HBOC
MDS/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:
1
hk (t )  lim 0 P T  [t , t  ) & K  k | T  t  , k  1,

,K
•Cumulative Incidence
(In the presence of other causes):
 a K

Fk (t )   hk (a)exp    hk (s)ds  da, k  1,
0
 0 k1

t
,K
•Actuarial Risk (“Removes” other causes):
FA,k (t )  1  exp
  h (s)ds  , k  1,
t
0
k
,K
B-Spline Basis Function
B-Spline Models of Cause-Specific Hazards:
1
0.75
Linear combination
0.5
0.25
0
0
10
20
30
t
40
50
hk (t ) 
mk

j  ORDER1
B j ,k (t ) j ,k , j ,k  0
•For each cause k separately:
X ik  min Yik , Cik  

 i  1,
 ik  I Yik  Cik  
xik


( k )    ik log h( xik )   hk ( s)ds 
i 1 

T0

n
,n
•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.
FA: Impact of Congenital Abnormalities
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
SCN: Impact of Hypo-Responsiveness to Rx
Covariate: Low
Response
Years on Rx
Covariate: Good
Response
Years on Rx
Rosenberg, P. S. et al. Blood 2006;107:4628-4635
•Low
Response is
associated with
hazard of both
endpoints.
•Both curves
go up or down
together.
Actuarial Risk vs.
Cumulative Incidence
•Actuarial Risk: F
A ,k
(t )  1  exp
  h (s)ds  , k  1,
t
0
k
,K
•“Removes” other causes.
•Estimate using 1 – KM curve.
•Cumulative Incidence:
 a K

Fk (t )   hk (a)exp    hk (s)ds  da, k  1,
0
 0 k1

t
,K
•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
Disease
Intervention
HBOC
Oophorectomy
BRCA1** to reduce risk
of Ovary
Cancer
1-KM
Prediction
Result of
Intervention
Moderate
Risk of Breast
increase in
Cancer declines
Cumulative
by 2.6-fold
Incidence of
Breast Cancer
**Kramer, J. L. et al. JCO 2005; 23: 8629-8635
Observed
Cumulative
Incidence
Much lower
than
expected.
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.
 [email protected]
•Much room for methodological refinements.