GROUP SEQUENTIAL SAMPLE SIZE: DOES STOPPING EARLY REQUIRE COMPROMISING SAFETY? Zmira Silman

GROUP SEQUENTIAL SAMPLE SIZE:
DOES STOPPING EARLY REQUIRE
COMPROMISING SAFETY?
Zmira Silman1 and Diklah Geva2
1 Industry
Consultnt, Netanya, 2 IntegriStat, TelAviv, Israel
EMR 2007
1
Introduction
Stopping the trial early, either due to efficacy or
futility, is the purpose of Group Sequential
designs, whilst still fully controlling the prespecified type I error.
These designs are usually employed to test a
single efficacy endpoint1.
A concern is raised as to the safety and
tolerability of a product when the clinical trial was
concluded early2.
2
Aim
We propose an approach for integrating the two
endpoints Efficacy and Safety for the group
sequential study design.
3
Application-Field Example
A study aiming to compare Novel and Standard
Acne treatment in a population of youngsters.
The standard treatment is efficient but has low
tolerability.
The novel treatment is expected to have similar
therapeutic effect but will be more tolerable.
4
Application-Field Example
The study endpoints are:
Efficacy (E): Percent of reduction in Acne lesions
compared to baseline (Average µ)
Safety (S): Incidence of side effects (Proportion π )
A sequential design was considered in order to
obtain an early stop if striking results are achieved.
Definitions:
TN-Novel Treatment
Ts-Standard Treatment
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Hypotheses
The two hypotheses will be tested with an
overall significance level of α=0.05 and 80%
power. Each hypothesis; HE and HS will be
tested with α=0.025.
1. HE : TN is not inferior TS wrt Efficacy.
2. HS: TN is superior to TS wrt Safety.
Formally these translates to:
1. HE: µ T - µ T ≤-δ (δ - non-inferiority margin)
N
S
2. HS: π T –πT >0
N
S
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Methods
Group sequential design was applied to obtain test
boundaries using O’Brien & Fleming’s method with
k=4 stops and α=0.025.
Efficacy and Safety boundaries were plotted in two
panels, along with the corresponding sample sizes.
The boundaries and sample size were calculated for
the pre-specified clinically meaningful effect size.
The upper boundaries represent the efficacy/safety
α-spending criteria
The lower boundaries represent the futility criteria
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Panel 1: Efficacy Boundaries
Efficacy Boundaries and Sample Size
Test Statistic
5.0
Efficacy
Futility
54
4.0
109
3.0
2.0
163
218
1.0
0.0
40
70
100 130 160 190 220
Overall Number of patients
250
280
310
O’Brien & Fleming’s design, with
k=4 stops, α=0.025, ∆=0.3, σ=1,δ= -0.1
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Panel 2: Safety Boundaries
Saftey Bounaries and Sample Size
5.0
Safety
Futility
77
4.0
3.0
154
2.0
231
308
1.0
0.0
40
70
100
130 160 190 220 250
Overall Number of patients
280
310
O’Brien & Fleming’s design, with
k=4 stops,
α=0.025, π1=0.15 and π 2=0.05
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How to decide on an early stop?
Rule:
Early stop will occur only when the boundaries are
crossed for the two panels simultaneously.
Problem:
How to apply the rule as the two panels call for
different sample size on the pre-specified time point.
Solution:
We propose to fix the boundaries with the larger-n,
i.e. safety panel and to extrapolate boundaries of the
lower-n, i.e. Efficacy panel. Such extrapolation can
follow the given boundary also called the α spending curve.
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Calculation procedure
Obtain the number of subjects at each k. (k=4)
Find the α-spending boundary function (power
function)
Re-calculate the lower-n boundaries by
extrapolating the larger-n on the α-spending
boundary
Draw an integrated boundaries graphs.
Decide to stop early if E and S boundaries are
crossed.
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Re-Calculation of efficacy boundaries
Test Statistic
Efficacy Boundaries Extrapulated at Safety S-Sizes
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
54
Safety
Futility
y = 29.32x-0.5
(77)
109
163
218
(308)
40
70
100
130
160
190
220
250
280
310
Overall Number of patients
Adjusted boundaries based on the power function (O’brien & Fleming)
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Integrated boundaries for Safety & efficacy
Safety
Efficacy
Futility
OBS-S
OBS-E
Intigrated Saftey& Efficacy Boundariesl
Test Statistic
5.0
4.0
77
154
3.0
231
2.0
308
1.0
0.0
40
70
100
130
160
190
220
250
280
310
Overall Number of patients
Stooping
Time
K1
K2
K3
K4
N
Boundaries
Observed Statistic
Efficacy Safety Safety EfficacyFutility OBS-S
OBS-E
54
77
4.0
3.3
0
2.78
2.5
109
154
2.8
2.4
0
2.87
2.55
163
231
2.3
1.9
0
2.95
2.65
218
308
2.0
1.7
1.99
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Discussion
We present here a method to simultaneously monitor
efficacy and safety, in a group sequential design of
clinical trial.
This is a simple method may lead to an early stop without
compromising safety information on one hand or inflating
the efficacy information on the other hand.
This method provides a combined interim test for both
efficacy & safety even though the initial evaluation
indicated different group sizes for each outcome.
We used the O’Brien & Fleming’s method here, however
other methods to calculate boundaries can also benefit
from this procedure.
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References
1.
Chow S. C., Shao J., Wang H.: Sample Size
Calculations in Clinical Research. CRC Press of
Taylor & Francis Group 2003, Chapter 8.
2.
EMEA: Reflection paper on methodological issues
in confirmatory clinical trials with flexible design
and analysis plan, CHMP/EWP2459/02, London
March 2003.
3.
The ADDPLAN software, www.addplan.com
Zmira E-Mail: zmiras@gmail.com
Diklah E-Mail: diklah.geva@gmail.com
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