Transcript Slides file
All-or-None procedure: An
outline
Nanayaw Gyadu -Ankama
Shoubhik Mondal
Steven Cheng
Summary
History of All or None procedure
Min test
Test by Cappizi and Zhang
Min test based on Restricted Null Space
Average Type I Error Approach
Discussion
References
Why All or None Procedure
All or none method was evolved in 1982 in context of
Quality control by Berger(1982) to test quality of a
product based on several parameters.
He compared producer’s and consumer’s risk.
Disease like migraine, Alzheimer’s disease and
Arthritis are characterized by more than one
endpoints.
• The primary objective of a clinical trial is met if the
test drug shows a significant effect with respect to all
the endpoints.
Two types of Multiplicity
• First case is to when treatment is effective if it
improves at least one of the multiple endpoints
• The second case is to when treatment is effective
when it improves on all the multiple endpoints .
• Multiple primary endpoints in second case is called
co-primary endpoints where simultaneous
improvement is required to declare a treatment
effective
Example of co-primary endpoints
General Sense
formulation of the multiple endpoint problem
pertains to the requirement that the treatment be
effective on all endpoints
This problem is referred to as the reverse
multiplicity problem represents the most stringent
inferential goal for multiple endpoints.
IU framework, the global hypothesis is defined as the
union of hypotheses
To reject null hypothesis, one needs to show that all
individual hypotheses are false
Formulation of IU test
Min Test
the goal of demonstrating the efficacy of the
treatment on all endpoints requires an all-or-none
or IU procedure of the union of individual
hypotheses
Reject all hypotheses if tmin= min 1≤i≤m
ti ≥ tα(ν), where tα(ν) is the (1 − α)-quantile of the tdistribution with ν = n1 + n2 − 2 df
This procedure is popularly known as the min test
(Laska and Meisner)
We take α = 0.025 for one sided
Min test Contd.
Advantage:
this procedure does not use a multiplicity adjustment
(each hypothesis Hi is tested at level α
Disadvantage:
Min test is not as powerful as it looks
Maximum power occurs when no treatment effect at
one-point and infinite treatment effects at other
points.
This leads to marginal t-test
Power Comparison of Min Test
Power Comparison of Min Test
Power of the min test is always less than the power of
individual test
When endpoints are highly correlated the power is
almost same because all the endpoints be merged to
one endpoints
When endpoints are independent then the overall
power is product of individual power
As correlation between endpoints increases, power
increases for min test when power for individual test
is fixed
Sample Size Increment For Min Tesr
there are three co-primary
end-points and correlation
among the test statistics is
0.2 the overall power for
detecting size corresponding
to an 80%power at the
individual subhypothesis
level is only 55%
Increase with the number of
co-prmary endpoint and the
decrease in correlatiom
Test by Cappizi and Zhang
Cappizi and Zhang (1996) suggested another alternative to
the min test which requires that the treatment be shown
effective at a more stringent significance level α1 on say m1
< m endpoints and at a less stringent significance level α2 >
α1 on the remaining m2=m-m1
For m=2, m1=1, m2=1, they take α1=0.05, α2= 0.1 or 0.2
They did not consider the null space for no treatment
effect on at least one endpoint
This rule does not control the experimentwise type I error
Restrict Null Space
Chuang-Stein et al. (2007) propose to take a
restricted null space.
Considering type I error between(0,0) (M,0) and
(0,M).
Adjusted significance level is minimal
Still not much gain in terms of power
Restrict the null space
Adjusted significance level
Average Type I Error Approach
Another approach to this formulation adopts a
modified definition of the error rate to improve the
power of the min test in clinical trials with several
endpoints.
Instead of looking at the maximum false positive rate
over a restricted null space, Chuang et al. proposes to
look at the “Average” false positive Rate over that
space
They find an upper bound of this Average False
positive Rate.
Average Type I Error
Formula of Average Type I Error
Adjusted significance level
Sample size increment
Discussion
Here assumption is that all points in restricted null space
are equally likely.
Have to use higher significance level to manage the lower
overall significance level.
The level of significance is a function of number of coprimary endpoints and the correlation among the
endpoints.
If the endpoints are highly correlated the level of
significance will be very close to 2.5%, because high
correlation essentially reduces multiple primary endpoints
to a single endpoint.
Discussion
The sample size needed to maintain a desirable
power under the new approach is much smaller than
IU test.
Assumption of equally likely is not realistic always.
This work is still not scientifically justifiable.
Refrences
1) Roger L. Berger(1982), Multiparametr Hypothesis Testing
and Acceptance Sampling., Tech-nometrices.
2) Offen et al.(2007), Multiple Co-primary Endpoints:
Medical and Statistical Solutions., Drug Information
Journal.
3)Eugene M Laska and Morris J. Meisner(1989), Testing
Whether an Identied Treatment Is Best., Biometrics.
4)Chuang et al.(2007), Challenge of multiple co-primary
endpoints: A new approach.,Statistics in Medicine.