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.