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# Four Types of Test Hypotheses

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## Yip Terry

on 9 July 2013

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#### Transcript of Four Types of Test Hypotheses

Non-inferiority/superiority
Stated in the alternative hypothesis.
The opposite is stated in the null hypothesis.

That is we expect to the test drug to be not inferior/superior to the control. We put what we expect in the alternative hypothesis.
For Testing Equality,
Equality is stated in null hypothesis
It is what we want to reject
Expect to have difference between two treatments, as stated in the alternative hypothesis
By convention, we call this as testing equality but not testing difference
Non-inferiority corresponds to the inequality suggested in alternative hypothesis.
Hypothesis: H : H :

Four Types of Test Hypotheses
Testing Equality
Assume larger value of T indicates better performance.
Null hypothesis states that the sample value equals the targeted value.
Alternative hypothesis is the sample value is not equal to the targeted value in either direction.
Testing Equality
In two samples cases, testing equality is testing whether the values from 2 samples equal or not
Equality
Definition
Testing Non-inferiority
Non-inferiority
It means
a treatment at least not appreciably worse than an active control/placebo by the non-inferiority margin δ
.

That means the new treatment does not perform poorer than the active control/placebo appreciably.
Definition
Assume the values to the right of zero correspond to a better response with the new drug
The values to the left indicate that the control is better,
Testing Superiority
Superiority means
a treatment is more effective than the active control by the superiority margin δ, stated in the alternative hypothesis
.

Hypothesis: H : H :
Non-inferiority vs. Superiority
Same setting of H and H
With different signs in margin

Assume that larger value of T represents better performance,
For -δ, H means that test drug is inferior to the control. H is the non-inferiority of the test drug.
For δ, H means test drug is not superior to control. H is the superiority of the test drug.

Confusion
In testing inferiority/superiority, the statement of inferiority/superiority is stated in alternative hypothesis.
But in testing equality, the statement of equality is stated in null hypothesis.
Sample size determination
For a superiority trial (S), the necessary sample size (N) depends on δ , the clinically important difference.

For a non-inferiority trial (NI), the necessary sample size depends on δ , the upper bound for non-inferiority.
Confusion
Confusion
E.g. In a test of superiority, to examine the effect of a test drug,
H is the response of test drug is less than that of placebo by δ.
H is the response of test drug is greater than that of placebo.

The test helps us to see whether the test drug is superior to the placebo by an amount of δ.
Introduction
Four Types of Test Hypotheses
Testing Equality
Testing Non-inferiority
Testing Superiority
Testing Equivalence
Recall
Null hypothesis
a general or default position that we want to disprove or reject

Alternative hypothesis
the position opposite to the null hypothesis that new belief is suggested
Recall
Hypothesis test check whether the evidence is significant or not to reject the null hypothesis (the original belief) and establish a new belief (the alternative hypothesis).

Tests for the equality of a sample value with a targeted constant value
Or
Tests for the equality between treatment and active control/placebo.
E.g.
E.g.
where δ>0 is the non-inferiority margin, superiority margin or equivalence margin
T: Treatment
C: Control

0
a
0
0
a
a
NI
Testing Equivalence
It refers to the difference of treatment and active control is within specific amount (δ) in either direction (positive or negative)

Hypothesis: H : H :
Equivalence
Equality and equivalence are two different concepts.
Equality only focuses on whether the values are equal or not.

Equivalence means the difference of treatment and active control is within specific amount (δ) in either direction (positive or negative)
Testing Equivalence
Note that the statement of equivalence is stated in the alternative hypothesis:
Testing Equivalence
This test aims at proving the treatment and control are equivalence, therefore this new belief is put in the alternative hypothesis.

Null hypothesis states that the difference is at least δ.
Alternative hypothesis states that the difference is less than δ, i.e. equivalence.
where δ > 0 is the margin of clinically accepted difference, called equivalence margin
where δ>0 is the non-inferiority margin
where δ>0 is the superiority margin
0
a
0
a
0
a
Testing Equivalence
In two sample cases, testing equivalence compares the values from two samples,
i.e.

a
Non-inferiority & Superiority
In two sample cases, testing non-inferiority/superiority compares the values from two samples, i.e.
Non-inferiority:
Superiority:

where δ > 0 is equivalence margin
where δ > 0 is equivalence margin
S
These are the four test hypotheses
Reference:
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2701110/
http://www.nyuhjdbulletin.org/mod/bulletin/v66n2/docs/v66n2_16.pdf
http://www.scielo.br/scielo.php?pid=S1677-54492010000300009&script=sci_arttext&tlng=en
Confusion
Reference: www.infocusmagazine.org
Reference: thismanskitchen.wordpress.com
0
Reference: pages.pomona.edu
where δ > 0 is equivalence margin
Full transcript