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