# Which hypothesis test to use to compare two lab tests?

#### sbpatel2009

##### New Member
I am a clinical lab director and need to compare two laboratory tests (Test A and Test B) to determine which one should be adopted by our laboratory. The gold standard test Test GS is tedious, time consuming, and expensive. Test A has been used as an alternative to the gold standard test because it is easier to perform, faster, and less expensive; although Test A is known not to be as accurate as Test GS. Test B is a newer test, and I need to compare its performance to Test A. To do this, 10 well-characterized samples with known results with Test GS were analyzed with Test A and Test B. The results are below:

Test GS = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Test A = 1.127922, 1.983795, 2.919603, 4.023458, 5.033923, 6.009637, 6.934596, 7.899715, 8.985030, 9.944403
Test B = 0.9491933, 1.9497254, 3.0806463, 4.1148046, 5.0162391, 6.0465623, 7.1581668, 7.9162072, 8.9367203, 10.0911837

I want to test whether Test B is "no worse than" Test A (i.e., non-inferiority hypothesis testing). How can I pose this question in a statistical framework and what are the appropriate statistical tests?

Thanks

#### Miner

##### TS Contributor
There are several options. You can use a Bland-Altman plot, a gauge linearity and bias study, and a paired equivalence test.

Attached are examples of each. NOTE: On the equivalence test, you have to define equivalence limits. These are the limits at which there is no practical difference between the tests. I arbitrarily added these limits in order to run the test.

#### sbpatel2009

##### New Member
Thank you! This is tremendously useful.

#### sbpatel2009

##### New Member
There are several options. You can use a Bland-Altman plot, a gauge linearity and bias study, and a paired equivalence test.

Attached are examples of each. NOTE: On the equivalence test, you have to define equivalence limits. These are the limits at which there is no practical difference between the tests. I arbitrarily added these limits in order to run the test.

View attachment 2815 View attachment 2816
I realized that these tests compare Test A and Test B with Test GS, but they do not show that the accuracy of Test A is noninferior to Test B. I was wondering if I can use a paired t-test for non-inferiority to compare the means of the absolute values of the differences between Test A vs. Test GS and Test B vs. Test GS. For noninferiority, I would just need to set the LEL to -0.1. Am I thinking about this correctly?

#### Miner

##### TS Contributor
Here are the A vs. B comparisons. Again, the equivalence limits were arbitrarily chosen by me. You need to decide what these should be.