1 General Purpose
The usual method for testing the
strength of association between the x-data and y-data in a linear
regression model, although widely applied for validating
quantitative diagnostic tests, is inaccurate. Stricter criteria
have to be applied for validation (For background information check
Statistics applied to clinical studies 5th edition, Chap. 50,
Springer Heidelberg, Germany, from the same authors). A stricter
method to test the association between the new-test-data (the
x-data) and the control-test-data (y-values) is required. First,
from the equation y = a + bx it is tested whether the b-value is
significantly different from 1,000, and the a-value is
significantly different from 0,000.
2 Schematic Overview of Type of Data File
3 Primary Scientific Question
Are the regression coefficient
significantly different from 1,000 and the intercept significantly
different from 0,000. If so, then the new test can not be
validated.
4 Data Example
In a study of 17 patients the
scientific question was: is angiographic volume an accurate method
for demonstrating the real cardiac volume. The first ten patients
of the data file are given underneath. The entire data file in
extras.springer.com, and is entitled
“chapter32validatingquantitative”. Start by opening the data in
SPSS.
|
Cast cardiac volume (ml)
|
Angiographic cardiac volume (ml)
|
|
494,00
|
512,00
|
|
395,00
|
430,00
|
|
516,00
|
520,00
|
|
434,00
|
428,00
|
|
476,00
|
500,00
|
|
557,00
|
600,00
|
|
413,00
|
364,00
|
|
442,00
|
380,00
|
|
650,00
|
658,00
|
|
433,00
|
445,00
|
5 Validating Quantitative Diagnostic Tests
For analysis the statistical model
Linear in the module Regression is required.
Command:
-
Analyze....Regression....Linear....Dependent: cast cardiac volume....Independent (s): angiographic cardiac volume....click OK .
Coefficientsa
|
Model
|
Unstandardized coefficients
|
Standardized coefficients
|
t
|
Sig.
|
||
|---|---|---|---|---|---|---|
|
B
|
Std. error
|
Beta
|
||||
|
1
|
(Constant)
|
39,340
|
38,704
|
1,016
|
,326
|
|
|
VAR0000
|
,917
|
,083
|
,943
|
11,004
|
,000
|
|
Four tables are given, but we will use
the bottom table entitled “coefficients” only.
-
B = regression coefficient = 0,917 ± 0,083 (std error)
-
A = intercept (otherwise called B0 or Constant) = 39,340 ± 38,704 (std error)
95 % confidence intervals of B
-
should not be different from 1,000.
-
=0,917 ± 1,96 × 0,0813
-
= between 0.751 and 1.08.
95 % confidence intervals of A
-
should not be different from 0,000.
-
=39,340 ± 1,96 × 38,704
-
= between −38,068 and 116,748.
Both the confidence intervals of B and
A are adequate for validating this diagnostic test. This diagnostic
test is, thus, accurate.
6 Conclusion
Quantitative diagnostic tests can be
validated using linear regression. If both the regression
coefficient and the intercept are not significantly different from
1,000 and 0,000, then the diagnostic test is valid. Alternative
methods are reviewed in the references given below.
7 Note
More background, theoretical and
mathematical information about validating quantitative diagnostic
test are given in Statistics applied to clinical studies 5th
edition, the Chaps. 50 and 51, Springer Heidelberg Germany, 2012,
from the same authors.