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"It has long been an axiom of mine that the little things are infinitely the most important" (Sherlock Holmes)

 

 

Validating measurement data Calibration and the Bland-Altman approach

Bland-Altman plot  Validating a proxy measure 

1.  Bland-Altman plot

Worked example

Blood pressure by two methods
(mm Hg)
Method 1 Method 2 Method 1 Method 2
85
82
87
88
90
95
97
101
103
115
89
97
93
101
105
105
117
106
120
130
120
122
131
134
140
156
162
170
190
201
132
129
141
149
145
171
182
179
195
221

These are data from a study on blood pressure of dogs using two methods of measurement. The first of these (method 1) is the current accepted standard, but is an invasive procedure which carries risks. The second method is a new technique which must be validated against the current standard.

As before, the first step is to plot the practical variable (method 2) against the criterion variable (method 1). In this case the variability does not increase with the mean so no transformation is required. The line of equality is drawn in.

You can see from the graph below that results from the two methods are closely correlated, but method 2 always gives a somewhat higher reading than method 1.

{Fig. 3}
U02bla3.gif

This bias is quantified by plotting for each pair of observations the difference between the two methods against the mean of the two methods, as shown in the second graph above. The mean bias is +11.9 mm Hg - in other words on average method 2 gives a reading 11.9 mm Hg greater than method 1.

The 'limits of agreement' are estimated by multiplying the standard deviation of the differences (5.39) by 1.96 which gives 10.6. Hence the lower and upper limits of agreement are 1.3 and 22.5. Providing the differences are normally distributed, and randomly obtained, on average these limits would include 95% of observations.

 

 

2.   Validating a proxy measure

Worked example

Numbers trapped from populations of known size
Popn. size No. trapped Popn. size No. trapped
12
12
12
12
12
35
35
35
35
35
56
56
56
3
5
3
4
3
8
10
6
9
7
14
18
9
56
56
79
79
79
79
79
98
98
98
98
98
 
12
11
25
15
14
20
22
25
32
17
19
23
 

These are data from a study seeking to validate relative population estimates of a small mammal (field mouse) against absolute population size. Live traps are used to sample the mice in artificially established populations of known size.

The first step is to plot the practical variable (numbers trapped) against the criterion variable (population size). The figure below shows clearly that variability increases with mean so each variable is log transformed. The effect of this is shown in the second figure.

{Fig. 2}
U02cat3.gif

A regression line is then fitted to the data using the standard methods (see pop-up on graph). If you wish to estimate population size from the trap catch, you would then obtain the calibration equation by rearranging the regression equation, namely:

Population size = [0.44 trap catch] / 0.891

Obtaining a confidence interval for the estimated population size is slightly problematic since one is using the equation to estimate X from Y rather than vice versa. However, we provide a method to do this in Unit 12