**8. Graphical presentation and analysis**

#### **8.1. Scatter plots**

Validation data first should be plotted on a graph that shows the relationship between the test and reference cardiac output readings. The simplest approach is to plot the data on a scatter plot where the x-axis represents the reference readings and the y-axis represents the test readings (Figure 12). The data points should lie within close proximity to the line of identity x=y for there to be good agreement. A regression line can be added. However, correlation is not performed if the aim of the analysis is to assess the agreement between two methods rather than assessing trending ability. This point was highlighted by Bland and Altman when they published their well known method of showing agreement [45].

**Figure 12.** Scatter plot showing test and reference cardiac output (CO) data points. The regression line (solid) crosses y-axis at 1.45 L/min, indicating an offset in calibration between the two methods. A line of identity (dashed) y=x is added. There is good agreement between the test and reference methods because data points lie close to the regres‐ sion line. The correlation coefficient (r) is not provided.

### **8.2. The Bland-Altman plot**

output. A wide range of values of cardiac output readings is also needed. A new parameter called delta cardiac output (∆CO) is calculated for both test and reference data which uses the difference between consecutive readings. Trend analysis is performed on the ∆COs. The data can be collected (a) at random or (b) at predetermined time points. Readings collected at random can lead to uneven data distribution. Thus, a more rigid protocol with data being collected at predetermined time points tends to be used. Commonly 6 to 10 time points are used. A typical protocol for a patient having cardiac surgery might be: (T1) - before anaesthesia, (T2) – after induction, (T3) - after sternotomy, (T4) – after by-pass, (T5) – after closure of the

Validation data first should be plotted on a graph that shows the relationship between the test and reference cardiac output readings. The simplest approach is to plot the data on a scatter plot where the x-axis represents the reference readings and the y-axis represents the test readings (Figure 12). The data points should lie within close proximity to the line of identity x=y for there to be good agreement. A regression line can be added. However, correlation is not performed if the aim of the analysis is to assess the agreement between two methods rather than assessing trending ability. This point was highlighted by Bland and Altman when they

**Figure 12.** Scatter plot showing test and reference cardiac output (CO) data points. The regression line (solid) crosses y-axis at 1.45 L/min, indicating an offset in calibration between the two methods. A line of identity (dashed) y=x is added. There is good agreement between the test and reference methods because data points lie close to the regres‐

chest and (T6-8) - at set times on the intensive care.

**8. Graphical presentation and analysis**

sion line. The correlation coefficient (r) is not provided.

published their well known method of showing agreement [45].

**8.1. Scatter plots**

66 Artery Bypass

The agreement between two measurement techniques, test and reference, is evaluated by cal‐ culating the bias, which is the difference between the each pair of readings, test minus refer‐ ence. In the Bland-Altman plot the bias of each pair of readings (y-axis) is plotted against the average of the two readings (x-axis) (Figure 13). Then, three horizontal lines are added to the plot: (a) The mean bias for all the data points and (b) The two 95% confidence interval lines for the bias (1.96 x standard deviation of the bias) known as the "Limits of Agreement". Sufficient data should also be provided to allow the calculation of percentage error.

**Figure 13.** Bland and Altman plot showing test and reference cardiac output (CO) data points. The mean bias and limits of agreement lines (dashed) have been added to plot. 95% of the data points falls between these limits. The percentage error has been calculated from the mean CO and limits of agreement. Note the slightly skewed distribu‐ tion of the data shown by the sloping regression line (dotted).

#### **8.3. Modifications to the B-A plot**

