3. 1 General characteristics of the population
In total, we studied 191 patients with a male predominance (68%). The sex ratio (M / F) was 2.13 (130 men and 61 women). The mean age was 68 ± 13 years (21–91 years). Table 1 summarizes the characteristics of the population studied.
Table 1. Characteristics of study population (N = 191)
Abreviations : MM, Manual Measurement ; EM, Echographic Measurement ; mm, milimeter
The means of preoperative echocardiographic (EM) measurements (Fig.
1) and manual intraoperative (MM) measurements (Fig.
2) of the mitral chordae were 23 ± 2.5 millimeters and 24 ± 2.4 millimeters respectively.
3. 2 Normality for manual measurement and echocardiographic measurement
We calculated the parameters (mean, standard deviation) of the variable MM and the variable EM (table 1).
The normality of the quantitative variables MM and EM was verified by the tests of Shapiro-Wilk, Kolmogorov-Smirnov, Cramer-Von Mises and Anderson-Darling. The quantitative results which are detailed in Table 2 revealed perfect normality (p-value > 0.05) for each of the tests which therefore allowed acceptance of the null hypothesis H0 and rejection of the alternative hypothesis H1.
Their spread around the central value was checked by the asymmetry coefficient (Skewness → SMM: 0.33; SME: 0.08) and the flattening coefficient (Kurtosis → KMM: 0.61; KME: 0, 17) (Fig. 3, Fig. 4).
3. 3 Correlation between echocardiographic measurement and manual measurement
We then verified and studied the statistical significance by a correlation with the Pearson correlation coefficient (r). For this, we posed the hypothesis H0 which signifies an independence (the inexistence of relation, H0: │r│ = 0) against the alternative hypothesis H1 signifying a dependence between the two variables echographic measurement and manual measurement of the mitral cords (H1: │r│ ≠ 0), we set a probability of 0.05 as risk of error for the rejection of H0.
We looked for the absolute value of the Pearson correlation coefficient r (MM, EM) in the corresponding table of the correlation coefficient which corresponds to 0.1946 for N > 100 and α: 0.05. (See the table of correlation coefficient in the annex).
We calculated the theoretical value of the correlation coefficient r which is 0.897. We thus rejected H0 and retained H1 because r-critical (0.1946) is less than r-calculated (0.897 with p < 10⁻⁴) (Table 3).
|
Table 3. Pearson Correlation Statistics (r)
|
|
Variable
|
With variable
|
N
|
Sampling correlation
|
Confidence interval (95%)
|
p-Value
|
|
EM
|
MM
|
191
|
0.897
|
0.865
|
0.921
|
0.0000
|
We have shown that the correlation coefficient is statistically significant because the calculated r is much higher than the critical r with a risk α: 0.05 and with degrees of freedom N-2 (191 inclusions-2: 189).
We therefore highlighted a strong positive relationship between echocardiographic measurements and manual measurements of the mitral cord. The coefficient of determination r² is 0.805 (Fig. 5).
3. 4 Simple linear regression
We therefore proceeded to analyze a simple linear regression in order to model the relationship between our two variables (MM and EM).
The relationship between the two variables is linear (the point cloud is best summarized by a line of equation Y = aX + b). The application condition is verified, it is therefore possible to use the correlation coefficient and the simple linear regression to quantify the link between the 2 variables (EM as dependent variable and MM independent variable).
Graphical analysis shows that the residues visually follow a normal distribution (Fig. 6). Errors are therefore distributed normally. The coefficient of determination R² which measures the percentage of variability in ultrasound values according to manual values is 80.5%, so the model seems adequate.
The adjustment curve of the dependent variable (EM) compared to the independent variable (MM) clearly shows good positive linearity (Fig. 7).
The results of the linear regression lead us to the following mathematical model:
Y = aX + b → Y = 0.87 ∙ X + 4
Where Y is the dependent variable: echocardiographic measurement (EM) to predict; X is the independent variable: manual measurement (MM) as a predictor variable; a is the slope of the regression line and b is the intercept.
This model gave an equation by the regression line with a better fit which is as follows : EM = 0.87 ∙ MM + 4.
The EM model = 0.87 ∙ MM + 4, allows us to predict, for example, that for a manual measurement of a 20 mm chordae, the estimated echocardiographic measurement would be 21.4 mm, which is a significant correction for good surgical repair of the mitral valve.