Applicability of supervised discriminant analysis models to analyze astigmatism clinical trial data

Figures & data

Table 1 Main ophthalmologic measures of treatment are compared for the three treatment modalities

Group	Mean (CI)	SD (CI)	Mean (IOS)	SD (IOS)	Mean (DV)	SD (DV)
Cross-cylinder	1.17	0.53	0.46	0.43	0.77	0.53
Single	1.21	0.85	0.56	0.78	0.60	0.37
Wavefront	1.28	5.35	0.39	0.74	0.50	0.33

Abbreviations: CI, correction index; DV, difference vector; IOS, index of success; SD, standard deviation.

Figure 1 Hottelling’s T-squared range plot of the partial least squares regression discriminant analysis model to separate three types of astigmatism treatments.

Abbreviation: PLS-DA, partial least squares discriminant analysis; T2crit, T2 critical limit.

Figure 2 Scores scatter plot for partial least squares regression discriminant analysis to separate three types of astigmatism treatments.

Abbreviations: PLS-DA, partial least squares discriminant analysis; SD, standard deviation.

Figure 3 Loadings plot of the partial least squares regression discriminant analysis model to compare the three astigmatism treatment methods.

Abbreviations: bSE, spherical equivalent (before treatment); aSE, spherical equivalent (after treatment); bUCVA, uncorrected visual acuity (before treatment); aUCVA, uncorrected visual acuity (after treatment); bBCVA, best corrected visual acuity (before treatment); aBCVA, best corrected visual acuity (after treatment); TIA, target induced astigmatism; TIA_AxDeg, target induced astigmatism axis in degrees; SIA, surgically-induced astigmatism; SIA AxDeg, surgically-induced astigmatism axis in degrees; DV, difference vector; AngEr, angle of error; MagErr, magnitude of error; CI, correction index; IOS, index of success; CA, coefficient of adjustment; FI, flattening index; Wc, W represents X-weights and c represents Y-weights.

Figure 4 Plot of coefficients of variables predicting the class membership for the three astigmatism treatment methods: (A) cross-cylinder, (B) single method, (C) wavefront.

Notes: Y-axis shows the scaled and centered coefficients; X-axis shows the model predictors; the coefficient is significant when the confidence interval does not cross the zero line.
Abbreviations: bSE, spherical equivalent (before treatment); aSE, spherical equivalent (after treatment); bUCVA, uncorrected visual acuity (before treatment); aUCVA, uncorrected visual acuity (after treatment); bBCVA, best corrected visual acuity (before treatment); aBCVA, best corrected visual acuity (after treatment); TIA, target induced astigmatism; TIA_AxDeg, target induced astigmatism axis in degrees; SIA, surgically-induced astigmatism; SIA AxDeg, surgically-induced astigmatism axis in degrees; DV, difference vector; AngEr, angle of error; MagErr, magnitude of error; CI, correction index; IOS, index of success; CA, coefficient of adjustment; FI, flattening index.

Figure 5 Validation plot to assess the validity of the fitted partial least squares regression discriminant analysis model for discriminant analysis of three astigmatism treatment modalities.

Abbreviations: PLS-DA, partial least squares regression discriminant analysis.

Figure 6 Pattern of change in R2 compared to Q2, with increasing model complexity (X-axis).