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

Mohammad Reza Sedghipour,¹ Homayoun Sadeghi-Bazargani<sup>2,3

1</sup>Nikoukari Ophthalmology University Hospital, Tabriz, Iran; ²Department of Statistics and Epidemiology, Neuroscience Research Center, Tabriz University of Medical Sciences, Tabriz, Iran; ³Department of Public Health Sciences, Karolinska Institute, Stockholm, Sweden

Background: In astigmatism clinical trials where more complex measurements are common, especially in nonrandomized small sized clinical trials, there is a demand for the development and application of newer statistical methods.
Methods: The source data belonged to a project on astigmatism treatment. Data were used regarding a total of 296 eyes undergoing different astigmatism treatment modalities: wavefront-guided photorefractive keratectomy, cross-cylinder photorefractive keratectomy, and monotoric (single) photorefractive keratectomy. Astigmatism analysis was primarily done using the Alpins method. Prior to fitting partial least squares regression discriminant analysis, a preliminary principal component analysis was done for data overview. Through fitting the partial least squares regression discriminant analysis statistical method, various model validity and predictability measures were assessed.
Results: The model found the patients treated by the wavefront method to be different from the two other treatments both in baseline and outcome measures. Also, the model found that patients treated with the cross-cylinder method versus the single method didn't appear to be different from each other. This analysis provided an opportunity to compare the three methods while including a substantial number of baseline and outcome variables.
Conclusion: Partial least squares regression discriminant analysis had applicability for the statistical analysis of astigmatism clinical trials and it may be used as an adjunct or alternative analysis method in small sized clinical trials.

Keywords: astigmatism, regression, partial least squares regression, multivariate regression, discriminant analysis