Posters

Optimising curve fitting techniques to enable standardised analysis of defocus curves derived from multifocal intraocular lenses

Poster Details

First Author: E.Law UK

Co Author(s):    R. Aggarwal   H. Buckhurst   H. Kasaby   P. Buckhurst   G. Shum   J. Marsden     

Abstract Details

Purpose:

Defocus profiles are a common feature in multifocal intraocular lens (MIOL) studies. Detailed analysis including range of focus and area under the curve metrics can highlight differences between MIOLs that are not illicit with simple direct comparison methods, but these metrics require a curve to be fitted. To date, there is no agreement on the methodology of the curve fitting process. This study aims to establish the most appropriate curve fitting method to allow accurate comparison of defocus curves derived from multifocal intraocular lenses (IOLs).

Setting:

BMI Southend Hospital, UK

Methods:

Defocus curves were plotted in 5 different IOL groups (monofocal, extended depth of focus, refractive bifocal, diffractive bifocal and trifocal) over -5.00DS to +1.50DS in 0.5DS steps. Polynomomial curves from 2nd to 11th order and a cubic spline curve were fitted. Goodness of fit was assessed using 5 different methods (Least squares, coefficient of determination, Akaike information criteria (AIC), visual inspection and the Snedecor & Cochrane method). In order to validate the predictive ability of the curve, additional defocus steps at -2.25D and -2.75D were measured and were compared to y values interpolated from the curves.

Results:

The statistical methods used to assess goodness of fit demonstrated variable results. More lenient methods such as adjusted r2 or the least squares methods can easily lead to overfitting, yet conservative methods such as AICc led to underfitting and the inflection points expected in bifocal and trifocal IOLs were diminished, and led to an underestimation of VA. Polynomial of at least 8th order was required for comparison of area methods but was indicative of over fitting in the EDoF and monofocal groups. However, the spline curve was consistent through all IOLs and methods.

Conclusions:

The study demonstrates the inherent difficulties faced when selecting a single polynomial function to best fit a variety of IOLs. The r2 method can be used cautiously to select a suitable polynomial order, with visual inspection as an additional step to guard against overfitting. However, if possible, spline curves should be fitted, although spline curves require more complex mathematical modelling to generate the desired metric values, they are guaranteed to pass through all data points and thus avoid the inaccuracies with over or under fitting.

Financial Disclosure:

research is funded, fully or partially, by a company producing, developing or supplying the product or procedure presented