Multivariate nonparametric techniques for astigmatism analysis

Department of Ophthalmology, Jules Stein Eye Institute, David Geffen School of Medicine at UCLA, Los Angeles, California 90095-7002, USA.
Journal of Cataract and Refractive Surgery (Impact Factor: 2.72). 04/2010; 36(4):594-602. DOI: 10.1016/j.jcrs.2009.11.002
Source: PubMed


To describe the application of nonparametric multivariate statistical methods to the analysis of astigmatism treatment outcomes.
Jules Stein Eye Institute and Department of Ophthalmology, David Geffen School of Medicine at UCLA, Los Angeles, California, USA.
Nonparametric methods were applied to a published data set and to 12 test data sets created for test purposes. Results of 3 multivariate nonparametric tests were compared with those obtained using the Hotelling T(2), a multivariate parametric test. The nonparametric tests were the rank-based multivariate analysis of variance (MANOVA), sign-based MANOVA, and bootstrapping based on the Hotelling T(2) statistic.
Reanalysis of the published data set using the 3 nonparametric tests detected statistically significant treatment effects at all postoperative examinations. The Hotelling T(2) and 3 nonparametric tests detected differences in astigmatism outcomes for multiple test data sets that simulated normal distributions. For test data sets simulating non-normal distributions, the Hotelling T(2) test and bootstrapping based on Hotelling T(2) detected a difference in 1 test data set while rank-based and sign-based MANOVA detected differences in outcomes for multiple data sets.
Rank-based and sign-based MANOVA had comparable or slightly lower power than the Hotelling T(2) test in detecting differences in normally distributed data. For data sets in which the rectangular components of astigmatism vectors do not distribute normally in both dimensions, only the nonparametric statistical methods were valid. The sign-based MANOVA was the most sensitive in detecting differences in non-normally distributed astigmatism outcomes in the data sets.

10 Reads
  • [Show abstract] [Hide abstract]
    ABSTRACT: To compare long-term change in corneal astigmatism with advancing age between eyes that underwent sutureless cataract surgery and those that did not undergo surgery. Case-control study. A total of 153 eyes that underwent phacoemulsification with a horizontal incision more than 11 years ago (surgery group) and 153 age-matched control eyes that did not undergo surgery (nonsurgery group) were enrolled. The keratometric cylinder at baseline (at 1 year or more postoperatively in the surgery group) and at 5 and 10 years after baseline was examined. The corneal astigmatic change, as calculated using polar value analysis and vector decomposition analysis, between baseline and 5 years after baseline and between 5 and 10 years was compared between the groups. The mean corneal astigmatic change, specifically ΔKP (90) in the polar analysis and against-the-rule component in the vector analysis, between baseline and 5 years and between 5 and 10 years showed an against-the-rule change in both groups. Using multivariate analysis, no significant difference was found in the corneal astigmatic change between the 2 groups at either time interval (P ≥ .126). Furthermore, the change between baseline and 5 years was similar to that between 5 and 10 years in both groups (P ≥ .315). Corneal astigmatism after sutureless cataract surgery shows a long-term against-the-rule change with advancing age, and this change is similar to that of normal cornea, suggesting that the against-the-rule change that occurs subsequently should be taken into consideration at the time of cataract surgery.
    American Journal of Ophthalmology 02/2011; 151(5):858-65. DOI:10.1016/j.ajo.2010.11.014 · 3.87 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: This paper presents a design of cooperative controllers that force a group of N mobile agents with an elliptic shape and limited sensing ranges to perform a desired formation and that guarantee no collisions between any agents in the group. The desired formation can be stabilized at feasible reference trajectories with bounded time derivatives. The formation control design is based on explicit algebraic separation conditions between ellipses, root conditions of cubic polynomials, the Lyapunov direct method, and smooth or p-times differentiable step functions. These functions are incorporated into novel potential functions to solve the collision avoidance problem without the need for switchings despite the agents' limited sensing ranges. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society
    Asian Journal of Control 07/2012; 14(6). DOI:10.1016/j.automatica.2011.05.026 · 1.56 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: To examine whether long-term corneal astigmatic change with age after cataract surgery depends on patient age at the time of surgery, and to evaluate whether this change is different from that in eyes that did not undergo surgery. Retrospective cohort study. A total of 437 eyes that underwent phacoemulsification with a 4.1-mm horizontal corneoscleral incision more than 11 year ago and 600 control eyes without surgery were divided into four age groups, 1) 60 years or younger, 2) 61-65 years, 3) 66-70 years, and 4) 71 years or older. The corneal astigmatic change between baseline and 5 years after baseline, between 5 and 10 years, and between baseline and 10 years, as calculated using the polar (X-Y) coordinate analysis, were compared among the age groups and between eyes with and without surgery. Corneal astigmatic change, expressed as X- and Y-coordinates, showed an against-the-rule change of 0.2 to 0.4 diopters during the 10 years in all age groups of the surgery and non-surgery groups. Using multivariate analysis of variance, the mean X- and Y-coordinates did not differ significantly among the age groups in either the surgery or nonsurgery groups (P ≥ .4112). Furthermore, the mean X- and Y-coordinates did not differ significantly between the surgery and nonsurgery groups in any age group (P ≥ .1359). Long-term corneal astigmatic change with age after cataract surgery does not differ significantly depending on patient age at the time of surgery, and is comparable to that of eyes without surgery. Copyright © 2015 Elsevier Inc. All rights reserved.
    American Journal of Ophthalmology 04/2015; 160(1). DOI:10.1016/j.ajo.2015.04.015 · 3.87 Impact Factor