Multivariate assessment of computer-analyzed corneal topographers

M. A. G. Viana; I. Olkin; T. T. McMahon

doi:10.1364/JOSAA.10.001826

Journal of the Optical Society of America A
Vol. 10,
Issue 8,
pp. 1826-1834
(1993)
•https://doi.org/10.1364/JOSAA.10.001826

Multivariate assessment of computer-analyzed corneal topographers

M. A. G. Viana, I. Olkin, and T. T. McMahon

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M. A. G. Viana, I. Olkin, and T. T. McMahon, "Multivariate assessment of computer-analyzed corneal topographers," J. Opt. Soc. Am. A 10, 1826-1834 (1993)

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Abstract

Methodological aspects of multivariate statistical models to describe and to assess data from computer-analyzed corneal topographers (CACT) are considered. The data generated by repeated curvature mappings of calibrated steel balls are discussed in detail with the objective of formulating the basic questions and suggesting directions to assess data from clinical applications of CACT. The interpretation of seemingly straightforward concepts such as accuracy and precision is revisited with the objective of understanding its meaning in future clinical and experimental applications of CACT. Some of the statistical problems related to the analysis of corneal astigmatism based on CACT data are also discussed.

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Ball	Ring	$\bar{x}$	$\bar{s}$	r	μ_l	μ_u	${\bar{x}}_{l}$	${\bar{x}}_{u}$
42.50	10	42.29	0.0026	0.839	42.20	42.38	42.03	42.55
42.50	11	42.30	0.0113	0.892	42.21	42.40	42.02	42.59
42.50	12	42.33	0.0099	0.900	42.25	42.42	42.06	42.60
42.50	13	42.37	0.0105	0.901	42.28	42.46	42.09	42.65
42.50	14	42.42	0.0094	0.890	42.33	42.50	42.15	42.68
42.50	15	42.45	0.0101	0.900	42.36	42.54	42.17	42.72
44.75	10	44.43	0.0148	0.811	44.53	44.53	44.10	44.76
44.75	11	44.43	0.0143	0.894	44.32	44.54	44.11	44.75
44.75	12	44.45	0.0149	0.880	44.34	44.56	44.12	44.78
44.75	13	44.47	0.0152	0.882	44.36	44.58	44.14	44.80
44.75	14	44.50	0.0157	0.861	44.39	44.62	44.16	44.84
44.75	15	44.54	0.0155	0.883	44.43	44.65	44.20	44.88

Ball	Ring	β	Δ₁	Δ₂
42.50	10	0.209	0.0860	0.2602
42.50	11	0.197	0.0950	0.2876
42.50	12	0.165	0.0890	0.2695
42.50	13	0.127	0.0918	0.2777
42.50	14	0.082	0.0869	0.2630
42.50	15	0.053	0.0899	0.2722
44.75	10	0.324	0.1088	0.3291
44.76	11	0.320	0.1074	0.3248
44.75	12	0.304	0.1092	0.3303
44.75	13	0.279	0.1103	0.3336
44.75	14	0.247	0.1122	0.3395
44.75	15	0.210	0.1113	0.3368

Ball	Ring	E(λ₁)	Sd(λ₁)	E(λ₂)	Sd(λ₂)	E( $A$ )	Sd( $A$ )
42.50	10	0.0925	0.0585	0.0075	0.0014	0.216	0.092
42.50	11	0.1132	0.0715	0.0045	0.0008	0.168	0.071
42.50	12	0.0993	0.0628	0.0027	0.0005	0.131	0.056
42.50	13	0.1055	0.0667	0.0021	0.0004	0.115	0.049
42.50	14	0.0945	0.0598	0.0023	0.0004	0.119	0.050
42.50	15	0.1013	0.0640	0.0024	0.0004	0.124	0.053
44.75	10	0.1481	0.0936	0.0093	0.0017	0.240	0.102
44.75	11	0.1442	0.0912	0.0055	0.0010	0.185	0.079
44.75	12	0.1492	0.0943	0.0047	0.0008	0.171	0.073
44.75	13	0.1522	0.0962	0.0063	0.0012	0.198	0.084
44.75	14	0.1576	0.0996	0.0084	0.0015	0.228	0.097
44.75	15	0.1552	0.0981	0.0080	0.0015	0.222	0.094

Ball	Ring	$\bar{x}$	$\bar{s}$	r	μ_l	μ_u	${\bar{x}}_{l}$	${\bar{x}}_{u}$
42.50	10	42.29	0.0026	0.839	42.20	42.38	42.03	42.55
42.50	11	42.30	0.0113	0.892	42.21	42.40	42.02	42.59
42.50	12	42.33	0.0099	0.900	42.25	42.42	42.06	42.60
42.50	13	42.37	0.0105	0.901	42.28	42.46	42.09	42.65
42.50	14	42.42	0.0094	0.890	42.33	42.50	42.15	42.68
42.50	15	42.45	0.0101	0.900	42.36	42.54	42.17	42.72
44.75	10	44.43	0.0148	0.811	44.53	44.53	44.10	44.76
44.75	11	44.43	0.0143	0.894	44.32	44.54	44.11	44.75
44.75	12	44.45	0.0149	0.880	44.34	44.56	44.12	44.78
44.75	13	44.47	0.0152	0.882	44.36	44.58	44.14	44.80
44.75	14	44.50	0.0157	0.861	44.39	44.62	44.16	44.84
44.75	15	44.54	0.0155	0.883	44.43	44.65	44.20	44.88

Ball	Ring	β	Δ₁	Δ₂
42.50	10	0.209	0.0860	0.2602
42.50	11	0.197	0.0950	0.2876
42.50	12	0.165	0.0890	0.2695
42.50	13	0.127	0.0918	0.2777
42.50	14	0.082	0.0869	0.2630
42.50	15	0.053	0.0899	0.2722
44.75	10	0.324	0.1088	0.3291
44.76	11	0.320	0.1074	0.3248
44.75	12	0.304	0.1092	0.3303
44.75	13	0.279	0.1103	0.3336
44.75	14	0.247	0.1122	0.3395
44.75	15	0.210	0.1113	0.3368

Abstract

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Tables (3)

Equations (27)

Journal of the Optical Society of America A