**Purpose.**:
To compare two methods of composite score generation in dry eye syndrome (DES).

**Methods.**:
Male patients seen in the Miami Veterans Affairs eye clinic with normal eyelid, corneal, and conjunctival anatomy were recruited to participate in the study. Patients filled out the Dry Eye Questionnaire 5 (DEQ5) and underwent measurement of tear film parameters. DES severity scores were generated by independent component analysis (ICA) and latent class analysis (LCA).

**Results.**:
A total of 247 men were included in the study. Mean age was 69 years (SD 9). Using ICA analysis, osmolarity was found to carry the largest weight, followed by eyelid vascularity and meibomian orifice plugging. Conjunctival injection and tear breakup time (TBUT) carried the lowest weights. Using LCA analysis, TBUT was found to be best at discriminating healthy from diseased eyes, followed closely by Schirmer's test. DEQ5, eyelid vascularity, and conjunctival injection were the poorest at discrimination. The adjusted correlation coefficient between the two generated composite scores was 0.63, indicating that the shared variance was less than 40%.

**Conclusions.**:
Both ICA and LCA produced composite scores for dry eye severity, with weak to moderate agreement; however, agreement for the relative importance of single diagnostic tests was poor between the two methods.

^{ 1–5 }DES is a leading cause of visits to optometry and ophthalmology clinics, and DES medications account for approximately $1.9 billion in US sales annually.

^{ 6–8 }Despite its significant morbidity and cost implications, the diagnosis of DES remains a problem for the clinician and researcher alike. This is largely due to the lack of a gold standard definition for the disease, which may arise from the complexity of the underlying disease process.

^{ 9,10 }To add to the complexity, some parameters provide information on one facet of disease, whereas others provide information on multiple facets. For example, although meibum quality mostly assesses lipid health, tear breakup time (TBUT) is a collective parameter influenced by the status of the aqueous, lipid, and mucous.

^{ 11 }

^{ 12 }created a composite score that considered multiple factors in its generation. The authors used independent component analysis (ICA),

^{ 13 }a method commonly used in signal processing, to arrive at such a score. Although there is a definite need for a reliable DES composite score, it is not clear if ICA is the optimal approach to use in its generation. ICA methodology has not been frequently applied to the problem of diagnostic tests and has not been previously applied to problems in ophthalmology. Latent class analysis (LCA), on the other hand, is a technique often applied to imperfect diagnostic tests in the absence of a gold standard. It has been applied in ophthalmology to estimate the sensitivity and specificity of laboratory and clinical tests for trachoma in the absence of a gold standard.

^{ 14 }

^{ 15 }The ocular surface examination consisted of assessment of conjunctival injection (range, 0–4), tear osmolarity (measured once in each eye) (TearLAB, San Diego, CA), TBUT (measured twice in each eye and averaged per eye) (range, 0–15), corneal staining (punctate epithelial erosions, range, 0–5),

^{ 16 }Schirmer's strips with anesthesia, and morphologic and qualitative eyelid and meibomian gland information. Morphologic information collected included the degree of eyelid vascularity (0, none; 1, mild engorgement; 2, moderate engorgement; 3, severe engorgement)

^{ 17 }and the presence of inferior eyelid meibomian orifice plugging (0, none; 1, less than one-third lid involvement; 2, between one-third and two-thirds involvement; 3, greater than two-thirds lid involvement). Meibum quality was graded on a scale of 0 to 4 (0, clear; 1, cloudy; 2, granular; 3, toothpaste; 4, no meibum extracted).

^{ 18 }Data were entered into a standardized database.

^{ 12 }This was done as there was a concern that our population of men aged 55 and older would have different “normal” values. As there is no age-adjusted nomogram for tear parameters, we elected to normalize values based on the severity relative to the rest of the cohort. To test the effect of transformation on the outcome, we performed a secondary analysis by normalizing the data to its SD.

^{ 12 }known as Ocular Surface Severity Score (OS

^{3}). ICA is a method that transforms multivariate data into components. As the name suggests, ICA attempts to maximize the statistical independence between components. The method assumes that observations arise from a linear mixture of unobserved “source signals” and solves for the matrices that convert between sources and observed data. The matrix that transforms sources into observations,

*A*, is called the

*mixing matrix*.

^{3}composite, we adapted code from OS

^{3}(Sullivan BD, written communication, 2011) and computed weights using GNU Octave (provided in the public domain at http://www.gnu.org/software/octave/). In summary, this method uses a fast infomax algorithm to solve for

*A*.

^{ 19 }To create the weights, we calculated the mean of each row of

*A*, normalized it, and took the multiplicative inverse of each entry. The resulting vector contained the weight for each diagnostic test. Composite scores were then computed from the sum of squares of parameters with their respective weights.

**Figure 1**

**Figure 1**

^{ 20,21 }package (Version 1.2.0-1926; OpenMx project, Charlottesville, VA) for the R statistical language and environment software (Version 2.15.1; R Foundation for Statistical Computing, Vienna, Austria).

^{ 22 }The model was estimated 40 times using starting values that were randomly selected from plausible ranges for each model parameter to ensure convergence to the maximum likelihood solution.

**Figure 2**

**Figure 2**

^{23}was implemented as structural equation models using thresholds. The corresponding path diagram is shown in Figure 3. The model assumes that each ordinal response has an underlying continuous scale whose mean differs by class. Each underlying continuous distribution is assumed to be normally distributed. For the healthy class, the mean

*M*is fixed to zero and the SD

_{H}*σ*is fixed to 1. For the diseased class, the mean

_{H}*M*and the SD

_{D}*σ*are estimated from the data. The thresholds

_{D}*C*are constrained to be the same for both classes and must be estimated. Using the bi-normal model, the ROC curve is given by: with and where

_{i}*t*is 1 − specificity and

*Φ*is the cumulative unit-standard normal distribution function. The AUC is then given by This approach avoids treating the ordinal categories as if they were quantitative, continuous measurements and avoids the inherent downward bias in the AUC estimates that would otherwise occur.

**Figure 3**

**Figure 3**

**Table 1.**

*R*

^{2}= 0.397) when compared with the primary ICA analysis.

**Table 2.**

**Table 2.**

Dry Eye Parameter | |

Osmolarity | 20.86 |

Eyelid vascularity | 10.26 |

Meibomian orifice plugging | 10.11 |

Symptoms, DEQ5 | 9.18 |

Schirmer's test | 8.77 |

Corneal staining | 8.41 |

Meibum quality | 8.00 |

Conjunctival injection | 7.77 |

TBUT | 6.25 |

**Table 3.**

**Table 3.**

Dry Eye Parameter | Bi-Normal Parameters | AUC | |||

a | b | Lower Bound | Estimate | Upper Bound | |

TBUT | −2.213 | 1.095 | 0.555 | 0.932 | 1.000 |

Schirmer's test | −1.488 | 0.677 | 0.750 | 0.891 | 0.982 |

Corneal staining | 0.979 | 0.621 | 0.708 | 0.797 | 0.863 |

Meibomian orifice plugging | −0.441 | 0.609 | 0.540 | 0.647 | 0.759 |

Meibum quality | 0.430 | 0.692 | 0.539 | 0.638 | 0.713 |

Osmolarity | NA | NA | 0.411 | 0.572 | 0.732 |

Symptoms, DEQ5 | NA | NA | 0.404 | 0.565 | 0.725 |

Eyelid vascularity | 0.067 | 0.610 | 0.408 | 0.523 | 0.624 |

Conjunctival injection | 0.048 | 0.295 | 0.411 | 0.518 | 0.624 |

*P*≪ 0.00001), the

*R*

^{2}was only 0.399, indicating a weak to moderate linear relationship.

**Figure 4**

**Figure 4**

*R*

^{2}= 0.399); however, agreement on the importance of single diagnostic tests was poor between the two methods.

^{ 14 }For our patients, based on the severity of their responses, it was easy to identify one latent class as diseased and the other as healthy. Although our LCA results do not “prove” there are two subpopulations, the results suggest that this may be a useful description for the observed data. Based on the LCA model, TBUT and Schirmer's test were superior to the other seven tests. Had TBUT and Schirmer's test results not been censored, it is likely their superiority would have been even greater. Although there appear to be two distinct classes, the degree of separation is small and the amount of overlap is large. Although for approximately 30 patients, the posterior probability for a given latent class was 1 (and 0 for the opposite class), for most patients the posterior probability ranged between 1 and 0. Compared to other commonly used statistical techniques, LCA methodology is complex and requires substantial mathematical and statistical knowledge to construct a model and interpret the results.

^{ 12 }appears to be the first and only published use of ICA to create composite scores from diagnostic tests. As such, ICA has never been validated for this application. The main strength of ICA is in the simplicity of implementation. The method occurs in two steps: the transformation of measurements onto (0,1) and the computation of weights via ICA. Once weights have been calculated for a population, the calculation of composites is accomplished through basic arithmetic, a feature that cannot be said for LCA. However, using simulated data and multiple transformations of our DES data, we consistently found that measurements with higher variance produced greater weights (data not shown). This likely arises from a simplification necessary to make the model solvable: fixing

*S*to have a variance of 1. Because

*A*×

*S*=

*X*, and weights are calculated from 1/

*A*, the weights are affected by the variance of the transformed measurements,

*X*. As such, a weakness of the ICA is the potential for analytic manipulation through alterations in the method of transformation.

**C. See**, None;

**R.A. Bilonick**, None;

**W. Feuer**, None;

**A. Galor**, None

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