For an isolated index (or a group of indices), and regardless of the cutoff value adopted, a screening method based on a cutoff value is unable to discriminate between two populations (green: reference population, red: population with subclinical keratoconus), which, by definition, present similar characteristics. Comparison of the distributions of the values of the index in each population generally reveals a normal distribution and an overlap between the two populations. However, the cutoff value can be adjusted in order to minimize the false-positive and false-negative rates
This chapter deals with the topographic indices and screening tests that have been proposed to facilitate early identification of subclinical keratoconus. The terms “test” and “index” are sometimes used interchangeably in the context of screening. According to a more rigorous definition, a test is an operation designed to provide a positive or negative result or a diagnostic probability. A test is based on the use of one or several numerical indices, which are then combined to produce a qualitative verdict, or a global numerical score. The verdict depends on the value of the score with respect to the defined cutoff value of the test. A test can also consist of a neural network, or a decision tree, into which are entered the values of various numerical indices. A test generally provides a qualitative or semiquantitative result (diagnostic probability of a particular disease).
This type of test is generally called an index, named after the person who designed the test (e.g., Rabinowitz’s indices), which contributes to the implicit confusion between “test” and “index.” The reader must remember that whenever he or she compares the value of an index to a defined cutoff, he/she performs a test.
8.2 History and Terminology
Historically, Amsler proposed the first classification of various stages of keratoconus: he used a photographic system equipped with a Placido disk . He initially distinguished two groups of keratoconus: one in which keratoconus is associated with detectable clinical signs (visible deformity on biomicroscopic examination, Fleischer’s ring, etc.) and the other in which the diagnosis can only be established by examination of the reflection of Placido rings, thereby anticipating the subsequent importance of corneal topography in this disease. In this second group of keratoconus, which can possibly be described as subclinical, Amsler called the earliest forms observed on examination of reflection of Placido rings “forme fruste” keratoconus.
The introduction of computerized corneal topography subsequently demonstrated the existence of a continuum between the examinations obtained in normal subjects and those with keratoconus. Since then, terms such as “subclinical keratoconus,” “keratoconus-suspect,” and “forme fruste keratoconus,” have been commonly and interchangeably used to describe early forms of keratoconus or forms sharing certain minor features of keratoconus. We have proposed generalizing the term “subclinical keratoconus” to all corneas in which the phenotypic expression of keratoconus is sufficiently minor to remain asymptomatic . Subclinical keratoconus is a topographic diagnosis: forme fruste keratoconus constitutes the earliest form of subclinical keratoconus; it cannot be detected by automated Placido topography and requires analysis of posterior corneal topography and corneal wall thickness variations. Early diagnosis of subclinical keratoconus therefore depends on the technology used to obtain topographic data. For example, some forms labeled as keratoconus-suspect in the 1990s would now be described as early forms of clinical keratoconus (Fig. 8.2). This diagnosis implicitly introduces the concept of the risk of post-LASIK ectasia. The definition of forme fruste keratoconus will undoubtedly evolve in the future, as new tests become accepted as new standards for the detection of early subclinical forms of keratoconus.
Example of the verdict of the automated keratoconus screening system used in 1996 on the TMS-2 topographer (Tomey): the appearance of the colorimetric map strongly suggests the presence of early but true keratoconus. The verdict of Rabinowitz and Klyce/Maeda automated indices is that of keratoconus-suspect
In the beginning of the 1990s, Rabinowitz et al. established Placido topographic  patterns suggestive of early keratoconus and proposed quantitative indices (e.g., the I–S index) in order to obtain precise numerical cutoff values for test results to define the presence of a topographic form of keratoconus-suspect [6, 7]. The fact that Placido topography was developed first, in the middle of the 1980s, partly explains the importance attributed to the anterior surface of the cornea for the positive diagnosis and differential diagnosis of keratoconus [8, 9]. The introduction of corneal elevation topography at the end of the 1990s provided clinicians with new data derived from pachymetry and posterior elevation, which can also suggest the presence of keratoconus-suspect . Increased central thinning and more marked elevation in relation to the reference sphere were generally observed on the anterior surface and especially on the posterior surface in corneas in which Placido topography was suggestive of keratoconus [11–13]. By studying the anterior and posterior corneal elevation characteristics of keratoconus-suspect corneas on Placido topography (objective diagnosis based on Klyce/Maeda criteria), we have demonstrated statistically significant differences with corneas in which anterior topography was considered to be normal. These differences were based on the use of a particular mode of representation of corneal elevation, called aconic; the reference surface used is not spherical but aspherical and toric. This mode allows more sensitive demonstration of topographic patterns related to surface asymmetry (effects of asphericity and toricity are absorbed by the reference surface).
When anterior Placido topography is considered to be normal (not suspicious of keratoconus), but the cornea is thinner with posterior steepening, the possibility a very early form of subclinical keratoconus cannot be excluded. We have shown that normal Placido topography (according to current criteria: Klyce/Maeda criteria) in no way excluded the possibility of a very early subclinical form (forme fruste) of keratoconus, and we have developed a discriminant analysis model to perform a screening test based on corneal elevation and thickness data .
Consistent with these findings and to eliminate any semiological confusion, we reserve the term “keratoconus-suspect” for objectively “suspect” forms, i.e., positive test (or higher than the cutoff) for keratoconus-suspect on Placido topography, according to validated criteria (Rabinowitz’s criteria, Klyce/Maeda criteria): keratoconus-suspect is therefore synonymous with Placido-suspect (see Table 8.1).
Table 8.1 Criteria for distinguishing between Forme fruste keratoconus, keratoconus suspect and clinical keratconus
Forme fruste keratoconus
Clinical or biomicroscopic signs
Detection by Placido topography
Detection by elevation topography and pachymetry
The term “forme fruste” designates topographic forms that raise little or no suspicion, but which are known to constitute a minor form of the disease, either because of the minimal Placido topographic abnormalities, i.e., below the accepted limit of detection for keratoconus-suspect, but other suggestive tomographic or topographic abnormalities (thickness) are present , or because of a suggestive clinical context. For example, in a patient presenting keratoconus in one eye, when the cornea of the fellow eye presents a negative test based on Placido topography data, this cornea can be considered to present forme fruste keratoconus, even if the phenotypic expression of keratoconus in this eye is below the limit of detection according to the same criteria (Fig. 8.3). Similarly, progression of a cornea initially considered to be normal (Placido topography negative for keratoconus) toward a clinical form of keratoconus can lead to a retrospective interpretation of the initial examination as forme fruste keratoconus. Detailed topographic documentation of these clinical situations is essential, as it allows the definition of new cutoffs or new criteria (indices) (Fig. 8.4). The study of the biomechanical properties of these corneas (hysteresis) is a promising alternative approach to facilitate the early detection of subclinical keratoconus .
Example of definite forme fruste forms of keratoconus (left eye). The right eye presents advanced keratoconus, while the right eye presents a very early subclinical form, as the values for all indices are below the defined cutoffs (Klyce/Maeda and Smolek/Klyce indices, Keratoconus Screening neural network, Magellan topographer, Nidek, Japan). This eye can be considered to be false-negative for these tests
Schematic representation of groups of interest, the distribution of the values of the index, and the verdict based on the value of the index with respect to a cutoff in the context of automated keratoconus screening based on corneal topography indices. Forme fruste keratoconus is not detected, at a given limit of detection, by a validated test recognized by the ophthalmological community. Corneas with a value just beyond the cutoff may correspond to true keratoconus, normal corneas (false-positive), or true subclinical keratoconus (true positives)
As emphasized above, it must be kept in mind that these nosological distinctions are not immutable: the terminology used depends on the quality of the tests used and can vary over time or with the topography system used. Regardless of progress in this field, keratoconus-suspect, by definition, will remain topographically more advanced than forme fruste keratoconus, but the screening indices proposed to facilitate the identification of early forms of keratoconus must be able to detect forme fruste keratoconus.
8.3 Topographic Indices
A topographic index is a numerical value calculated from analysis of the data obtained by topography. Topographic indices allow more quantitative analysis of topographic data and use explanatory variables to perform statistical tests designed to distinguish the population of corneas presenting subclinical keratoconus from normal corneas (discriminant analysis). Mean simulated keratometry (SimK) is an example of a topographic index, as, in addition to the estimation of the mean apical keratometric power that it provides, this parameter can be indicative of the presence of keratoconus beyond certain cutoff values (e.g., 53 D). Moreover, most indices were initially proposed to facilitate the detection of keratoconus, and their cutoffs were defined from preliminary studies or were integrated into predictive statistical models. Other fields of application have been developed, ranging from the study of the quality of the topographic examination to the detection of various corneal diseases and conditions (pellucid marginal degeneration, previous photoablative surgery, etc.)
8.3.2 Categories of Indices
The various indices can be classified as a function of the type of data from which they are calculated:
Global indices: they are calculated from all of the topographic data derived from the corneal surface studied (e.g., Q asphericity factor).
Local indices: they are calculated from partial/local topographic data (e.g., I–S index).
Composite indices: they are calculated from the values of several indices (e.g., KISA%).
The first indices proposed for keratoconus screening were local indices , but in view of their low specificity at cutoffs allowing adequate sensitivity, composite indices were subsequently developed (e.g., KISA%) .
In the absence of standardization between the various manufacturers, types of maps, scales, etc., the majority of indices (particularly composite indices) are specific to a particular type of topographer. However, some indices, developed by independent investigators, are common to various topography systems.
8.3.3 Sensitivity and Specificity of Screening Tests
The development of efficient screening techniques is designed to overcome the problems related to detection of early forms of keratoconus. To assess the efficacy of screening techniques, i.e., their ability to detect early forms of keratoconus by discriminating them from healthy corneas, various indices can be studied in a population of corneas comprising a proportion of early forms of keratoconus, as well as normal corneas. These topographic screening tests were therefore performed in a group of patients known to present keratoconus in order to define the variables of interest and their cutoff values.
Isolated analysis of the values of certain topographic variables is not sufficient to reliably discriminate between healthy corneas and corneas with subclinical keratoconus. Calculation of the mean of any non-composite index (e.g., SimK) in a reference healthy population may be informative because it provides an overview of the median value of this parameter. However, it is also essential to determine the scatter of these values (e.g., standard deviation), which, to a certain degree, reflects the homogeneity of the group in relation to this index. This mean and this standard deviation can then be compared with those of a population of pathological corneas. When comparing healthy corneas and corneas with early forms of keratoconus, although the two groups present different means, there is a considerable overlap of values, regardless of the index used. It would be reasonable to postulate that this overlap of values would be even more marked for very early forms, corresponding to the earliest stages of the disease.
Even when a so-called “statistically significant” difference is observed between the values of the index measured in the two groups, the essential question that must be resolved is: what cutoff value of this index should be used to diagnose the presence of early subclinical keratoconus? If an excessively high cutoff value is used, a large number of corneas could be missed (increased false-negative rate, decreased sensitivity). An excessively low cutoff value is associated with the opposite risk: normal corneas could be considered to be pathological (increased false-positive rate, decreased specificity).
The combination of a number of indices within a so-called “discriminant” function could allow more effective classification of lesions than that based on a single index: this type of analysis is called “predictive discriminant analysis.” This statistical technique is designed to predictively attribute a population of individuals to several predefined groups based on a series of predictive variables (in this case, topographic indices expressed as numerical values). Linear combinations of these predictive variables are used to construct a final score, and the value of this score is compared to a cutoff that has been carefully defined to discriminate the various individuals measured as precisely as possible, for example, normal corneas vs keratoconus. Construction of a neural network is another method designed to classify a subject within a group on the basis of successive tests, in which one or several indices are used and compared to a predefined cutoff value. The neural network is constructed according to a set of data (in this case topographic indices) on corneas for which some of the characteristics are already known. Neural network training from a sufficient number of topographic data can define characteristics that can be used to establish effective segregation to test new maps: neural networks are often represented by a group of neurons (each neuron corresponding to a particular test operation) connected by arrows indicating transfer of information within the network. For example, depending on the value of a first predetermined index, the corneal topography studied is classified into one of several subgroups. A second test (using another index) is then performed, and a new layer is created to refine the diagnosis. A final diagnosis may be established according to the direction of the connections in the network. In contrast with methods based on linear discriminant analysis, the order in which the successive tests are performed has an impact on the output. Regardless of the methodology used, the choice of cutoff is particularly important in order to ensure optimal test performance. However, no cutoff is perfectly discriminant: an excessively low cutoff can wrongly consider a high proportion of normal corneas to be pathological, and an excessively high cutoff will miss too many pathological corneas that are incorrectly considered to be normal. For example, the degree of central curvature of the cornea could be used as an index of the presence of an early form of keratoconus. The use of a simulated keratometry (SimK) cutoff of 45 D for the detection of early keratoconus could result in overdiagnosis of this disease (without detecting all cases of early keratoconus). Using a SimK cutoff of 49 D would certainly be more selective, but less sensitive, as a large number of pathological corneas would not be considered to be the suspect on this simple test. One solution to increase the discriminant capacity consists of adding another variable. For example, taking into account the asphericity factor (Q) in addition to simulated keratometry should allow more accurate detection of early forms of keratoconus, which are characterized by increased apical curvature and a tendency to steeper decline of this curvature at the periphery (more prolate asphericity).
In general, increasing the number of variables results in more efficient, i.e., more discriminant tests, in which an optimal cutoff can be more easily defined. For this reason, the most efficient indices are composite indices (i.e., composed of several variables) in order to increase the probability of clearly discriminating subclinical and normal populations with the various tests used in these indices.
However, descriptive statistics techniques based on the collection and calculation of indices are not infallible, as they always comprise a proportion of patients in whom the cornea may be incorrectly classified. A false-negative (FN) result corresponds to a topographic examination that is considered to be normal, despite the presence of an early form of keratoconus, and a false-positive (FP) result corresponds to a topographic examination considered to be abnormal in the absence of keratoconus. Correctly classified corneas correspond to true negatives (TN) in the absence of keratoconus and true positives (TP) in the presence of keratoconus.
A good screening test is a test associated with a relatively small number of false-positive and false-negative results, which can therefore be considered to be sufficiently reliable. The performances of the examinations used to screen for any given disease can be measured by means of two criteria: sensitivity and specificity (the modalities used to study the performances of a screening test are described in Appendix 2).
Sensitivity is a criterion that describes the capacity of the test to detect a particular disease. Sensitivity can be measured in a group of patients (keratoconus), selected independently of the test to be analyzed. Sensitivity is expressed by a percentage between 0 and 100%, defined by the following ratio:
Sensitivity = TP/(TP + FN)
0% indicates that the examination fails to detect the disease, and 100% indicates that all pathological cases are detected (the test is constantly positive in affected subjects). The higher the sensitivity of the test, the lower is the proportion of subjects in whom the disease studied will not be detected.
Specificity is a criterion that describes the possibility of declaring a subject to be free of the disease studied. It corresponds to the proportion of true negatives (TN) in the overall population of healthy subjects.
Sensitivity = TP/(TP + FN)
The higher the specificity and the closer it is to 100%, the lower is the false-positive rate and vice versa.
A specificity of 100% indicates that a healthy person is identified with certainty.
The best screening test would be a test with a specificity and a sensitivity both equal to 100% (no false-positives, no false-negatives). Unfortunately, no tests in medicine are perfectly accurate, and each test is associated with a certain number of false-positive or false-negative results.