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Discriminant analysis.

Discriminant analysis (DA) is a pattern recognition technique that has been widely applied in medical studies. It allows multivariate observations ("patterns" or points in multidimensional space) to be allocated to previously defined groups (diagnostic categories). The relationships between DA and other multivariate statistical techniques of interest in medical studies will be briefly discussed. The main emphasis is on linear discriminant functions (LDF). The theoretic assumptions underlying DA using LDFs will be presented, and the effect of violations to these assumptions will be reviewed in detail. Alternative methods will be presented when violations cause serious problems. It has been shown that the familiar LDF is fairly robust to departures from the assumptions. The application of the LDF in less than ideal situations therefore often does not cause much harm (if the violations are not too grotesque). Another set of problems reviewed is how to estimate the misallocation probabilities when using discriminant functions. The selection of the "best" subset of variables out of the complete set will be discussed. Practical guide lines are given based on the theoretic studies reviewed. When possible, available computer programs for various problems of DA will be indicated. The review does not aim at covering all medical studies where DA has been applied, since emphasis is on the practical conclusions of the theory of DA.

Discriminant Analysis

Discriminant analysis of bronchial asthma by linear discriminant function with parameters of flow-volumes: discriminant analysis of bronchial asthma in young male non-smokers.

With the parameters of a flow-volume and a volume-time curve, the discriminant analysis of bronchial asthma is described. The subjects were classified into three groups (healthy adults, mild asthmatic patients and moderates ones). The difference of the mean vectors of the parameters of the three groups was made clear by the selection methods of the discriminant analysis between any two of the groups both with 6 parameters (%FVC, FEV1.0%, peak flow rate (PF), flow rate at 50% of FVC (V50), flow rate at 25% of FVC (V25), and V50/V25) and with 8 (6 parameters mentioned above and V75, V10). Forced expiratory volume in 1 second percent (FEV1.0%) or V50 was selected at the first step with 6 parameters, and V75 was selected at the first step with 8 parameters. Probabilities of misclassification with 8 parameters were lower than those with 6 ones and the probability of misclassification at the discriminant analysis between healthy adults and mild asthmatic patients with 8 parameters was 15.75% at the final step.

Adult

Quantitative nuclear image analysis: differentiation between normal, hyperplastic, and malignant appearing uterine glands in a paraffin section. IV. The use of Markov chain texture features in discriminant analysis.

Discriminant analysis was applied to Markov chain texture features and elementary features calculated from data from microscope photometry of nuclei in a paraffin section. The results from measurements on the nuclei of morphologically normal, atypical hyperplastic and carcinomatous uterine glands were used in discriminant analysis. With this technique it is possible to classify up to 88.1% of the nuclei correctly in one of the three groups of uterine glands. The discriminating power of several smaller subsets indicated that with more than 28 features there is hardly any increase in discriminating power. Discriminant analysis with a selection from elementary and Markov chain features provides objective criteria of assistance in histopathological diagnosis.

Cell Nucleus

[Repeated characterization, analysis of variance limitation and discrimination analysis classification of EEG-activity patterns in human sleep].

1. To describe quantitatively and to deliminate nine EEG sleep patterns, mean values and standard deviations of abundances of the frequencies 0.8 ... 1.8 c/sec, 2...3.5 c/sec, 4...13c/sec, 14 to 17 c/sec, 18 to 22 c/sec, and 23 to 40 c/sec as well as of the average amplitudes in selected frequency ranges were calaculated and the distributions represented. 2. All nine EEG activity patterns could be separated by means of univariate and multivariate analyses of variance on the basis of all 28 as well as the 17 indispensable variables. 3. In the course of a stepwise reduction of variables within the framework of a linear discriminant analysis an optimal set of 17 variables was determined for the separation of the patterns, comprising: the percent quantity of the frequencies 0.8 ... 3.5 c/sec, 7 ... 9 c/sec and 18 to 40 c/sec as well as the average amplitudes in the frequency ranges 0.8 to 3.5 c/sec and 7.5 to 40 c/sec. 4. By linear regression analyses it could be shown that the sleep scording system used, can be reflected on an interval scale with the aid of discriminant functions; this can be achieved on the basis of the optimal set of variables as well as of the five most indispensable variables. 5. Finally the degree of the objectivity of the scoring procedures was demonstrated. Advantages and disadvantages of sleep scoring systems were discussed and possibilities of the utilization of results suggested, also in respect to the further development of the automatic recognition of EEG activity patterns.

Analysis of Variance

Quantitative nuclear image analysis: differentiation between normal, hyperplastic, and malignant appearing uterine glands in a paraffin section. II. Computer assisted recognition by discriminant analysis.

Quantitative image analysis was applied to data from microscope photometry of nuclei in a paraffin section. The data were essentially the same as described in a previous publication (Baak and Diegenbach, 1977). The results from measurements on the nuclei of morphologically normal, atypical hyperplastic and carcinomatous uterine glands were used in discriminant analysis. With this method it is possible to discriminate between the three groups of nuclei. Depending on the (sub)set of the variables used, 60-70% of all nuclei are correctly classified in one of the three groups. Discrimination of one of the groups against the other two results in up to 81% correct classifications. Therefore, discriminant analysis offers a possibility of assisting diagnosis in an objective way.

Cell Nucleus

Genetics of classic von Willebrand's disease. II. Optimal assignment of the heterozygous genotype (diagnosis) by discriminant analysis.

In classic von Willebrand's disease (vWd), assignment of the heterozygous genotype for genetic studies and diagnosis for clinical purposes (which are not exactly the same) are formidable problems. We have pointed out in the first report in this series that almost 50% of the members of two large kindred who transmitted this disease, and were therefore heterozygous, were scored as normal by the usual tests of hemostasis. This report describes how this large proportion can be significantly reduced by application of discriminant analysis. Using linear discriminants in three variables--coagulation factor VIII (VIII:C), factor-VII-related antigen (VIIIR:Ag), and the ristocetin cofactor related to factor VIII (VIIIR:WF)--we were able to classify as heterozygous more than 80% of the transmitters in the two large kindred. It was of particular interest that the four parents of two related vWd homozygotes could be scored as heterozygous by discriminant analysis even though all their laboratory tests were within the normal ranges.

Adult

A simulation study of the efficacy of stepwise discriminant analysis in the detection and comparison of event related potentials.

Cortical average evoked potentials were simulated by summing five damped sinusoids. The characteristics of these "evoked" responses could be manipulated by changing parameters of the sinusoids. The synthesized signals were mixed with noise processes whose power and band-width were manipulated. Thus data were generated to stimulate a variety of conditions which could conceivably occur in an experiment on evoked potentials. Stepwise discriminant analysis (BMD07M) has been applied to these simulated data in an attempt to determine the degree to which the program identifies, in a sensible manner, the differences we introduced into the synthesized evoked responses. The simulation results indicate that stepwise discriminant analysis can indeed be an efficacious tool in research on evoked potentials. The program does detect differences in evoked potentials. It can be used, with some reservations, to identify the components of an evoked potential which the experimental variables have affected. In a special set of simulations we have attempted to determine the degree to which stepwise discriminant analysis could serve to detect the presence or absence of an evoked potential. These simulations show that the score of an average evoked potential in the data. The implications of this finding to the use of evoked potentials in sensory sensitivity testing were evaluated in studies for the effect on them of stimulus intensity.

Electroencephalography

[Audiologic diagnosis of sensorineural deafness by discriminant analysis (author's transl)].

The audiometric test-battery surely is a help to the diagnosis of a lesion of the VIIIth nerve. The discriminant analysis is the most suitable statistic procedure for reduction of the test-battery and for clearer decision in cases of ambigous constellation of findings. The persons are divided into three groups: normals, patients with presumable inner-ear disturbance, and those with lesions of the acoustic nerve. By means of the classification-coefficients (a result of the discriminant analysis) in new cases a diagnosis per conclusionem can be found on-line.

Audiometry

Diagnosis of liver diseases by laboratory results and discriminant analysis. Identification of best combinations of laboratory tests.

Patients with different liver diseases were studied by discriminant analysis. Groups of patients classified mainly on the basis of liver biopsy findings showed functional differences which permitted a consistent reclassification by discriminant functions using laboratory results. Optimal combinations of laboratory tests for the separation of liver diseases were defined. Different combinations were found, dependent on the subsets of liver diseases studied.

Acute Disease

Discriminant analysis, exemplified with quantitative features of endometrium.

In this paper we illustrate the potential usefulness of discriminant analysis as a means of separating groups of patients and aiding in differential diagnosis of an individual patient. Some of the most important problems are discussed. The analysis is performed with various microscopical endometrial features of endometrial biopsies from 4 groups of 7 patients in different hormonal conditions. There is some evidence that a combination of stereological features gives a better separation of the groups than the usual histological examinations.

Biopsy

Differentiation between benign and malignant monoclonal gammopathies by discriminant analysis on serum and bone marrow parameters.

Bone marrow samples of 28 individuals with clinically benign and of 41 patients with malignant monoclonal gammopathy were analyzed for the total number of lymphoplasmocellular elements containing cytoplasmic immunoglobulins and for the monoclonal fraction of these cells. Monoclonal immunoglobulin components were determined in sera. A discriminant analysis was performed on the data: the variables were transformed and in a stepwise procedure used for the construction of a discriminant function which by adividing point allowed a good distinction between the two groups of patients. By use of this discriminant function, 91% of the patients in the sample were correctly classified.

Adult

Use of discriminant analysis in relating maternal anti-D levels to the severity of haemolytic disease of the Newborn.

The automated assay of maternal anit-D levels has been compared with manual methods and correlated with the severity of haemolytic disease of the newborn using discriminant analysis. The automated assay of anti-D proved to be marginally better than manual techniques in predicting the need for amniocentesis. The level at which amniocentesis should be considered has been calculated to be 4IU/ml of maternal serum.

Animals

Application of discriminant analysis to level of performance of alcoholics and nonalcoholics on Wechsler-Bellevue and Halstead-Reitan subtests.

Investigated the utility of subtests from the Wechsler-Bellevue Intelligence Scale and the Halstead-Reitan Neuropsychological Test Battery to differentiate between alcoholics and nonalcoholics (N = 76). Analyses of variance indicated that the alcoholics were more impaired than nonalcoholics. It was found that the Wechsler-Bellevue Performance subtests were more discriminative than were Verbal subtests, with performance on the Halstead-Reitan variables being intermediate. The nine measures that differentiated most significantly between groups were subjected to a stepwise multivariate discriminant analysis. The resulting function correctly classified Ss with an overall accuracy of 74.7%. It was found that the Block Design subtest was the best single discriminator. The findings were discussed in relationship to previous findings and with respect to general issues of clinical neuropsychological assessment.

Alcoholism

Discriminant analysis: a method of identifying foci of vector-borne diseases.

Identification of foci of vector-borne diseases does not require knowledge of exact abundances of vectors and pathogens; rather, a focus is defined by the presence, or some minimal level of abundance, of a vector and pathogen. Stepwise discriminant analysis (DA) was applied to data on free-ranging adult wood ticks (the vector) and to data on isolations of Colorado tick fever virus from small mammals. Trap stations were grouped on the basis of relative abundance of wood ticks for one set of analyses and on the presence or absence of virus for another set of analyses. Additional data consisted of easily measured environmental variables. It is concluded that DA provides a useful tool for analysis of ecosystem structure and an effective means of identifying foci of infection.

Animals

Computer discriminant analysis of atypical urothelial cells.

Prior computer studies of digitized cell images by the TICAS system have shown that the category of urothelial cells classified visually as atypical may be composed of 2 subgroups, one clustering mainly with benign cells and the other with malignant cells. As a consequence, a visual review of the group of atypical cells was conducted and tested by computer discriminant analysis. The computer classification confirmed the visual reclassification and subdivision of atypical urothelial cells into 2 subgroups, ATY I and ATY II. This is yet another example of feedback from computer diagnosis to visual assessment of cells. The significance of these observations in terms of diagnosis will be the subject of subsequent communications.

Computers

Discriminant analysis on cells from developing squamous cancer of the respiratory tract.

Cytologic preparations made from the tracheobronchial tree taken by the Schreiber catheter have been scanned by three color microphotometry. The digitized cell images were processed by the analytical cytodiagnostic programs of the TICAS system. Cells were sorted into two control groups and five groups of increasing atypia ranging from normal epithelium to invasive squamous cell carcinoma. Standard statistical tests, including Wilk's Lambda, Rao's V, and the Kruskal-Wallis tests are performed on these subsets of cell image features. This study demonstrates that discriminant analyses permit differentiation between normal cells and those from marked atypia or carcinoma and that the classification achieves a high degree of agreement with visual assignment.

Animals