List of Figures List of Tables Preface to Second Edition Acknowledgments Preface to First Edition Notation I INTRODUCTION 1 Discriminant Analysis in Research 11 A Little History 12 Overview 13 Descriptive Discriminant Analysis 14 Predictive Discriminant Analysis 15 Design in Discriminant Analysis 2 Preliminaries 21 Introduction 22 Research Context 23 Data, Analysis Units, Variables, and Constructs 24 Summarizing Data 25 Matrix Operations 26 Distance 27 Linear Composite 28 Probability 29 Statistical Testing 210 Judgment in Data Analysis 211 Summary II ONE-FACTOR MANOVA/DDA 3 Group Separation 31 Introduction 32 Two-Group Analyses 33 Test for Covariance Matrix Equality 34 Yao Test 35 Multiple-Group Analyses-Single Factor 36 Computer Application 37 Summary 4 Assessing MANOVA Effects 41 Introduction 42 Strength of Association 43 Computer Application I 44 Group Contrasts 45 Computer Application II 46 Covariance Matrix Heterogeneity 47 Sample Size 48 Summary 5 Describing MANOVA Effects 51 Introduction 52 Omnibus Effects 53 Computer Application I 54 Standardized LDFWeights 55 LDF Space Dimension 56 Computer Application II 57 Computer Application III 58 Contrast Effects 59 Computer Application IV 510 Summary 6 Deleting and Ordering Variables 61 Introduction 62 Variable Deletion 63 Variable Ordering 64 Contrast Analyses 65 Computer Application II 66 Comments 7 Reporting DDA Results 71 Introduction 72 Example of Reporting DDA Results 73 Computer Package Information 74 Reporting Terms 75 MANOVA/DDA Applications 76 Concerns 77 Overview III FACTORIAL MANOVA, MANCOVA, AND REPEATED MEASURES 8 Factorial MANOVA 81 Introduction 82 Research Context 83 Univariate Analysis 84 Multivariate Analysis 85 Computer Application I 86 Computer Application II 87 Nonorthogonal Design 88 Outcome Variable Ordering and Deletion 89 Summary 9 Analysis of Covariance 91 Introduction 92 Research Context 93 Univariate ANCOVA 94 Multivariate ANCOVA (MANCOVA) 95 Computer Application I 96 Comparing Adjusted Means-Omnibus Test 97 Computer Application II 98 Contrast Analysis 99 Computer Application III 910 Summary 10 Repeated-Measures Analysis 101 Introduction 102 Research Context 103 Univariate Analyses 104 Multivariate Analysis 105 Computer Application I 106 Univariate and Multivariate Analyses 107 Testing for Sphericity 108 Computer Application II 109 Contrast Analysis 1010 Computer Application III 1011 Summary 11 Mixed-Model Analysis 111 Introduction 112 Research Context 113 Univariate Analysis 114 Multivariate Analysis 115 Computer Application I 116 Contrast Analysis 117 Computer Application II 118 Summary IV GROUP MEMBERSHIP PREDICTION 12 Classification Basics 121 Introduction 122 Notion of Distance 123 Distance and Classification 124 Classification Rules in General 125 Comments 13 Multivariate Normal Rules 131 Introduction 132 Normal Density Functions 133 Classification Rules Based on Normality 134 Classification Functions 135 Summary of Classification Statistics 136 Choice of Rule Form 137 Comments 14 Classification Results 141 Introduction 142 Research Context 143 Computer Application 144 Individual Unit Results 145 Group Results 146 Comments 15 Hit Rate Estimation 151 Introduction 152 True Hit Rates 153 Hit Rate Estimators 154 Computer Application 155 Choice of Hit Rate Estimator 156 Outliers and In-Doubt Units 157 Sample Size 158 Comments 16 Effectiveness of Classification Rules 161 Introduction 162 Proportional Chance Criterion 163 Maximum-Chance Criterion 164 Improvement over Chance 165 Comparison of Rules 166 Computer Application I 167 Effect of Unequal Priors 168 PDA Validity/Reliability 169 Applying a Classification Rule to New Units 1610 Comments 17 Deleting and Ordering Predictors 171 Introduction 172 Predictor Deletion 173 Computer Application 174 Predictor Ordering 175 Reanalysis 176 Comments 177 Side Note 18 Two-Group Classification 181 Introduction 182 Two-Group Rule 183 Regression Analogy 184 MRA-PDA Relationship 185 Necessary Sample Size 186 Univariate Classification 19 Nonnormal Rules 191 Introduction 192 Continuous Variables 193 Categorical Variables 194 Predictor Mixtures 195 Comments 20 Reporting PDA Results 201 Introduction 202 Example of Reporting PDA Results 203 Some Additional Specific PDA Information 204 Computer Package Information 205 Reporting Terms 206 Sources of PDA Applications 207 Concerns 208 Overview Further Reading Exercises 21 PDA-Related Analyses 211 Introduction 212 Nonlinear Methods 213 Other Methods V ISSUES AND PROBLEMS 22 Issues in PDA and DDA 221 Introduction 222 Five Choices in PDA 223 Stepwise Analyses 224 StandardizedWeights Versus Structure r's 225 Data-Based Structure 23 Problems in PDA and DDA 231 Introduction 232 Missing Data 233 Outliers and Influential Observations 234 Initial Group Misclassification 235 Misclassification Costs 236 Statistical Versus Clinical Prediction 237 Other Problems Appendix A: Data Set Descriptions Appendix B: Some DA-Related Originators Appendix C: List of Computer Syntax Appendix D: Contents ofWileyWebsite References Answers to Exercises Index

Applied MANOVA and discriminant analysis

Objective. There is limited information regarding the long-term outcome of inflicted traumatic brain injury (TBI), including shaken infant syndrome. The purpose of this study was to describe the long-term neurologic, behavioral, and cognitive sequelae seen in this population. Methods. A cross-sectional and prospective longitudinal study was conducted of 25 children with inflicted TBI in Scotland between 1980 and 1999. After consent was obtained, neurologic and cognitive examinations were performed on all participants and sequentially in the prospective cohort. Two global outcome measures were used: Glasgow Outcome Score (GOS) and Seshia’s outcome score. Cognitive outcome was assessed using the Bayley Scales of Infant Development, British Ability Scales, and the Vineland Adaptive Behavior Scales. Results. The mean length of follow-up was 59 months. A total of 68% of survivors were abnormal on follow-up, 36% had severe difficulties and were totally dependant, 16% had moderate difficulties, and 16% had mild difficulties on follow-up. A wide range of neurologic sequelae were seen, including motor deficits (60%), visual deficits (48%), epilepsy (20%), speech and language abnormalities (64%), and behavioral problems (52%). There was a wide range of cognitive abilities: the mean psychomotor index, 69.9 (SD: ±25.73); and mean mental development index, 74.53 (SD: ±28.55). Adaptive functioning showed a wide range of difficulties across all domains: communication domain (mean: 76.1; SD: ±25.4), Daily living skills domain (mean: 76.9; SD: ±24.3), and socialization domain (mean: 79.1; SD: ±23.1). Outcome was found to correlate with the Pediatric Trauma Score and the Glasgow Coma Score but did not correlate with age at injury or mechanism of injury. Conclusions. Inflicted TBI has a very poor prognosis and correlates with severity of injury. Extended follow-up is necessary so as not to underestimate problems such as specific learning difficulties and attentional and memory problems that may become apparent only once the child is in school. Behavioral problems are present in 52% and begin to manifest clinically between the second and third years of life, although the consequences of frontal lobe injury may be underestimated unless follow-up is extended into adolescence and early adulthood.

Late Neurologic and Cognitive Sequelae of Inflicted Traumatic Brain Injury in Infancy

The pediatric risk of mortality III— Acute physiology score (PRISM III-APS): A method of assessing physiologic instability for pediatric intensive care unit patients

A parental questionnaire was used to investigate the outcome for children who had had ischaemic stroke, who were seen at Great Ormond Street Hospital, London between 1990 and 1996. The results of functional assessments carried out by a physiotherapist and an occupational therapist, and of quantitative evaluations carried out by a neuropsychologist were used for validation where possible. The relationship between clinical and radiological factors and outcome were examined. The children were aged between 3 months and 15 years at the time of stroke (median age 5 years) and the period of follow‐up ranged from 3 months to 13 years (median duration 3 years). Of the 90 children for whom data were obtained, 13 (14%) had no residual impairments. Outcome was good in 37 children (40%) and poor in 53 (60%) (defined according to whether impairments interfered with daily life). Agreement, as measured by Cohen's kappa, was good or very good between the parents’responses and the qualitative measures provided by the medical professionals and the therapists, but only fair to moderate for the quantitative measures provided by the neuropsychologists. This may reflect different parental perceptions of the physical and cognitive aspects of outcome. Younger age at time of the stroke was the only significant predictor of adverse outcome.

Outcome after ischaemic stroke in childhood.

The Blantyre coma scale (BCS) is used to assess children with severe falciparum malaria, particularly as a criterion for cerebral malaria, but it has not been formally validated. We compared the BCS to the Adelaide coma scale (ACS), for Kenyan children with severe malaria. We examined the inter-observer agreement between 3 observers in the assessment of coma scales on 17 children by measuring the proportion of agreement (PA), disagreement rate (DR) and fixed sample size kappa (kappa n). We assessed the sensitivity and specificity of the scales in detecting events (seizures and hypoglycaemia) in 240 children during admission and the usefulness of the scales in predicting outcome. There was considerable disagreement between observers in the assessment of both scales (BCS: PA = 0.55, DR = 0.09 and kappa n = 0.27; ACS: PA = 0.36, DR = 0.31, and kappa n = 0.31), particularly with the verbal component of the BCS (kappa n = 0.02). Compared to the ACS, the BCS was more specific (0.85 for BCS and 0.80 for ACS), but less sensitive (0.25-0.69 vs. 0.38-0.88 respectively) in detecting events and was a worse predictor of neurological sequelae. The BCS provided a better overall assessment of a child's incapacity from falciparum malaria, but the ACS was more useful in assessing neurological disturbances.

Coma scales for children with severe falciparum malaria

SUMMARY

One hundred and four children suffering from non-traumatic coma were referred to the Pediatric Neurology Service, Children's Hospital, Winnipeg, between February 1976 and December 1978. Stepwise discriminant analysis was used to obtain a classification function of outcome, based on clinical variables determined at two separate time-periods of examination: (1) the time of admission and (2) about 24 hours after onset of coma. 12 clinical variables were included in the stepwise procedure. Seven of these: coma severity, extra-ocular movements, pupils, motor patterns, blood pressure, temperature and seizure type, entered the classification function for the first time-period, data being available for 102 children. 75 per cent of these cases were correctly classified into one of five outcome groups and 8 per cent were seriously misclassified. Similarly, 67 per cent of the 66 children evaluated in the second time-period were correctly classified and 3 per cent seriously misclassified. The variables that entered the classification function in this second time-period were age, coma severity, motor patterns, blood pressure and seizure type. The data suggest that the analysis of clinical variables recorded early in the comatose state can provide predictive information, and stepwise discriminant analysis may be one method of determining the most likely outcome for individual cases.



RESUME

Coma non traumatique de l'enfance: variables cliniques et leur incidence pronostique



104 enfants souffrant d'un coma non traumatique ont ete adresses au Service de Neurologie Pediatrique du Children's Hospital de Winnipeg, entre fevrier 1976 et decembre 1978. Une analyse discriminative par etapes a ete utilisee pour obtenir une classification de devenir basee sur les variables cliniques appreciees a deux epoques d'examen: (1) au moment de l'admission et (2) 24 heures apres le debut du coma. 12 variables cliniques ont fait I'objet de cette appreciation par etapes. Sept d'entre elles: gravite du coma, mouvements extra-oculaires, etats des pupilles, allure de la motricite, tension arterielle, temperature et type de crise, sont entrees dans la classification le premier temps d'examen, toutes les donnees etant disponibles pour 102 enfants. 75 pour cent des cas etaient correctement classes dans I'un des cinq groupes a venir et huit pour cent ont fait I'objet d'un classement fortement errone. De la meme facon, 67 pour cent des 66 enfants examines au deuxieme temps ont ete correctement classes, trois pour cent ont fait I'objet d'une erreur de classification importante: les variables qui sont entrees dans ce second examen ont ete l'âge, la gravite de coma, l'allure de la motricite, la tension arterielle et le type de crise. Nos donnees suggerent que l'analyse des variables cliniques recueillies tot dans I'etat de coma peut fournir des informations predictives et des elements d'analyse discriminative classificatrice, peut etre I'une des methodes a utiliser pour determiner un pronostic individuel



ZUSAMMENFASSUNG

Nicht traumatisches Coma im Kindesalter: klinische Parameter fur die Prognose



In der Zeit von Februar 1976 bis Dezember 1978 wurden 104 Kinder mit einem nicht traumatischen Coma in die Abteilung fur Padiatrische Neurologie des Kinderkrankenhauses in Winnipeg uberwiesen. Eine schrittweise unterscheidende Analyse wurde fur die Prognosestellung zugrundegelegt, diese basierte auf klinischen Parametern von zwei verschiedenen Untersuchungen: (1) bei der Aufnahme und (2) ungefahr 24 Stunden nach Beginn des Comas. 12 klinische Parameter wurden bei diesem schrittweisen Vorgehen berucksichtigt. Sieben davon waren: Schweregrad des Comas, extraokulare Bewegungen, Pupillen, Motorisches Verhalten, Blutdruck, Temperatur und Anfallstyp, diese gingen in die Einteilung der ersten Untersuchungsphase ein, die Daten waren von 102 Kindern vorhanden; 75 Prozent dieser Falle waren in eine von funf Prognosegruppen richtig eingestuft und 8 Prozent waren vollig falsch eingestuft. In ahnlicher Weise waren 67 Prozent der 66 Kinder, die in der zweiten Untersuchungsphase beurteilt wurden, richtig eingestuft und drei Prozent vollig falsch. Die Parameter, die bei dieser zweiten Untersuchungsphase berucksichtigt wurden waren: Alter, Schweregrad des Comas, motorisches Verhalten, Blutdruck und Anfallstyp. Unsere Daten lassen vermuten, das die Analyse der klinischen Parameter aus der Fruhphase des comatosen Zustandes eine prognostische Information geben kann und das die schrittweise unterscheidende Analyse vielleicht eine Methode ist. um fur den individuellen Fall die wahrscheinlichste Prognose zu bestimmen.



RESUMEN

Coma no traumatico en ninos: variables clinicas en la prediccion del curso posterior



Ciento cuatro ninos que sufrian coma no traumatico fueron enviados al Servicio de Neurologia Pediatrica del Hospital Infantil de Winnipeg, entre Febrero de 1976 y Diciembre de 1978. Se aplico un analisis discriminatorio para obtener una clasificacion funcional del curso posterior basado en las variables clinicas registradas en dos periodos de tiempo de examen: (1) en el momento del ingreso y (2) hacia las 24 horas despues del inicio del coma. En el procedimiento se incluyeron 12 variables clinicas. Siete de ellas: gravedad del coma, movimientos extraoculares, pupilas, esquemas motores, esquemas tension arterial, temperatura y tipo de convulsion, se incluyeron en la clasificacion functional en el primer periodo de tiempo con datos obtenidos de 102 ninos: 75 per ciento de estos casos fueron correctamente clasificados dentro de uno de los cinco grupos de curso y 8 por ciento fueron gravemente mal clasificados. Igualmente 67 por ciento de los 66 ninos evaluados en el segundo periodo de tiempo fueron clasificados correctamente y 3 por ciento mal clasificados gravemente. Las variables que entraron en la clasification funcional en segundo periodo de tiempo fueron: edad, gravedad del coma, esquemas motores, tension arterial y tipo de convulsion. Nuestros datos sugieren que el analisis de las variables clinicas registradas precozmente en el estado comatoso puede suministrar informacion predictiva y el analisis discriminatorio puede ser uno de los metodos que pueden ser usados para determinar el curso mas probable en casos individuales.

Non-traumatic coma in childhood: clinical variables in prediction of outcome

The authors evaluated the inter-observer agreement between two experienced clinicians examining 19 unconscious children who were not paralysed or ventilated. Inter-observer reliability was assessed by proportion of agreement, disagreement rate and kappa statistics. Corneal reflexes, pupillary responses to light and motor responses were the most reliably elicited. Reduction of the number of categories improved inter-observer agreement. Some of the disagreement may be attributed to changes in the child's condition during the period of assessment. There was more agreement about the five-category 0-IV scale than the summated Adelaide (10-category) and Jacobi (13-category) scales. The ability of these scales to follow changes in the patient's condition and to predict outcome needs to be evaluated in a prospective trial.

Inter‐observer agreement of the assessment of coma scales and brainstem signs in non‐traumatic coma

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Non-traumatic coma in childhood: clinical variables in prediction of outcome

Inter‐observer agreement of the assessment of coma scales and brainstem signs in non‐traumatic coma