PERMUTATION TESTS FOR COMPLEX DATA

Transcription

1 PERMUTATION TESTS FOR COMPLEX DATA Theory, Applications and Software Fortunato Pesarin Luigi Salmaso University of Padua, Italy TECHNISCHE INFORMATIONSBiBUOTHEK UNIVERSITATSBIBLIOTHEK HANNOVER V WILEY A John Wiley and Sons, Ltd., Publication

2 Preface xv Notation and Abbreviations xix 1 Introduction 1 1. J On Permutation Analysis The Permutation Testing Principle Nonparametric Family of Distributions The Permutation Testing Principle Permutation Approaches When and Why Conditioning is Appropriate Randomization and Permutation Computational Aspects Basic Notation A Problem with Paired Observations Modelling Responses Symmetry Induced by Exchangeability Further Aspects The Student's t-paired Solution The Signed Rank Test Solution The McNemar Solution The Permutation Solution General Aspects The Permutation Sample Space The Conditional Monte Carlo Method Approximating the Permutation Distribution Problems and Exercises A Two-Sample Problem Modelling Responses The Student t Solution The Permutation Solution Rank Solutions Problems and Exercises One-WayANOVA Modelling Responses Permutation Solutions Problems and Exercises 32

3 viii 2 Theory of One-Dimensional Permutation Tests Introduction Notation and Basic Assumptions The Conditional Reference Space Conditioning on a Set of Sufficient Statistics Definition of Permutation Tests / General Aspects Randomized Permutation Tests Non-randomized Permutation Tests The p-value A CMC Algorithm for Estimating the p-value Some Useful Test Statistics Equivalence of Permutation Statistics Some Examples Problems and Exercises Arguments for Selecting Permutation Tests Examples of One-Sample Problems A Problem with Repeated Observations Problems and Exercises Examples of Multi-Sample Problems Analysis of Ordered Categorical Variables General Aspects A Solution Based on Score Transformations Typical Goodness-of-Eit Solutions Extension to Non-Dominance Alternatives and C Groups Problems and Exercises 80 3 Further Properties of Permutation Tests Unbiasedness of Two-sample Tests One-Sided Alternatives Two-Sided Alternatives Power Functions of Permutation Tests Definition and Algorithmfor the Conditional Power The Empirical Conditional ROC Curve Definition and Algorithmfor the Unconditional Power: Fixed Effects Unconditional Power; Random Effects Comments on Power Functions Consistency of Permutation Tests Permutation Confidence Interval for S Problems and Exercises Extending Inference from Conditional to Unconditional Optimal Properties J Problems and Exercises Some Asymptotic Properties Introduction Two Basic Theorems Permutation Central Limit Theorems Basic Notions Permutation Central Limit Theorems Problems and Exercises 113

4 ix 4 The Nonparametric Combination Methodology Introduction General Aspects Bibliographic Nates Main Assumptions and Notation Some Comments The Nonparametric Combination Methodology Assumptions on Partial Tests Desirable Properties of Combining Functions A Two-Phase Algorithm for Nonparametric Combination Some Useful Combining Functions Why Combination is Nonparametric On Admissible Combining Functions Problems and Exercises Consistency, Unbiasedness and Power of Combined Tests Consistency Unbiasedness A Non-consistent Combining Function Power of Combined Tests Conditional Multivariate Confidence Region for S Problems and Exercises Some Further Asymptotic Properties General Conditions Asymptotic Properties Finite-Sample Consistency Introduction Finite-Sample Consistency Some Applications of Finite-Sample Consistency Some Examples of Nonparametric Combination Problems and Exercises Comments on the Nonparametric Combination General Comments Final Remarks Multiplicity Control and Closed Testing Defining Raw and Adjusted p-values Controlling for Multiplicity Multiple Comparison and Multiple Testing Some Definitions of the Global Type I Error Multiple Testing The Closed Testing Approach Closed Testing for Multiple Testing Closed Testing Using the MinP Bonferroni-Holm Procedure Mult Data Example Analysis Using MATLAB Analysis Using R Washing Test Data Analysis Using MATLAB Analysis Using R Weighted Methods for Controlling FWE and FDR 193

5 X 5.8 Adjusting Stepwise p-values Showing Biasedness of Standard p-values for Stepwise Regression Algorithm Description Optimal Subset Procedures Analysis of Multivariate Categorical Variables Introduction The Multivariate McNemar Test An Extension of the Multivariate McNemar Test Multivariate Goodness-of-Fit Testing for Ordered Variables Multivariate Extension of Fisher's Exact Probability Test MANOVA with Nominal Categorical Data Stochastic Ordering Formal Description Further Breaking Down the Hypotheses Permutation Test Mullifocus Analysis General Aspects The Multifocus Solution An Application Isotonic Inference Introduction Allelic Association Analysis in Genetics Parametric Solutions Permutation Approach Test on Moments for Ordered Variables General Aspects Score Transformations and Univariate Tests Multivariate Extension Heterogeneity Comparisons Introduction Tests for Comparing Heterogeneities A Case Study in Population Genetics Application to PhD Programme Evaluation Using SAS Description of the Problem Global Satisfaction Index Multivariate Performance Comparisons Permutation Testing for Repeated Measurements Introduction Carry-Over Effects in Repeated Measures Designs Modelling Repeated Measurements A General Additive Model Hypotheses of Interest Testing Solutions J Solutions Using the NPC Approach Analysis of Two-Sample Dominance Problems Analysis of the Cross-Over (AB-BA) Design Analysis of a Cross-Over Design with Paired Data Testing for Repeated Measurements with Missing Data 232

6 xi 7.6 General Aspects of Permutation Testing with Missing Data Bibliographic Notes On Missing Data Processes Data Missing Completely at Random Data Missing Not at Random The Permutation Approach Deletion, Imputation and Intention to Treat Strategies Breaking Down the Hypotheses The Structure of Testing Problems Hypotheses for MNAR Models Hypotheses for MCAR Models Permutation Structure with Missing Values Permutation Analysis of Missing Values Partitioning the Permutation Sample Space Solution for Two-Sample MCAR Problems Extensions to Multivariate C-Sample Problems Extension to MNAR Models Germina Data: An Example of an MNAR Model Problem Description The Permutation Solution Analysis Using MATLAB Analysis Using R Multivariate Paired Observations Repeated Measures and Missing Data An Example Botulinum Data Analysis Using MATLAB Analysis Using R Waterfalls Data Analysis Using MATLAB Analysis Using R Some Stochastic Ordering Problems Multivariate Ordered Alternatives Testing for Umbrella Alternatives Hypotheses and Tests in Simple Stochastic Ordering Permutation Tests for Umbrella Alternatives Analysis of Experimental Tumour Growth Curves Analysis of PERC Data Introduction A Permutation Solution Analysis Using MATLAB Analysis Using R NPC Tests for Survival Analysis Introduction and Main Notation Failure Time Distributions Data Structure Comparison of Survival Curves An Overview of the Literature 292

7 xii 9.3,1 Permutation Tests in Sunival Analysis Two NPC Tests Breaking Down the Hypotheses The Test Structure NPC Test for Treatment-Independent Censoring NPC Test for Treatment-Dependent Censoring An Application to a Biomedical Study NPC Tests in Shape Analysis Introduction A Brief Overview of Statistical Shape Analysis How to Describe Shapes Multivariate Morphometries Inference with Shape Data NPC Approach to Shape Analysis Notation ,4.2 Comparative Simulation Study NPC Analysis with Correlated Landmarks An Application to Mediterranean Monk Seal Skulls The Case Study Some Remarks Shape Analysis Using MATLAB Shape Analysis Using R Multivariate Correlation Analysis and Two-Way ANOVA Autofluorescence Case Study A Permutation Solution Analysis Using MATLAB Analysis Using R Confocal Case Study A Permutation Solution MATLAB and R Codes Two-Way (M)ANOVA Brief Overview of Permutation Tests in Two-Way ANOVA MANOVA Using MATLAB and R Codes Some Case Studies Using NPC Test R10 and SAS Macros An Integrated Approach to Survival Analysis in Observational Studies A Case Study on Oesophageal Cancer A Permutation Solution Suivival Analysis with Stratification by Propensity Score Integrating Propensity Score and NPC Testing Analysis Using MATLAB Further Applications with NPC Test R10 and SAS Macros A Two-Sample Epidemiological Survey: Problem Description Analysing SETIG Data Using MATLAB Analysing the SETIG Data Using R Analysing the SETIG Data Using NPC Test Analysis of the SETIG Data Using SAS A Comparison of Three Survival Curves 370

8 xiii Unstratified Survival Analysis Survival Analysis with Stratification by Propensity Score Survival Analysis Using NPC Test and SAS Survival Analysis Using NPC Test Survival Analysis Using SAS Survival Analysis Using MATLAB Logistic Regression and NPC Test for Multivariate Analysis / Application to Lymph Application Node Metastases 378 to Bladder Cancer NPC Results Analysis by Logistic Regression Some Comments 385 References 387 Index 409