Statistical Methods in Laboratory Medicine

Preface1 Introduction2 Getting the Picture 2.1 Quantitative Variables 2.3 Random Variables 2.4 Measures 2.5 Collecting the Right Data 2.6 Looking at Sample Data 2.7 The Histogram 2.8 Central Tendency 2.9 Scatter 2.10 Exploratory Data Analysis (EDA) References Software3 Probability 3.1 Introduction 3.2 A State of Nature 3.3 A State of Mind 3.4 Axioms of Probability: Terminology 3.5 Axioms of Probability 3.6 Conditional Probability and Statistical Independence 3.7 Rules of Probability 3.8 Bayes’ Theorem 3.9 Odds and Ends References4 Probability Distributions I: Discrete Variables 4.1 Getting the Picture 4.2 The Binomial Distribution 4.3 Fitting the Binomial Model to Sample Data 4.4 The Poisson Distribution 4.5 Non-Random Distributions 4.6 The Negative Binomial Distribution 4.7 Final Thoughts References5 Probability Distributions II: Continuous Variables 5.1 The Normal Distribution 5.2 Probability Density 5.3 Fitting the Normal Distribution Function 5.4 Testing the Normal Model Assumption 5.5 Transformations of Non-Normal Data 5.6 Other Distributions References6 Inference I 6.1 Populations and Samples 6.2 Survey and Experiment 6.3 Sample Selection: Surveys 6.4 Sampling for Experiment 6.5 From Numbers to Knowledge 6.6 Hypothesis Testing 6.7 Sample Size: Inference on a Single Population Mean 6.8 Comparing Two Independent Samples 6.9 Paired Comparisons 6.10 Non-Parametric Tests 6.11 More than Two Samples References7 Regression I: Straight-Line Relationships 7.1 Introduction 7.2 The Nature of Relationships 7.3 Functional Relationships 7.4 Least-Squares Estimates Of The Functional Relation Parameters 7.5 From Arithmetic to Inference 7.6 Inference on the Linear Regression Model 7.7 The Calibration Problem 7.8 Weighted Regression 7.9 The Bivariate Regression Model 7.10 Through the Looking Glass 7.11 Rank Correlation 7.12 Looking Ahead References8 Measurement and Control 8.1 Introduction 8.2 Accuracy 8.3 Functional Assays 8.4 Structural Assays 8.5 Indirect Structural Assays 8.6 The Origins of Inaccuracy 8.7 Analytical Goals for Assay Accuracy 8.8 Precision 8.9 Estimating the Error Variance Components 8.10 Analytical Goals for Assay Precision 8.11 Control 8.12 Cumulative Sum Charts (CUSUMS) 8.13 Patient-Based Imprecision Studies 8.14 Patients' Daily Means 8.15 Qualitative Test Control 8.16 A Parting Thought References9 Assay Method Comparison Studies 9.1 Introduction 9.2 The Statistical Problem 9.3 A Little History 9.4 Calculations 9.5 Cautions 9.6 The Sample Correlation Coefficient 9.7 Final Thoughts References10 Test Interpretation 10.1 Introduction 10.2 A Quest for the Fabulous Norm 10.3 The 95% Reference Paradox 10.4 Multi Variate Reference Ranges 10.5 Screening 10.6 Qualitative Screening Tests 10.7 Quantitative Screening Tests 10.8 Assessing the Individual Patient 10.9 Kernel Density Estimation 10.10 Computer Assisted Diagnosis References11 Multivariate Analysis 11.1 Introduction 11.2 Linear Discriminant Function 11.3 Multivariate Normal Discrimination 11.4 Assessing the Performance of the Classification Rule 11.5 Assessing the Individual Patient 11.6 Quadratic Discrimination and Beyond 11.7 Variable Selection 11.8 Regression Revisited 11.9 Polynomial Regression 11.10 Is there a Pattern? References12 Forecasting And Control 12.1 Introduction 12.2 Time Series Structure and Terminology 12.3 Recursive Estimation 12.4 The Ewma Discount Coefficient W 12.5 Monitoring a Forecasting System 12.6 Following a Trend 12.7 Holt's Local Linear Trend Model 12.8 The Kaiman Filter 12.9 Following a Trend Appendix 12.A GW-BASIC Program-Tracker References13 Inference II: Analysis of 2X2 Tables 13.1 Sampling Models for 2X2 Tables 13.2 The 2X2 Chi-Square Test 13.3 Fisher's Exact Probability Test 13.4 Estimation I: Comparing Proportions 13.5 Estimation I: The Odds-Ratio 13.6 Paired Comparisons 13.7 Combining 2X2 Tables 13.8 Multidimensional Problems 13.9 Regression with Counted Proportions Note 13.A Derivation of a 2X2 X2 Statistic A Note on Notation ReferencesAppendix A Statistical Tables A.1 to A.8 Table A.1 2000 Random Digits Table A.2 Areas Under the Standard Normal Curve Table A.3 Coefficients and Critical Values: Shapiro-Wilk Test Table A.4 Percentiles of the t Distribution (Two-Sided) Table A.5 Upper 100α Percentile Points of the Χ2 Distribution Table A.6 Percentile Points of the F-Distribution (5%) Table A.7 Critical Values of the Linear Correlation Coefficient Table A.8 Random Numbers from a Specified Normal DistributionIndex