Statistical Methods in Laboratory Medicine (eBook)

Front Cover 1
Statistical Methods in Laboratory Medicine 4
Copyright Page 5
Table of Contents 8
Preface 6
Chapter 1. Introduction 12
Chapter 2. Getting the picture 17
2.1 Quantitative variables 17
2.3 Random variables 19
2.4 Measures 20
2.5 Collecting the right data 22
2.6 Looking at sample data 24
2.7 The histogram 27
2.8 Central tendency 30
2.9 Scatter 34
2.10 Exploratory data analysis (EDA) 40
References 48
Software 48
Chapter 3. Probability 49
3.1 Introduction 49
3.2 A state of nature 50
3.3 A state of mind 53
3.4 Axioms of probability: terminology 54
3.5 Axioms of probability 58
3.6 Conditional probability and statistical independence 59
3.7 Rules of probability 64
3.8 Bayes' theorem 68
3.9 Odds and ends 78
References 80
Chapter 4. Probability distributions I: discrete variables 81
4.1 Getting the picture 81
4.2 The binomial distribution 83
4.3 Fitting the binomial model to sample data 86
4.4 The Poisson distribution 93
4.5 Non-random distributions 97
4.6 The negative binomial distribution 100
4.7 Final thoughts 105
References 106
Chapter 5. Probability distributions II: continuous variables 107
5.1 The Normal distribution 107
5.2 Probability density 109
5.3 Fitting the Normal distribution function 113
5.4 Testing the Normal model assumption 119
5.5 Transformations of non-Normal data 126
5.6 Other distributions 137
References 139
Chapter 6. Inference I 140
6.1 Populations and samples 140
6.2 Survey and experiment 141
6.3 Sample selection: surveys 141
6.4 Sampling for experiment 146
6.5 From numbers to knowledge 156
6.6 Hypothesis testing 170
6.7 Sample size: inference on a single population mean 174
6.8 Comparing two independent samples 180
6.9 Paired comparisons 186
6.10 Non-parametric tests 191
6.11 More than two samples 191
References 193
Chapter 7. Regression I: straight-line relationships 195
7.1 Introduction 195
7.2 The nature of relationships 198
7.3 Functional relationships 199
7.4 Least-squares estimates of the functional relation parameters 206
7.5 From arithmetic to inference 209
7.6 Inference on the linear regression model 229
7.7 The calibration problem 236
7.8 Weighted regression 243
7.9 The bivariate regression model 247
7.10 Through the looking glass 262
7.11 Rank correlation 262
7.12 Looking ahead 263
References 263
Chapter 8. Measurement and control 265
8.1 Introduction 265
8.2 Accuracy 266
8.3 Functional assays 266
8.4 Structural assays 270
8.5 Indirect structural assays 271
8.6 The origins of inaccuracy 273
8.7 Analytical goals for assay accuracy 279
8.8 Precision 280
8.9 Estimating the error variance components 284
8.10 Analytical goals for assay precision 290
8.11 Control 295
8.12 Cumulative sum charts (CUSUMS) 299
8.13 Patient-based imprecision studies 311
8.14 Patients' daily means 312
8.15 Qualitative test control 314
8.16 A parting thought 315
References 315
Chapter 9. Assay method comparison studies 318
9.1 Introduction 318
9.2 The statistical problem 320
9.3 A little history 325
9.4 Calculations 329
9.5 Cautions 335
9.6 The sample correlation coefficient 339
9.7 Final thoughts 340
References 341
Chapter 10. Test interpretation 342
10.1 Introduction 342
10.2 A quest for the fabulous norm 343
10.3 The 95% reference paradox 344
10.4 Multivariate reference ranges 346
10.5 Screening 347
10.6 Qualitative screening tests 350
10.7 Quantitative screening tests 353
10.8 Assessing the individual patient 370
10.9 Kernel density estimation 380
10.10 Computer assisted diagnosis 388
References 392
Chapter 11. Multivariate analysis 394
11.1 Introduction 394
11.2 Linear discriminant function 394
11.3 Multivariate Normal discrimination 406
11.4 Assessing the performance of the classification rule 410
11.5 Assessing the individual patient 415
11.6 Quadratic discrimination and beyond 417
11.7 Variable selection 421
11.8 Regression revisited 421
11.9 Polynomial regression 426
11.10 Is there a pattern? 430
References 431
Chapter 12. Forecasting and control 433
12.1 Introduction 433
12.2 Time series structure and terminology 434
12.3 Recursive estimation 438
12.4 The EWMA discount coefficient W 448
12.5 Monitoring a forecasting system 449
12.6 Following a trend 456
12.7 Holt's local linear trend model 460
12.8 The Kalman filter 466
12.9 Following a trend 475
Appendix 12.A GW-BASIC program-tracker 482
References 485
Chapter 13. Inference II: analysis of 2x2 tables 488
13.1 Sampling models for 2 x 2 tables 488
13.2 The 2 x 2 chi-square test 491
13.3 Fisher's exact probability test 495
13.4 Estimation I: comparing proportions 498
13.5 Estimation II: the odds-ratio 502
13.6 Paired comparisons 506
13.7 Combining 2 x 2 tables 510
13.8 Multidimensional problems 518
13.9 Regression with counted proportions 519
Note 13.A Derivation of a 2 x 2 X2 statistic 529
A note on notation 532
References 532
Appendix A: Statistical Tables A.1 to A.8 534
Table A.1 2000 random digits 534
Table A.2 Areas under the standard Normal curve 535
Table A.3 Coefficients and critical values: Shapiro-Wilk test 537
Table A.4 Percentiles of the t distribution (two-sided) 540
Table A.5 Upper 100a percentile points of the x2 distribution 541
Table A.6 Percentile points of the F-distribution (5%) 542
Table A.7 Critical values of the linear correlation coefficient 543
Table A.8 Random numbers from a specified Normal distribution 544
Index 545