Introductory Medical Statistics, 3rd edition

Introductory Medical Statistics: 3rd edition......Page 1
Contents......Page 6
Preface......Page 13
1.3 PIE CHART......Page 15
1.4 HISTOGRAM......Page 17
1.5 PICTOGRAM......Page 18
1.6 SCATTER DIAGRAM......Page 20
1.8 GRAPHS: LINEAR AND LOGARITHMIC AXES......Page 21
1.9 EXPONENTIALS......Page 26
1.10 VENN AND EULER DIAGRAMS......Page 30
1.11 BOX AND WHISKERS PLOT......Page 31
2.2 MEAN, MODE AND MEDIAN......Page 32
2.3 SKEWNESS......Page 36
2.4 STANDARD DEVIATION AND VARIANCE......Page 38
2.5 COEFFICIENT OF VARIATION......Page 41
2.6 PROBABILITY DENSITY FUNCTION......Page 42
3.2 MATHEMATICAL FORMULA......Page 44
3.3 MATHEMATICAL TABLES......Page 45
3.4 NORMAL PROBABILITY GRAPH PAPER......Page 51
3.5 TESTING FOR NORMALITY USING THE CHI-SQUARED TEST......Page 54
3.6 THE LOGNORMAL CURVE......Page 56
4.1 INTRODUCTION......Page 65
4.3 CENTRAL LIMIT THEOREM......Page 67
4.4 FORMULAE FOR STANDARD ERRORS......Page 69
4.7 ERRORS OF INTERPRETATION......Page 70
4.8 RANDOM ERRORS......Page 71
4.10 ROOT MEAN SQUARE ERROR......Page 72
4.11 CONFIDENCE LIMITS......Page 73
5.1 DESCRIPTIONS OF PROBABILITY......Page 74
5.3 BAYESIAN PROBABILITY......Page 76
6.1 PERMUTATIONS AND COMBINATIONS......Page 79
6.2 THE BINOMIAL DISTRIBUTION......Page 81
6.3 EXAMPLES OF BINOMIAL PROBLEMS......Page 82
6.4 THE NORMAL APPROXIMATION TO THE BINOMIAL......Page 85
6.5 GAMBLING WITH DICE......Page 88
7.1 THE POISSON DISTRIBUTION......Page 92
7.2 EXAMPLES OF POISSON PROBLEMS......Page 94
7.5 RADIOACTIVE DECAY......Page 96
8.1 THE NULL HYPOTHESIS......Page 99
8.2 NULL, POSITIVE AND NEGATIVE RESULTS OF STUDIES......Page 100
8.3.2 Clinical and Statistical Significance......Page 101
8.4 TYPE-I AND TYPE-II ERRORS AND ALPHA AND BETA RISKS......Page 102
8.5 A GENERALISED SCHEDULE FOR SIGNIFICANCE TESTING......Page 104
8.6 DEGREES OF FREEDOM......Page 105
9.1 INTRODUCTION......Page 107
9.2 GOODNESS OF FIT: PRECISION OF NUCLEAR MEDICINE COUNTING INSTRUMENTS......Page 110
9.3 GOODNESS OF FIT: A RACING PROBLEM......Page 111
9.4 GOODNESS OF FIT: A POISSON PROBLEM......Page 114
9.5 GOODNESS OF FIT: A LOGNORMAL CURVE FITTING PROBLEM......Page 115
9.6 THE 2 x 2 CONTINGENCY TABLE......Page 116
9.7 A 2 x 2 CONTINGENCY TABLE: A CHOLERA EPIDEMIC PROBLEM......Page 118
9.8 THE GENERALISED r x c CONTINGENCY TABLE......Page 119
9.9 YATES CORRECTION FOR SMALL SAMPLES......Page 121
9.10 DID MENDEL CHEAT?......Page 122
10.2 ONE-TAILED EXAMPLE......Page 124
10.3 TWO-TAILED EXAMPLE......Page 127
11.1 INTRODUCTION......Page 129
11.2 ESTIMATE OF THE POPULATION MEAN p FROM THE SAMPLE MEAN zm AND CALCULATION OF CONFIDENCE LIMITS......Page 131
11.4 PAIRED t-TEST: DIFFERENCE BETWEEN MEANS......Page 134
11.5 UNPAIRED TWO-SAMPLE t-TEST......Page 135
11.6 NORMAL TEST FOR THE DIFFERENCE BETWEEN MEANS OF LARGE SAMPLES......Page 138
12.1 INDEPENDENT SAMPLES FROM NORMAL POPULATIONS......Page 141
12.2 McNEMAR’S TEST FOR DIFFERENCE BETWEEN PAIRED PROPORTIONS......Page 142
13.2 WILCOXON SIGNED RANKS TEST FOR MATCHED PAIRS......Page 146
13.3 WILCOXON RANK SUM TEST FOR UNPAIRED DATA......Page 149
13.4 MANN-WHITNEY U TEST......Page 155
13.5 KRUSKAL-WALLIS TEST......Page 156
13.6 SIGN TEST......Page 157
14.1 INTRODUCTION......Page 161
14.2 BASIC DATA FOR THE WORKED EXAMPLES......Page 165
14.3.1 Ranking procedure for survival times......Page 166
14.3.2 Probability of dying at time Ti......Page 167
14.3.4 Calculation of cancer-specific survival rates......Page 168
14.3.5 Standard errors......Page 173
14.4.1 When to group data and when not to group data......Page 174
14.4.3 Grouping procedure for the survival times......Page 175
14.4.4 Probability of dying at time T......Page 176
14.4.7 Standard errors......Page 178
15.1 INTRODUCTION......Page 182
15.2.2 Worked example......Page 183
15.3.2 Worked example......Page 185
16.1 INTRODUCTION......Page 192
16.2 METHOD OF LEAST SQUARES FOR ESTIMATION OF THE SLOPE AND INTERCEPT OF A STRAIGHT LINE......Page 197
16.3 REGRESSION LINES......Page 201
16.5 TESTING FOR A SIGNIFICANT CORRELATION: AN APPLICATION OF THE t-TEST......Page 202
16.6 SPEARMAN’S RANK CORRELATION COEFFICIENT......Page 205
16.7 KENDALL’S t RANK CORRELATION COEFFICIENT......Page 206
17.1 INTRODUCTION......Page 210
17.2 THE F-TEST......Page 213
17.3 ONE-WAY ANOVA: WORKED EXAMPLE......Page 217
17.4.1 Example 1......Page 222
17.4.2 Example 2......Page 223
17.5 RELATIONSHIP BETWEEN CORRELATION COEFFICIENT AND A ONE-WAY ANOVA TABLE......Page 225
18.1 INTRODUCTION......Page 227
18.2 HAZARD FUNCTION, CUMULATIVE DISTRIBUTION FUNCTION AND SURVIVOR FUNCTION......Page 228
18.4 HAZARD EQUATION FOR THREE PROGNOSTIC FACTORS......Page 230
18.5 RELAXATION OF THE ASSUMPTION OF PROPORTIONALITY OF HAZARDS......Page 231
18.6 EXAMPLE: LOCOREGIONAL RECURRENCE OF BREAST CANCER......Page 232
18.7.2 Likelihood Ratio Test......Page 235
18.7.3 Table of Results......Page 237
18.7.4 Relative Risk: Ratio Between Hazards......Page 238
18.7.5 Stepwise Selection of Variables......Page 239
18.8 EXAMPLES: BREAST CANCER......Page 241
19.1 DEFINITIONS......Page 246
19.3 RECEIVER OPERATING CHARACTERISTIC ROC CURVE......Page 247
19.4 EXAMPLE: PROSTATE CANCER EARLY DETECTION......Page 249
19.5 EXAMPLE: NUCLEAR MEDICINE IMAGING INTERLABORATORY COMPARISON STUDIES......Page 251
19.6 KAPPA TEST......Page 253
20.2 TRIAL AIMS AND OBJECTIVES......Page 256
20.3 TRIAL DESCRIPTION BY PHASES I-III......Page 257
20.4 PHASE I TRIALS......Page 258
20.5.1 Methods of Randomisation......Page 260
20.5.2 Single Randomisation......Page 261
20.5.4 Balanced Randomisation......Page 264
20.7 PHASE II TRIALS......Page 265
20.7.1 Gehan’s Design......Page 267
20.7.1.1 Number of Patients Required for a Phase IIA Trial......Page 268
20.7.1.2 Number of Patients Required for a Phase IIB Trial......Page 269
20.8 PHASE III TRIALS......Page 270
20.8.1 Number of Patients Required for a Phase III Trial......Page 273
20.8.2 Power Curves......Page 277
20.8.3 Interim Analyses......Page 278
20.8.5 Inflation Factor Due to Patient Refusals......Page 280
20.9 SEQUENTIAL TRIALS......Page 281
20.1 1 META-ANALYSIS......Page 284
20.12 REPORTING CLINICAL TRIAL RESULTS......Page 287
21.1 INTRODUCTION......Page 292
21.2 QUALITATIVE ASSESSMENT......Page 297
21.4 QUALITY OF LIFE: 10-POINT OR FOUR-POINT SCALE?......Page 298
21.5 FURTHER EXAMPLES OF QUALITY OF LIFE STATUS SCORING......Page 300
21.5.1 Lung......Page 303
21.5.2 Limbs......Page 304
21.5.3 Head and Neck......Page 306
21.6 SELF ASSESSMENT VERSUS EXTERNAL EVALUATION......Page 307
21.7.1 Relative Survival Rate and Cohort Interpolated Life Tables......Page 308
21.7.2 Method of Easson and Russell......Page 310
21.8 ENDPOINTS: DISEASE-FREE SURVIVAL VERSUS OVERALL SURVIVAL......Page 311
21.10 SCORING OF COMPLICATIONS......Page 315
21.11 QUALITY OF LIFE OF CANCER PATIENTS IN DEVELOPING COUNTRIES......Page 317
21.12.1 Introduction......Page 318
21.12.2 Bayesian Statistics Application: Treatment Optimisation......Page 319
21.13 ECONOMIC THEORY APPLICATION AND QUALITY OF LIFE......Page 320
21.13.3 Net Benefit and Net Detriment......Page 321
22.1 INTRODUCTION......Page 324
22.2 DEFINITIONS OF ABSOLUTE RISK AND RELATIVE RISK......Page 326
22.4 HIROSHIMA AND NAGASAKI......Page 329
22.5 CHERNOBYL......Page 331
22.6 BREAST CANCER......Page 334
22.7 MORTALITY RATIO......Page 335
22.8 LUNG CANCER AND SMOKING......Page 336
22.9 EDUCATIONAL CARTOONS ON CANCER RISK......Page 338
23.1 INTRODUCTION......Page 341
23.2.1 Selection of Cases......Page 342
23.2.2 Selection of Controls......Page 343
23.3 COHORT STUDIES......Page 345
23.3.1 Example: The Framingham Study......Page 346
23.5 CROSS-SECTIONAL STUDIES......Page 348
23.6.2 Confounding......Page 350
23.7 OTHER TYPES OF EPIDEMIOLOGICAL STUDY: CLUSTER ANALYSES OF HISTORICAL INTEREST......Page 351
23.7.1 The Unique Hostel......Page 352
23.7.2 The Broad Street Pump......Page 355
23.7.3 Typhoid Mary......Page 356
Glossary of Rates and Ratios: Terminology in Vital Statistics......Page 361
References......Page 374