Medical Statistics From Scratch: An Introduction For Health Professionals

Cover......Page 1
Title Page......Page 5
Copyright Page......Page 6
Brief Contents......Page 7
Contents......Page 11
Preface to the 4th Edition......Page 21
Preface to the 3rd Edition......Page 23
Preface to the 2nd Edition......Page 25
Preface to the 1st Edition......Page 27
Introduction......Page 29
Part I Some Fundamental Stuff......Page 31
Variables and data......Page 33
The good, the bad, and the ugly – types of variables......Page 35
Nominal categorical data......Page 36
Ordinal categorical data......Page 37
Discrete metric data......Page 38
Continuous metric data......Page 39
How can I tell what type of variable I am dealing with?......Page 40
The baseline table......Page 41
Part II Descriptive Statistics......Page 45
Chapter 2 Describing data with tables......Page 47
Frequency tables – nominal data......Page 48
The frequency distribution......Page 49
Frequency tables – ordinal data......Page 50
Frequency tables with discrete metric data......Page 52
Cumulative frequency......Page 54
Frequency tables with continuous metric data – grouping the raw data......Page 55
Open-ended groups
......Page 57
Cross-tabulation – contingency tables
......Page 58
Ranking data......Page 60
Chapter 3 Every picture tells a story – describing data with charts......Page 61
The pie chart......Page 62
The simple bar chart......Page 64
The clustered bar chart......Page 65
The stacked bar chart......Page 67
The histogram......Page 69
The box (and whisker) plot......Page 72
The cumulative frequency curve with continuous metric data......Page 74
Charting time-based data – the time series chart......Page 77
The scatterplot......Page 78
The bubbleplot......Page 79
The shape of things to come......Page 81
Skewness and kurtosis as measures of shape......Page 82
Kurtosis......Page 85
Normalness – the Normal distribution......Page 86
Bimodal distributions......Page 88
Determining skew from a box plot......Page 89
Numbers, percentages, and proportions......Page 92
Preamble......Page 93
Numbers, percentages, and proportions......Page 94
Handling percentages – for those of us who might need a reminder......Page 95
Summary measures of location......Page 97
The mode......Page 98
The median......Page 99
The mean......Page 100
Percentiles......Page 101
Calculating a percentile value......Page 102
What is the most appropriate measure of location?......Page 103
Chapter 6 Measures of spread – Numbers R Us – (again)......Page 105
The interquartile range (IQR)......Page 106
Estimating the median and interquartile range from the cumulative frequency curve......Page 107
The boxplot (also known as the box and whisker plot)......Page 109
Standard deviation......Page 112
Standard deviation and the Normal distribution......Page 114
Using SPSS......Page 116
Using Minitab......Page 117
Transforming data......Page 118
Chapter 7 Incidence, prevalence, and standardisation......Page 122
The incidence rate and the incidence rate ratio (IRR)......Page 123
Prevalence......Page 124
Crude mortality rate......Page 127
Case fatality rate......Page 128
Age-specific mortality rate
......Page 129
Standardisation – the age-standardised mortality rate
......Page 131
The direct method......Page 132
The standard population and the comparative mortality ratio (CMR)......Page 133
The indirect method......Page 136
The standardised mortality rate......Page 137
Part III The Confounding Problem......Page 141
Chapter 8 Confounding – like the poor, (nearly) always with us......Page 143
What is confounding?......Page 144
Confounding by indication......Page 147
Detecting confounding......Page 149
Using restriction......Page 150
One-to-one matching
......Page 151
Using randomisation......Page 152
Part IV Design and Data......Page 155
Chapter 9 Research design – Part I: Observational study designs......Page 157
Preamble......Page 158
Types of study......Page 159
Case reports......Page 160
Cross-sectional studies
......Page 161
Confounding in descriptive cross-sectional studies
......Page 162
Analytic cross-sectional studies
......Page 163
Confounding in analytic cross-sectional studies
......Page 164
From here to eternity – cohort studies......Page 165
Back to the future – case–control studies......Page 169
Confounding in the case–control study design......Page 171
Another example of a case–control study......Page 172
Comparing cohort and case–control designs......Page 173
Ecological studies......Page 174
The ecological fallacy......Page 175
Chapter 10 Research design – Part II: Getting stuck in – experimental studies......Page 176
Clinical trials......Page 177
Randomisation and the randomised controlled trial (RCT)......Page 178
Blinding......Page 179
The crossover RCT......Page 180
Selection of participants for an RCT......Page 183
Intention to treat analysis (ITT)......Page 184
Chapter 11 Getting the participants for your study: ways of sampling......Page 186
From populations to samples – statistical inference......Page 187
Collecting the data – types of sample......Page 188
The systematic random sample......Page 189
The cluster sample......Page 190
Consecutive and convenience samples......Page 191
Inclusion and exclusion criteria......Page 192
Getting the data......Page 193
Part V Chance Would Be a Fine Thing......Page 195
Preamble......Page 197
Calculating probability – proportional frequency......Page 198
Rule 1. The multiplication rule for independent events......Page 199
Rule 2. The addition rule for mutually exclusive events......Page 200
Probability distributions......Page 201
The binomial probability distribution......Page 202
The Poisson probability distribution......Page 203
The normal probability distribution......Page 204
Chapter 13 Risk and odds......Page 205
Absolute risk and the absolute risk reduction (ARR)......Page 206
The reduction in the risk ratio (or relative risk reduction (RRR))......Page 208
Reference value......Page 209
Number needed to treat (NNT)......Page 210
What happens if the initial risk is small?......Page 211
Confounding with the risk ratio......Page 212
Odds......Page 213
Why you can’t calculate risk in a case–control study......Page 215
The odds ratio......Page 216
Approximating the risk ratio from the odds ratio......Page 219
Part VI The Informed Guess – An Introduction to Confidence Intervals......Page 221
Chapter 14 Estimating the value of a single population parameter – the idea of confidence intervals......Page 223
Confidence interval estimation for a population mean......Page 224
The standard error of the mean......Page 225
How we use the standard error of the mean to calculate a confidence interval for a population mean......Page 227
An example from practice......Page 229
Confidence interval for a population proportion......Page 230
Estimating a confidence interval for the median of a single population......Page 233
Chapter 15 Using confidence intervals to compare two population parameters......Page 236
Comparing two independent population means......Page 237
An example using birthweights......Page 238
Assessing the evidence using the confidence interval (and was the sample size large enough?)......Page 241
Within-subject and between‐subject variations
......Page 245
Comparing two independent population proportions......Page 247
An example from practice......Page 248
Comparing two independent population medians – the Mann–Whitney rank sums method......Page 249
Comparing two matched population medians – the Wilcoxon signed‐ranks method......Page 250
An example from practice......Page 252
Chapter 16 Confidence intervals for the ratio of two population parameters......Page 254
An example from practice......Page 255
Confidence interval for a population risk ratio......Page 256
An example from practice......Page 257
An example from practice......Page 258
Confidence intervals for a population odds ratio......Page 259
An example from practice......Page 260
Confidence intervals for hazard ratios......Page 262
Part VII Putting it to the Test......Page 265
Chapter 17 Testing hypotheses about the difference between two population parameters......Page 267
The hypothesis......Page 268
The null hypothesis......Page 269
The hypothesis testing process......Page 270
The p-value and the decision rule
......Page 271
A brief summary of a few of the commonest tests......Page 272
Using the p-value to compare the means of two independent populations
......Page 274
Output from Minitab – two‐sample t test of difference in mean birthweights of babies born to white mothers and to non-white mothers
......Page 275
Output from SPSS: two‐sample t test of difference in mean birthweights of babies born to white mothers and to non-white mothers
......Page 276
Using p-values to compare the medians of two independent populations: the Mann–Whitney rank-sums test
......Page 278
How the Mann–Whitney test works......Page 279
The Bonferroni correction for multiple testing......Page 280
With SPSS......Page 282
Confidence intervals versus hypothesis testing......Page 284
What could possibly go wrong?......Page 285
Types of error......Page 286
An example from practice......Page 287
Rule of thumb 1. Comparing the means of two independent populations (metric data)......Page 288
Rule of thumb 2. Comparing the proportions of two independent populations (binary data)......Page 289
Chapter 18 The Chi-squared (2) test – what, why, and how?
......Page 291
Using chi-squared to test for related-ness or for the equality of proportions
......Page 292
Calculating the chi-squared statistic
......Page 295
Using the chi-squared statistic......Page 297
Fisher’s exact test......Page 298
The chi-squared test with Minitab
......Page 299
The chi-squared test with spss
......Page 300
The chi-squared test for trend
......Page 302
Spss output for chi-squared trend test
......Page 304
Preamble......Page 306
The chi-squared test with the risk ratio
......Page 307
The chi-squared test with odds ratios
......Page 309
The chi-squared test with hazard ratios
......Page 311
Part VIII Becoming Acquainted......Page 313
Chapter 20 Measuring the association between two variables......Page 315
Preamble – plotting data......Page 316
The scatterplot......Page 317
Pearson’s correlation coefficient......Page 320
Is the correlation coefficient statistically significant in the population?......Page 322
An example from practice......Page 323
Spearman’s rank correlation coefficient......Page 324
An example from practice......Page 325
To agree or not agree: that is the question......Page 328
Cohen’s kappa ()......Page 330
Measuring the agreement between two metric continuous variables, the Bland–Altmann plot......Page 333
Part IX Getting into a Relationship......Page 337
Chapter 22 Straight line models: linear regression......Page 339
Relationship and association......Page 340
A causal relationship – explaining variation......Page 342
Refresher – finding the equation of a straight line from a graph......Page 343
The linear regression model......Page 344
First, is the relationship linear?......Page 345
Estimating the regression parameters – the method of ordinary least squares (OLS)......Page 346
Basic assumptions of the ordinary least squares procedure......Page 347
Using spss to regress birthweight on mother’s weight......Page 348
Using Minitab......Page 349
Goodness-of-fit, R2
......Page 350
Multiple linear regression......Page 352
Adjusted goodness-of-fit: R2
......Page 354
Including nominal covariates in the regression model: design variables and coding......Page 356
Building your model. Which variables to include?......Page 357
Automated variable selection methods......Page 358
Manual variable selection methods......Page 359
Adjustment and confounding......Page 360
An example from practice......Page 361
Diagnostics – checking the basic assumptions of the multiple linear regression model......Page 362
Analysis of variance......Page 363
Chapter 23 Curvy models: logistic regression......Page 364
Finding an appropriate model when the outcome variable is binary......Page 365
The logistic regression model......Page 367
Interpreting the regression coefficients......Page 368
Have we got a significant result? statistical inference in the logistic regression model......Page 370
The Odds Ratio......Page 371
The multiple logistic regression model......Page 373
Building the model......Page 374
Goodness-of-fit
......Page 376
Chapter 24 Counting models: Poisson regression......Page 379
Poisson regression......Page 380
The Poisson regression equation......Page 381
Interpreting the estimated coefficients of a Poisson regression, b0 and b1......Page 382
Model building – variable selection......Page 385
Goodness-of-fit
......Page 387
Zero-inflated Poisson regression
......Page 388
Negative binomial regression......Page 389
Zero-inflated negative binomial regression
......Page 391
Part X Four More Chapters......Page 393
Chapter 25 Measuring survival......Page 395
A simple example of survival in a single group......Page 396
Calculating survival probabilities and the proportion surviving: the Kaplan–Meier table......Page 398
Determining median survival time......Page 399
Comparing survival with two groups......Page 400
The log-rank test
......Page 401
The hazard ratio......Page 402
The proportional hazards (Cox’s) regression model – introduction......Page 403
The proportional hazards (Cox’s) regression model – the detail......Page 406
An example of proportional hazards regression......Page 407
Chapter 26 Systematic review and meta‐analysis......Page 410
Systematic review......Page 411
The forest plot......Page 413
Publication and other biases......Page 414
The funnel plot......Page 416
Significance tests for bias – Begg’s and Egger’s tests......Page 417
The problem of heterogeneity – the Q and I2 tests......Page 419
Preamble......Page 423
The measures – sensitivity and specificity......Page 424
The positive prediction and negative prediction values (PPV and NPV)......Page 425
The sensitivity–specificity trade-off
......Page 426
Using the ROC curve to find the optimal sensitivity versus specificity trade‐off......Page 427
The missing data problem......Page 430
Missing at Random (MAR)......Page 433
Missing not at random (MNAR)......Page 434
Dealing with missing data......Page 435
List-wise deletion
......Page 436
Pair-wise deletion
......Page 437
Replacement by the Mean......Page 438
Last observation carried forward......Page 439
Regression-based imputation
......Page 440
Multiple imputation......Page 441
Full Information Maximum Likelihood (FIML) and other methods......Page 442
Table of random numbers......Page 444
References......Page 445
Solutions to exercises......Page 454
Index......Page 487
EULA......Page 498