Medical Statistics From Scratch: An Introduction For Health Professionals

Description

Correctly understanding and using medical statistics is a key skill for all medical students and health professionals. In an informal and friendly style, Medical Statistics from Scratch provides a practical foundation for everyone whose first interest is probably not medical statistics. Keeping the level of mathematics to a minimum, it clearly illustrates statistical concepts and practice with numerous real-world examples and cases drawn from current medical literature. Medical Statistics from Scratch is an ideal learning partner for all medical students and health professionals needing an accessible introduction, or a friendly refresher, to the fundamentals of medical statistics. 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