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Contents

Preface to the 4th Edition xix Preface to the 3rd Edition xxi Preface to the 2nd Edition xxiii Preface to the 1st Edition xxv Introduction xxvii I Some Fundamental Stuff 1 1 First things first - the nature of data 3 Variables and data 3 Where are we going ...? 5 The good, the bad, and the ugly - types of variables 5 Categorical data 6 Nominal categorical data 6 Ordinal categorical data 7 Metric data 8 Discrete metric data 8 Continuous metric data 9 How can I tell what type of variable I am dealing with? 10 The baseline table 11 II Descriptive Statistics 15 2 Describing data with tables 17 Descriptive statistics. What can we do with raw data? 18 Frequency tables - nominal data 18 The frequency distribution 19 Relative frequency 20 Frequency tables - ordinal data 20 Frequency tables - metric data 22 Frequency tables with discrete metric data 22 Cumulative frequency 24 Frequency tables with continuous metric data - grouping the raw data 25 Open-ended groups 27 Cross-tabulation - contingency tables 28 Ranking data 30 3 Every picture tells a story - describing data with charts 31 Picture it! 32 Charting nominal and ordinal data 32 The pie chart 32 The simple bar chart 34 The clustered bar chart 35 The stacked bar chart 37 Charting discrete metric data 39 Charting continuous metric data 39 The histogram 39 The box (and whisker) plot 42 Charting cumulative data 44 The cumulative frequency curve with discrete metric data 44 The cumulative frequency curve with continuous metric data 44 Charting time-based data - the time series chart 47 The scatterplot 48 The bubbleplot 49 4 Describing data from its shape 51 The shape of things to come 51 Skewness and kurtosis as measures of shape 52 Kurtosis 55 Symmetric or mound-shaped distributions 56 Normalness - the Normal distribution 56 Bimodal distributions 58 Determining skew from a box plot 59 5 Measures of location - Numbers R us 62 Numbers, percentages, and proportions 62 Preamble 63 N umbers, percentages, and proportions 64 Handling percentages - for those of us who might need a reminder 65 Summary measures of location 67 The mode 68 The median 69 The mean 70 Percentiles 71 Calculating a percentile value 72 What is the most appropriate measure of location? 73 6 Measures of spread - Numbers R us - (again) 75 Preamble 76 The range 76 The interquartile range (IQR) 76 Estimating the median and interquartile range from the cumulative frequency curve 77 The boxplot (also known as the box and whisker plot) 79 Standard deviation 82 Standard deviation and the Normal distribution 84 Testing for Normality 86 Using SPSS 86 Using Minitab 87 Transforming data 88 7 Incidence, prevalence, and standardisation 92 Preamble 93 The incidence rate and the incidence rate ratio (IRR) 93 The incidence rate ratio 94 Prevalence 94 A couple of difficulties with measuring incidence and prevalence 97 Some other useful rates 97 Crude mortality rate 97 Case fatality rate 98 Crude maternal mortality rate 99 Crude birth rate 99 Attack rate 99 Age-specific mortality rate 99 Standardisation - the age-standardised mortality rate 101 The direct method 102 The standard population and the comparative mortality ratio (CMR) 103 The indirect method 106 The standardised mortality rate 107 III The Confounding Problem 111 8 Confounding - like the poor, (nearly) always with us 113 Preamble 114 What is confounding? 114 Confounding by indication 117 Residual confounding 119 Detecting confounding 119 Dealing with confounding - if confounding is such a problem, what can we do about it? 120 Using restriction 120 Using matching 121 Frequency matching 121 One-to-one matching 121 Using stratification 122 Using adjustment 122 Using randomisation 122 IV Design and Data 125 9 Research design - Part I: Observational study designs 127 Preamble 128 Hey ho! Hey ho! it's off to work we go 129 Types of study 129 Observational studies 130 Case reports 130 Case series studies 131 Cross-sectional studies 131 Descriptive cross-sectional studies 132 Confounding in descriptive cross-sectional studies 132 Analytic cross-sectional studies 133 Confounding in analytic cross-sectional studies 134 From here to eternity - cohort studies 135 Confounding in the cohort study design 139 Back to the future - case-control studies 139 Confounding in the case-control study design 141 Another example of a case-control study 142 Comparing cohort and case-control designs 143 Ecological studies 144 The ecological fallacy 145 10 Research design - Part II: getting stuck in - experimental studies 146 Clinical trials 147 Randomisation and the randomised controlled trial (RCT) 148 Block randomisation 149 Stratification 149 Blinding 149 The crossover RCT 150 Selection of participants for an RCT 153 Intention to treat analysis (ITT) 154 11 Getting the participants for your study: ways of sampling 156 From populations to samples - statistical inference 157 Collecting the data - types of sample 158 The simple random sample and its offspring 159 The systematic random sample 159 The stratified random sample 160 The cluster sample 160 Consecutive and convenience samples 161 How many participants should we have? Sample size 162 Inclusion and exclusion criteria 162 Getting the data 163 V Chance Would Be a Fine Thing 165 12 The idea of probability 167 Preamble 167 Calculating probability - proportional frequency 168 Two useful rules for simple probability 169 Rule 1. The multiplication rule for independent events 169 Rule 2. The addition rule for mutually exclusive events 170 Conditional and Bayesian statistics 171 Probability distributions 171 Discrete versus continuous probability distributions 172 The binomial probability distribution 172 The Poisson probability distribution 173 The Normal probability distribution 174 13 Risk and odds 175 Absolute risk and the absolute risk reduction (ARR) 176 The risk ratio 178 The reduction in the risk ratio (or relative risk reduction (RRR)) 178 A general formula for the risk ratio 179 Reference value 179 N umber needed to treat (NNT) 180 What happens if the initial risk is small? 181 Confounding with the risk ratio 182 Odds 183 Why you can't calculate risk in a case-control study 185 The link between probability and odds 186 The odds ratio 186 Confounding with the odds ratio 189 Approximating the risk ratio from the odds ratio 189 VI The Informed Guess - An Introduction to Confidence Intervals 191 14 Estimating the value of a single population parameter - the idea of confidence intervals 193 Confidence interval estimation for a population mean 194 The standard error of the mean 195 How we use the standard error of the mean to calculate a confidence interval for a population mean 197 Confidence interval for a population proportion 200 Estimating a confidence interval for the median of a single population 203 15 Using confidence intervals to compare two population parameters 206 What's the difference? 207 Comparing two independent population means 207 An example using birthweights 208 Assessing the evidence using the confidence interval 211 Comparing two paired population means 215 Within-subject and between-subject variations 215 Comparing two independent population proportions 217 Comparing two independent population medians - the Mann-Whitney rank sums method 219 Comparing two matched population medians - the Wilcoxon signed-ranks method 220 16 Confidence intervals for the ratio of two population parameters 224 Getting a confidence interval for the ratio of two independent population means 225 Confidence interval for a population risk ratio 226 Confidence intervals for a population odds ratio 229 Confidence intervals for hazard ratios 232 VII Putting it to the Test 235 17 Testing hypotheses about the difference between two population parameters 237 Answering the question 238 The hypothesis 238 The null hypothesis 239 The hypothesis testing process 240 The p-value and the decision rule 241 A brief summary of a few of the commonest tests 242 Using the p-value to compare the means of two independent populations 244 Interpreting computer hypothesis test results for the difference in two independent population means - the two-sample t test 245 Output from Minitab - two-sample t test of difference in mean birthweights of babies born to white mothers and to non-white mothers 245 Output from SPSS_: two-sample t test of difference in mean birthweights of babies born to white mothers and to non-white mothers 246 Comparing the means of two paired populations - the matched-pairs t test 248 Using p-values to compare the medians of two independent populations: the Mann-Whitney rank-sums test 248 How the Mann-Whitney test works 249 Correction for multiple comparisons 250 The Bonferroni correction for multiple testing 250 Interpreting computer output for the Mann-Whitney test 252 With Minitab 252 With SPSS 252 Two matched medians - the Wilcoxon signed-ranks test 254 Confidence intervals versus hypothesis testing 254 What could possibly go wrong? 255 Types of error 256 The power of a test 257 Maximising power - calculating sample size 258 Rule of thumb 1. Comparing the means of two independent populations (metric data) 258 Rule of thumb 2. Comparing the proportions of two independent populations (binary data) 259 18 The Chi-squared (?2) test - what, why, and how? 261 Of all the tests in all the world - you had to walk into my hypothesis testing procedure 262 Using chi-squared to test for related-ness or for the equality of proportions 262 Calculating the chi-squared statistic 265 Using the chi-squared statistic 267 Yate's correction (continuity correction) 268 Fisher's exact test 268 The chi-squared test with Minitab 269 The chi-squared test with SPSS 270 The chi-squared test for trend 272 SPSS output for chi-squared trend test 274 19 Testing hypotheses about the ratio of two population parameters 276 Preamble 276 The chi-squared test with the risk ratio 277 The chi-squared test with odds ratios 279 The chi-squared test with hazard ratios 281 VIII Becoming Acquainted 283 20 Measuring the association between two variables 285 Preamble - plotting data 286 Association 287 The scatterplot 287 The correlation coefficient 290 Pearson's correlation coefficient 290 Is the correlation coefficient statistically significant in the population? 292 Spearman's rank correlation coefficient 294 21 Measuring agreement 298 To agree or not agree: that is the question 298 Cohen's kappa (?) 300 Some shortcomings of kappa 303 Weighted kappa 303 Measuring the agreement between two metric continuous variables, the Bland-Altmann plot 303 IX Getting into a Relationship 307 22 Straight line models: linear regression 309 Health warning! 310 Relationship and association 310 A causal relationship - explaining variation 312 Refresher - finding the equation of a straight line from a graph 313 The linear regression model 314 First, is the relationship linear? 315 Estimating the regression parameters - the method of ordinary least squares (OLS) 316 Basic assumptions of the ordinary least squares procedure 317 Back to the example - is the relationship statistically significant? 318 Using SPSS to regress birthweight on mother's weight 318 Using Minitab 319 Interpreting the regression coefficients 320 Goodness-of-fit, R2 320 Multiple linear regression 322 Adjusted goodness-of-fit: R¯2 324 Including nominal covariates in the regression model: design variables and coding 326 Building your model. Which variables to include? 327 Automated variable selection methods 328 Manual variable selection methods 329 Adjustment and confounding 330 Diagnostics - checking the basic assumptions of the multiple linear regression model 332 Analysis of variance 333 23 Curvy models: logistic regression 334 A second health warning! 335 The binary outcome variable 335 Finding an appropriate model when the outcome variable is binary 335 The logistic regression model 337 Estimating the parameter values 338 Interpreting the regression coefficients 338 Have we got a significant result? statistical inference in the logistic regression model 340 The Odds Ratio 341 The multiple logistic regression model 343 Building the model 344 Goodness-of-fit 346 24 Counting models: Poisson regression 349 Preamble 350 Poisson regression 350 The Poisson regression equation 351 Estimating ß1 and ß2 with the estimators b0 and b1 352 Interpreting the estimated coefficients of a Poisson regression, b0 and b1 352 Model building - variable selection 355 Goodness-of-fit 357 Zero-inflated Poisson regression 358 Negative binomial regression 359 Zero-inflated negative binomial regression 361 X Four More Chapters 363 25 Measuring survival 365 Preamble 366 Censored data 366 A simple example of survival in a single group 366 Calculating survival probabilities and the proportion surviving: the Kaplan-Meier table 368 The Kaplan-Meier curve 369 Determining median survival time 369 Comparing survival with two groups 370 The log-rank test 371 An example of the log-rank test in practice 372 The hazard ratio 372 The proportional hazards (Cox's) regression model - introduction 373 The proportional hazards (Cox's) regression model - the detail 376 Checking the assumptions of the proportional hazards model 377 An example of proportional hazards regression 377 26 Systematic review and meta-analysis 380 Introduction 381 Systematic review 381 The forest plot 383 Publication and other biases 384 The funnel plot 386 Significance tests for bias - Begg's and Egger's tests 387 Combining the studies: meta-analysis 389 The problem of heterogeneity - the Q and I2 tests 389 27 Diagnostic testing 393 Preamble 393 The measures - sensitivity and specificity 394 The positive prediction and negative prediction values (PPV and NPV) 395 The sensitivity-specificity trade-off 396 Using the ROC curve to find the optimal sensitivity versus specificity trade-off 397 28 Missing data 400 The missing data problem 400 Types of missing data 403 Missing completely at random (MCAR) 403 Missing at Random (MAR) 403 Missing not at random (MNAR) 404 Consequences of missing data 405 Dealing with missing data 405 Do nothing - the wing and prayer approach 406 List-wise deletion 406 Pair-wise deletion 407 Imputation methods - simple imputation 408 Replacement by the Mean 408 Last observation carried forward 409 Regression-based imputation 410 Multiple imputation 411 Full Information Maximum Likelihood (FIML) and other methods 412 Appendix: Table of random numbers 414 References 415 Solutions to Exercises 424 Index 457

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