{"product_id":"medical-statistics-from-scratch-9781119523888","title":"Medical Statistics from Scratch","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface to the 4th Edition xix\u003c\/p\u003e \u003cp\u003ePreface to the 3rd Edition xxi\u003c\/p\u003e \u003cp\u003ePreface to the 2nd Edition xxiii\u003c\/p\u003e \u003cp\u003ePreface to the 1st Edition xxv\u003c\/p\u003e \u003cp\u003eIntroduction xxvii\u003c\/p\u003e \u003cp\u003e\u003cb\u003eI Some Fundamental Stuff 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 First things first – the nature of data 3\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eVariables and data 3\u003c\/p\u003e \u003cp\u003eWhere are we going …? 5\u003c\/p\u003e \u003cp\u003eThe good, the bad, and the ugly – types of variables 5\u003c\/p\u003e \u003cp\u003eCategorical data 6\u003c\/p\u003e \u003cp\u003eNominal categorical data 6\u003c\/p\u003e \u003cp\u003eOrdinal categorical data 7\u003c\/p\u003e \u003cp\u003eMetric data 8\u003c\/p\u003e \u003cp\u003eDiscrete metric data 8\u003c\/p\u003e \u003cp\u003eContinuous metric data 9\u003c\/p\u003e \u003cp\u003eHow can I tell what type of variable I am dealing with? 10\u003c\/p\u003e \u003cp\u003eThe baseline table 11\u003c\/p\u003e \u003cp\u003e\u003cb\u003eII Descriptive Statistics 15\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Describing data with tables 17\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eDescriptive statistics. What can we do with raw data? 18\u003c\/p\u003e \u003cp\u003eFrequency tables – nominal data 18\u003c\/p\u003e \u003cp\u003eThe frequency distribution 19\u003c\/p\u003e \u003cp\u003eRelative frequency 20\u003c\/p\u003e \u003cp\u003eFrequency tables – ordinal data 20\u003c\/p\u003e \u003cp\u003eFrequency tables – metric data 22\u003c\/p\u003e \u003cp\u003eFrequency tables with discrete metric data 22\u003c\/p\u003e \u003cp\u003eCumulative frequency 24\u003c\/p\u003e \u003cp\u003eFrequency tables with continuous metric data – grouping the raw data 25\u003c\/p\u003e \u003cp\u003eOpen‐ended groups 27\u003c\/p\u003e \u003cp\u003eCross‐tabulation – contingency tables 28\u003c\/p\u003e \u003cp\u003eRanking data 30\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Every picture tells a story – describing data with charts 31\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003ePicture it! 32\u003c\/p\u003e \u003cp\u003eCharting nominal and ordinal data 32\u003c\/p\u003e \u003cp\u003eThe pie chart 32\u003c\/p\u003e \u003cp\u003eThe simple bar chart 34\u003c\/p\u003e \u003cp\u003eThe clustered bar chart 35\u003c\/p\u003e \u003cp\u003eThe stacked bar chart 37\u003c\/p\u003e \u003cp\u003eCharting discrete metric data 39\u003c\/p\u003e \u003cp\u003eCharting continuous metric data 39\u003c\/p\u003e \u003cp\u003eThe histogram 39\u003c\/p\u003e \u003cp\u003eThe box (and whisker) plot 42\u003c\/p\u003e \u003cp\u003eCharting cumulative data 44\u003c\/p\u003e \u003cp\u003eThe cumulative frequency curve with discrete metric data 44\u003c\/p\u003e \u003cp\u003eThe cumulative frequency curve with continuous metric data 44\u003c\/p\u003e \u003cp\u003eCharting time‐based data – the time series chart 47\u003c\/p\u003e \u003cp\u003eThe scatterplot 48\u003c\/p\u003e \u003cp\u003eThe bubbleplot 49\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Describing data from its shape 51\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eThe shape of things to come 51\u003c\/p\u003e \u003cp\u003eSkewness and kurtosis as measures of shape 52\u003c\/p\u003e \u003cp\u003eKurtosis 55\u003c\/p\u003e \u003cp\u003eSymmetric or mound‐shaped distributions 56\u003c\/p\u003e \u003cp\u003eNormalness – the Normal distribution 56\u003c\/p\u003e \u003cp\u003eBimodal distributions 58\u003c\/p\u003e \u003cp\u003eDetermining skew from a box plot 59\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Measures of location – Numbers R us 62\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eNumbers, percentages, and proportions 62\u003c\/p\u003e \u003cp\u003ePreamble 63\u003c\/p\u003e \u003cp\u003eN umbers, percentages, and proportions 64\u003c\/p\u003e \u003cp\u003eHandling percentages – for those of us who might need a reminder 65\u003c\/p\u003e \u003cp\u003eSummary measures of location 67\u003c\/p\u003e \u003cp\u003eThe mode 68\u003c\/p\u003e \u003cp\u003eThe median 69\u003c\/p\u003e \u003cp\u003eThe mean 70\u003c\/p\u003e \u003cp\u003ePercentiles 71\u003c\/p\u003e \u003cp\u003eCalculating a percentile value 72\u003c\/p\u003e \u003cp\u003eWhat is the most appropriate measure of location? 73\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Measures of spread – Numbers R us – (again) 75\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003ePreamble 76\u003c\/p\u003e \u003cp\u003eThe range 76\u003c\/p\u003e \u003cp\u003eThe interquartile range (IQR) 76\u003c\/p\u003e \u003cp\u003eEstimating the median and interquartile range from the cumulative frequency curve 77\u003c\/p\u003e \u003cp\u003eThe boxplot (also known as the box and whisker plot) 79\u003c\/p\u003e \u003cp\u003eStandard deviation 82\u003c\/p\u003e \u003cp\u003eStandard deviation and the Normal distribution 84\u003c\/p\u003e \u003cp\u003eTesting for Normality 86\u003c\/p\u003e \u003cp\u003eUsing SPSS 86\u003c\/p\u003e \u003cp\u003eUsing Minitab 87\u003c\/p\u003e \u003cp\u003eTransforming data 88\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Incidence, prevalence, and standardisation 92\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003ePreamble 93\u003c\/p\u003e \u003cp\u003eThe incidence rate and the incidence rate ratio (IRR) 93\u003c\/p\u003e \u003cp\u003eThe incidence rate ratio 94\u003c\/p\u003e \u003cp\u003ePrevalence 94\u003c\/p\u003e \u003cp\u003eA couple of difficulties with measuring incidence and prevalence 97\u003c\/p\u003e \u003cp\u003eSome other useful rates 97\u003c\/p\u003e \u003cp\u003eCrude mortality rate 97\u003c\/p\u003e \u003cp\u003eCase fatality rate 98\u003c\/p\u003e \u003cp\u003eCrude maternal mortality rate 99\u003c\/p\u003e \u003cp\u003eCrude birth rate 99\u003c\/p\u003e \u003cp\u003eAttack rate 99\u003c\/p\u003e \u003cp\u003eAge‐specific mortality rate 99\u003c\/p\u003e \u003cp\u003eStandardisation – the age‐standardised mortality rate 101\u003c\/p\u003e \u003cp\u003eThe direct method 102\u003c\/p\u003e \u003cp\u003eThe standard population and the comparative mortality ratio (CMR) 103\u003c\/p\u003e \u003cp\u003eThe indirect method 106\u003c\/p\u003e \u003cp\u003eThe standardised mortality rate 107\u003c\/p\u003e \u003cp\u003e\u003cb\u003eIII The Confounding Problem 111\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Confounding – like the poor, (nearly) always with us 113\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003ePreamble 114\u003c\/p\u003e \u003cp\u003eWhat is confounding? 114\u003c\/p\u003e \u003cp\u003eConfounding by indication 117\u003c\/p\u003e \u003cp\u003eResidual confounding 119\u003c\/p\u003e \u003cp\u003eDetecting confounding 119\u003c\/p\u003e \u003cp\u003eDealing with confounding – if confounding is such a problem, what can we do about it? 120\u003c\/p\u003e \u003cp\u003eUsing restriction 120\u003c\/p\u003e \u003cp\u003eUsing matching 121\u003c\/p\u003e \u003cp\u003eFrequency matching 121\u003c\/p\u003e \u003cp\u003eOne‐to‐one matching 121\u003c\/p\u003e \u003cp\u003eUsing stratification 122\u003c\/p\u003e \u003cp\u003eUsing adjustment 122\u003c\/p\u003e \u003cp\u003eUsing randomisation 122\u003c\/p\u003e \u003cp\u003e\u003cb\u003eIV Design and Data 125\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Research design – Part I: Observational study designs 127\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003ePreamble 128\u003c\/p\u003e \u003cp\u003eHey ho! Hey ho! it’s off to work we go 129\u003c\/p\u003e \u003cp\u003eTypes of study 129\u003c\/p\u003e \u003cp\u003eObservational studies 130\u003c\/p\u003e \u003cp\u003eCase reports 130\u003c\/p\u003e \u003cp\u003eCase series studies 131\u003c\/p\u003e \u003cp\u003eCross‐sectional studies 131\u003c\/p\u003e \u003cp\u003eDescriptive cross‐sectional studies 132\u003c\/p\u003e \u003cp\u003eConfounding in descriptive cross‐sectional studies 132\u003c\/p\u003e \u003cp\u003eAnalytic cross‐sectional studies 133\u003c\/p\u003e \u003cp\u003eConfounding in analytic cross‐sectional studies 134\u003c\/p\u003e \u003cp\u003eFrom here to eternity – cohort studies 135\u003c\/p\u003e \u003cp\u003eConfounding in the cohort study design 139\u003c\/p\u003e \u003cp\u003eBack to the future – case–control studies 139\u003c\/p\u003e \u003cp\u003eConfounding in the case–control study design 141\u003c\/p\u003e \u003cp\u003eAnother example of a case–control study 142\u003c\/p\u003e \u003cp\u003eComparing cohort and case–control designs 143\u003c\/p\u003e \u003cp\u003eEcological studies 144\u003c\/p\u003e \u003cp\u003eThe ecological fallacy 145\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Research design – Part II: getting stuck in – experimental studies 146\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eClinical trials 147\u003c\/p\u003e \u003cp\u003eRandomisation and the randomised controlled trial (RCT) 148\u003c\/p\u003e \u003cp\u003eBlock randomisation 149\u003c\/p\u003e \u003cp\u003eStratification 149\u003c\/p\u003e \u003cp\u003eBlinding 149\u003c\/p\u003e \u003cp\u003eThe crossover RCT 150\u003c\/p\u003e \u003cp\u003eSelection of participants for an RCT 153\u003c\/p\u003e \u003cp\u003eIntention to treat analysis (ITT) 154\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Getting the participants for your study: ways of sampling 156\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eFrom populations to samples – statistical inference 157\u003c\/p\u003e \u003cp\u003eCollecting the data – types of sample 158\u003c\/p\u003e \u003cp\u003eThe simple random sample and its offspring 159\u003c\/p\u003e \u003cp\u003eThe systematic random sample 159\u003c\/p\u003e \u003cp\u003eThe stratified random sample 160\u003c\/p\u003e \u003cp\u003eThe cluster sample 160\u003c\/p\u003e \u003cp\u003eConsecutive and convenience samples 161\u003c\/p\u003e \u003cp\u003eHow many participants should we have? Sample size 162\u003c\/p\u003e \u003cp\u003eInclusion and exclusion criteria 162\u003c\/p\u003e \u003cp\u003eGetting the data 163\u003c\/p\u003e \u003cp\u003e\u003cb\u003eV Chance Would Be a Fine Thing 165\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 The idea of probability 167\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003ePreamble 167\u003c\/p\u003e \u003cp\u003eCalculating probability – proportional frequency 168\u003c\/p\u003e \u003cp\u003eTwo useful rules for simple probability 169\u003c\/p\u003e \u003cp\u003eRule 1. The multiplication rule for independent events 169\u003c\/p\u003e \u003cp\u003eRule 2. The addition rule for mutually exclusive events 170\u003c\/p\u003e \u003cp\u003eConditional and Bayesian statistics 171\u003c\/p\u003e \u003cp\u003eProbability distributions 171\u003c\/p\u003e \u003cp\u003eDiscrete versus continuous probability distributions 172\u003c\/p\u003e \u003cp\u003eThe binomial probability distribution 172\u003c\/p\u003e \u003cp\u003eThe Poisson probability distribution 173\u003c\/p\u003e \u003cp\u003eThe Normal probability distribution 174\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Risk and odds 175\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eAbsolute risk and the absolute risk reduction (ARR) 176\u003c\/p\u003e \u003cp\u003eThe risk ratio 178\u003c\/p\u003e \u003cp\u003eThe reduction in the risk ratio (or relative risk reduction (RRR)) 178\u003c\/p\u003e \u003cp\u003eA general formula for the risk ratio 179\u003c\/p\u003e \u003cp\u003eReference value 179\u003c\/p\u003e \u003cp\u003eN umber needed to treat (NNT) 180\u003c\/p\u003e \u003cp\u003eWhat happens if the initial risk is small? 181\u003c\/p\u003e \u003cp\u003eConfounding with the risk ratio 182\u003c\/p\u003e \u003cp\u003eOdds 183\u003c\/p\u003e \u003cp\u003eWhy you can’t calculate risk in a case–control study 185\u003c\/p\u003e \u003cp\u003eThe link between probability and odds 186\u003c\/p\u003e \u003cp\u003eThe odds ratio 186\u003c\/p\u003e \u003cp\u003eConfounding with the odds ratio 189\u003c\/p\u003e \u003cp\u003eApproximating the risk ratio from the odds ratio 189\u003c\/p\u003e \u003cp\u003e\u003cb\u003eVI The Informed Guess – An Introduction to Confidence Intervals 191\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Estimating the value of a \u003ci\u003esingle \u003c\/i\u003epopulation parameter – the idea of confidence intervals 193\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eConfidence interval estimation for a population mean 194\u003c\/p\u003e \u003cp\u003eThe standard error of the mean 195\u003c\/p\u003e \u003cp\u003eHow we use the standard error of the mean to calculate a confidence interval for a population mean 197\u003c\/p\u003e \u003cp\u003eConfidence interval for a population proportion 200\u003c\/p\u003e \u003cp\u003eEstimating a confidence interval for the median of a single population 203\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Using confidence intervals to compare two population parameters 206\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eWhat’s the difference? 207\u003c\/p\u003e \u003cp\u003eComparing two \u003ci\u003eindependent \u003c\/i\u003epopulation means 207\u003c\/p\u003e \u003cp\u003eAn example using birthweights 208\u003c\/p\u003e \u003cp\u003eAssessing the evidence using the confidence interval 211\u003c\/p\u003e \u003cp\u003eComparing two \u003ci\u003epaired \u003c\/i\u003epopulation means 215\u003c\/p\u003e \u003cp\u003eWithin‐subject and between‐subject variations 215\u003c\/p\u003e \u003cp\u003eComparing two \u003ci\u003eindependent \u003c\/i\u003epopulation proportions 217\u003c\/p\u003e \u003cp\u003eComparing two \u003ci\u003eindependent \u003c\/i\u003epopulation medians – the Mann–Whitney rank sums method 219\u003c\/p\u003e \u003cp\u003eComparing two \u003ci\u003ematched \u003c\/i\u003epopulation medians – the Wilcoxon signed‐ranks method 220\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 Confidence intervals for the \u003ci\u003eratio \u003c\/i\u003eof two population parameters 224\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eGetting a confidence interval for the \u003ci\u003eratio \u003c\/i\u003eof two independent population means 225\u003c\/p\u003e \u003cp\u003eConfidence interval for a population risk ratio 226\u003c\/p\u003e \u003cp\u003eConfidence intervals for a population odds ratio 229\u003c\/p\u003e \u003cp\u003eConfidence intervals for hazard ratios 232\u003c\/p\u003e \u003cp\u003e\u003cb\u003eVII Putting it to the Test 235\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e17 Testing hypotheses about the \u003ci\u003edifference \u003c\/i\u003ebetween two population parameters 237\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eAnswering the question 238\u003c\/p\u003e \u003cp\u003eThe hypothesis 238\u003c\/p\u003e \u003cp\u003eThe null hypothesis 239\u003c\/p\u003e \u003cp\u003eThe hypothesis testing process 240\u003c\/p\u003e \u003cp\u003eThe p‐value and the decision rule 241\u003c\/p\u003e \u003cp\u003eA brief summary of a few of the commonest tests 242\u003c\/p\u003e \u003cp\u003eUsing the \u003ci\u003ep\u003c\/i\u003e‐value to compare the means of two independent populations 244\u003c\/p\u003e \u003cp\u003eInterpreting computer hypothesis test results for the difference in two independent population means – the two‐sample \u003ci\u003et \u003c\/i\u003etest 245\u003c\/p\u003e \u003cp\u003eOutput from Minitab – two‐sample \u003ci\u003et \u003c\/i\u003etest of difference in mean birthweights of babies born to white mothers and to non‐white mothers 245\u003c\/p\u003e \u003cp\u003eOutput from SPSS_: two‐sample \u003ci\u003et \u003c\/i\u003etest of difference in mean birthweights of babies born to white mothers and to non‐white mothers 246\u003c\/p\u003e \u003cp\u003eComparing the means of two paired populations – the matched‐pairs \u003ci\u003et \u003c\/i\u003etest 248\u003c\/p\u003e \u003cp\u003eUsing \u003ci\u003ep\u003c\/i\u003e‐values to compare the medians of two independent populations: the Mann–Whitney rank‐sums test 248\u003c\/p\u003e \u003cp\u003eHow the Mann–Whitney test works 249\u003c\/p\u003e \u003cp\u003eCorrection for multiple comparisons 250\u003c\/p\u003e \u003cp\u003eThe Bonferroni correction for multiple testing 250\u003c\/p\u003e \u003cp\u003eInterpreting computer output for the Mann–Whitney test 252\u003c\/p\u003e \u003cp\u003eWith Minitab 252\u003c\/p\u003e \u003cp\u003eWith SPSS 252\u003c\/p\u003e \u003cp\u003eTwo matched medians – the Wilcoxon signed‐ranks test 254\u003c\/p\u003e \u003cp\u003eConfidence intervals versus hypothesis testing 254\u003c\/p\u003e \u003cp\u003eWhat could possibly go wrong? 255\u003c\/p\u003e \u003cp\u003eTypes of error 256\u003c\/p\u003e \u003cp\u003eThe power of a test 257\u003c\/p\u003e \u003cp\u003eMaximising power – calculating sample size 258\u003c\/p\u003e \u003cp\u003eRule of thumb 1. Comparing the means of two independent populations (metric data) 258\u003c\/p\u003e \u003cp\u003eRule of thumb 2. Comparing the proportions of two independent populations (binary data) 259\u003c\/p\u003e \u003cp\u003e\u003cb\u003e18 The Chi‐squared (χ\u003csup\u003e\u003ci\u003e2\u003c\/i\u003e\u003c\/sup\u003e) test – what, why, and how? 261\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eOf all the tests in all the world – you had to walk into my hypothesis testing procedure 262\u003c\/p\u003e \u003cp\u003eUsing chi‐squared to test for related‐ness or for the equality of proportions 262\u003c\/p\u003e \u003cp\u003eCalculating the chi‐squared statistic 265\u003c\/p\u003e \u003cp\u003eUsing the chi-squared statistic 267\u003c\/p\u003e \u003cp\u003eYate’s correction (continuity correction) 268\u003c\/p\u003e \u003cp\u003eFisher’s exact test 268\u003c\/p\u003e \u003cp\u003eThe chi‐squared test with Minitab 269\u003c\/p\u003e \u003cp\u003eThe chi‐squared test with SPSS 270\u003c\/p\u003e \u003cp\u003eThe chi‐squared test for trend 272\u003c\/p\u003e \u003cp\u003eSPSS output for chi‐squared trend test 274\u003c\/p\u003e \u003cp\u003e\u003cb\u003e19 Testing hypotheses about the \u003ci\u003eratio \u003c\/i\u003eof two population parameters 276\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003ePreamble 276\u003c\/p\u003e \u003cp\u003eThe chi‐squared test with the risk ratio 277\u003c\/p\u003e \u003cp\u003eThe chi‐squared test with odds ratios 279\u003c\/p\u003e \u003cp\u003eThe chi‐squared test with hazard ratios 281\u003c\/p\u003e \u003cp\u003e\u003cb\u003eVIII Becoming Acquainted 283\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e20 Measuring the association between two variables 285\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003ePreamble – plotting data 286\u003c\/p\u003e \u003cp\u003eAssociation 287\u003c\/p\u003e \u003cp\u003eThe scatterplot 287\u003c\/p\u003e \u003cp\u003eThe correlation coefficient 290\u003c\/p\u003e \u003cp\u003ePearson’s correlation coefficient 290\u003c\/p\u003e \u003cp\u003eIs the correlation coefficient statistically significant in the population? 292\u003c\/p\u003e \u003cp\u003eSpearman’s rank correlation coefficient 294\u003c\/p\u003e \u003cp\u003e\u003cb\u003e21 Measuring agreement 298\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eTo agree or not agree: that is the question 298\u003c\/p\u003e \u003cp\u003eCohen’s kappa (\u003ci\u003eκ\u003c\/i\u003e) 300\u003c\/p\u003e \u003cp\u003eSome shortcomings of kappa 303\u003c\/p\u003e \u003cp\u003eWeighted kappa 303\u003c\/p\u003e \u003cp\u003eMeasuring the agreement between two metric continuous variables, the Bland–Altmann plot 303\u003c\/p\u003e \u003cp\u003e\u003cb\u003eIX Getting into a Relationship 307\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e22 Straight line models: linear regression 309\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eHealth warning! 310\u003c\/p\u003e \u003cp\u003eRelationship and association 310\u003c\/p\u003e \u003cp\u003eA causal relationship – explaining variation 312\u003c\/p\u003e \u003cp\u003eRefresher – finding the equation of a straight line from a graph 313\u003c\/p\u003e \u003cp\u003eThe linear regression model 314\u003c\/p\u003e \u003cp\u003eFirst, is the relationship linear? 315\u003c\/p\u003e \u003cp\u003eEstimating the regression parameters – the method of ordinary least squares (OLS) 316\u003c\/p\u003e \u003cp\u003eBasic assumptions of the ordinary least squares procedure 317\u003c\/p\u003e \u003cp\u003eBack to the example – is the relationship statistically significant? 318\u003c\/p\u003e \u003cp\u003eUsing SPSS to regress birthweight on mother’s weight 318\u003c\/p\u003e \u003cp\u003eUsing Minitab 319\u003c\/p\u003e \u003cp\u003eInterpreting the regression coefficients 320\u003c\/p\u003e \u003cp\u003eGoodness‐of‐fit, \u003ci\u003eR\u003csup\u003e2\u003c\/sup\u003e \u003c\/i\u003e320\u003c\/p\u003e \u003cp\u003eMultiple linear regression 322\u003c\/p\u003e \u003cp\u003eAdjusted goodness‐of‐fit: \u003ci\u003eR̄\u003c\/i\u003e\u003csup\u003e2\u003c\/sup\u003e\u003cb\u003e\u003csup\u003e \u003c\/sup\u003e\u003c\/b\u003e324\u003c\/p\u003e \u003cp\u003eIncluding nominal covariates in the regression model: design variables and coding 326\u003c\/p\u003e \u003cp\u003eBuilding your model. Which variables to include? 327\u003c\/p\u003e \u003cp\u003eAutomated variable selection methods 328\u003c\/p\u003e \u003cp\u003eManual variable selection methods 329\u003c\/p\u003e \u003cp\u003eAdjustment and confounding 330\u003c\/p\u003e \u003cp\u003eDiagnostics – checking the basic assumptions of the multiple linear regression model 332\u003c\/p\u003e \u003cp\u003eAnalysis of variance 333\u003c\/p\u003e \u003cp\u003e\u003cb\u003e23 Curvy models: logistic regression 334\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eA second health warning! 335\u003c\/p\u003e \u003cp\u003eThe binary outcome variable 335\u003c\/p\u003e \u003cp\u003eFinding an appropriate model when the outcome variable is binary 335\u003c\/p\u003e \u003cp\u003eThe logistic regression model 337\u003c\/p\u003e \u003cp\u003eEstimating the parameter values 338\u003c\/p\u003e \u003cp\u003eInterpreting the regression coefficients 338\u003c\/p\u003e \u003cp\u003eHave we got a significant result? statistical inference in the logistic regression model 340\u003c\/p\u003e \u003cp\u003eThe Odds Ratio 341\u003c\/p\u003e \u003cp\u003eThe multiple logistic regression model 343\u003c\/p\u003e \u003cp\u003eBuilding the model 344\u003c\/p\u003e \u003cp\u003eGoodness‐of‐fit 346\u003c\/p\u003e \u003cp\u003e\u003cb\u003e24 Counting models: Poisson regression 349\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003ePreamble 350\u003c\/p\u003e \u003cp\u003ePoisson regression 350\u003c\/p\u003e \u003cp\u003eThe Poisson regression equation 351\u003c\/p\u003e \u003cp\u003eEstimating β\u003csub\u003e1\u003c\/sub\u003e and β\u003csub\u003e2\u003c\/sub\u003e with the estimators \u003ci\u003eb\u003c\/i\u003e\u003csub\u003e0\u003c\/sub\u003e and \u003ci\u003eb\u003c\/i\u003e\u003csub\u003e1\u003c\/sub\u003e 352\u003c\/p\u003e \u003cp\u003eInterpreting the estimated coefficients of a Poisson regression, \u003ci\u003eb\u003c\/i\u003e\u003csub\u003e0\u003c\/sub\u003e and \u003ci\u003eb\u003c\/i\u003e\u003csub\u003e1\u003c\/sub\u003e 352\u003c\/p\u003e \u003cp\u003eModel building – variable selection 355\u003c\/p\u003e \u003cp\u003eGoodness‐of‐fit 357\u003c\/p\u003e \u003cp\u003eZero‐inflated Poisson regression 358\u003c\/p\u003e \u003cp\u003eNegative binomial regression 359\u003c\/p\u003e \u003cp\u003eZero‐inflated negative binomial regression 361\u003c\/p\u003e \u003cp\u003e\u003cb\u003eX Four More Chapters 363\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e25 Measuring survival 365\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003ePreamble 366\u003c\/p\u003e \u003cp\u003eCensored data 366\u003c\/p\u003e \u003cp\u003eA simple example of survival in a single group 366\u003c\/p\u003e \u003cp\u003eCalculating survival probabilities and the proportion surviving: the Kaplan–Meier table 368\u003c\/p\u003e \u003cp\u003eThe Kaplan–Meier curve 369\u003c\/p\u003e \u003cp\u003eDetermining median survival time 369\u003c\/p\u003e \u003cp\u003eComparing survival with two groups 370\u003c\/p\u003e \u003cp\u003eThe log‐rank test 371\u003c\/p\u003e \u003cp\u003eAn example of the log‐rank test in practice 372\u003c\/p\u003e \u003cp\u003eThe hazard ratio 372\u003c\/p\u003e \u003cp\u003eThe proportional hazards (Cox’s) regression model – introduction 373\u003c\/p\u003e \u003cp\u003eThe proportional hazards (Cox’s) regression model – the detail 376\u003c\/p\u003e \u003cp\u003eChecking the assumptions of the proportional hazards model 377\u003c\/p\u003e \u003cp\u003eAn example of proportional hazards regression 377\u003c\/p\u003e \u003cp\u003e\u003cb\u003e26 Systematic review and meta‐analysis 380\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIntroduction 381\u003c\/p\u003e \u003cp\u003eSystematic review 381\u003c\/p\u003e \u003cp\u003eThe forest plot 383\u003c\/p\u003e \u003cp\u003ePublication and other biases 384\u003c\/p\u003e \u003cp\u003eThe funnel plot 386\u003c\/p\u003e \u003cp\u003eSignificance tests for bias – Begg’s and Egger’s tests 387\u003c\/p\u003e \u003cp\u003eCombining the studies: meta‐analysis 389\u003c\/p\u003e \u003cp\u003eThe problem of heterogeneity – the Q and I\u003csup\u003e2\u003c\/sup\u003e tests 389\u003c\/p\u003e \u003cp\u003e\u003cb\u003e27 Diagnostic testing 393\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003ePreamble 393\u003c\/p\u003e \u003cp\u003eThe measures – sensitivity and specificity 394\u003c\/p\u003e \u003cp\u003eThe positive prediction and negative prediction values (PPV and NPV) 395\u003c\/p\u003e \u003cp\u003eThe sensitivity–specificity trade‐off 396\u003c\/p\u003e \u003cp\u003eUsing the ROC curve to find the optimal sensitivity versus specificity trade‐off 397\u003c\/p\u003e \u003cp\u003e\u003cb\u003e28 Missing data 400\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eThe missing data problem 400\u003c\/p\u003e \u003cp\u003eTypes of missing data 403\u003c\/p\u003e \u003cp\u003eMissing completely at random (MCAR) 403\u003c\/p\u003e \u003cp\u003eMissing at Random (MAR) 403\u003c\/p\u003e \u003cp\u003eMissing not at random (MNAR) 404\u003c\/p\u003e \u003cp\u003eConsequences of missing data 405\u003c\/p\u003e \u003cp\u003eDealing with missing data 405\u003c\/p\u003e \u003cp\u003eDo nothing – the wing and prayer approach 406\u003c\/p\u003e \u003cp\u003eList‐wise deletion 406\u003c\/p\u003e \u003cp\u003ePair‐wise deletion 407\u003c\/p\u003e \u003cp\u003eImputation methods – simple imputation 408\u003c\/p\u003e \u003cp\u003eReplacement by the Mean 408\u003c\/p\u003e \u003cp\u003eLast observation carried forward 409\u003c\/p\u003e \u003cp\u003eRegression‐based imputation 410\u003c\/p\u003e \u003cp\u003eMultiple imputation 411\u003c\/p\u003e \u003cp\u003eFull Information Maximum Likelihood (FIML) and other methods 412\u003c\/p\u003e \u003cp\u003eAppendix: Table of random numbers 414\u003c\/p\u003e \u003cp\u003eReferences 415\u003c\/p\u003e \u003cp\u003eSolutions to Exercises 424\u003c\/p\u003e \u003cp\u003eIndex 457\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default 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