Index

addition rule, 106, 126 , 128 adjacent values, 76 , 128 adjusted rate, 13, 15 binomial probability, 126 agreement, 112 bioassay, 330 AIC. see Akaike Information Criterion blinded study Akaike Information Criterion, 418 double, 496 alpha, 198 triple, 496 (ANOVA), 253, 273 block, 273, 280 analysis of variance (ANOVA) table, 254, complete, 281 276, 310 fixed, 281 antibody response, 316 random, 284 antilog. see exponentiation factor. see block area under the density curve, 117, 124 Bonferroni’s type I error adjustment, 258 average. see mean , 76

, 7 case–control study, 2, 130, 199, 358, baseline hazard, 451, 456, 460 439, 494 Bayesian Information Criterion, 418 matched, 518 Bayes’ theorem, 111 pair matched, 464 Bernoulli distribution, 354 unmatched, 516, 520 mean, 359 censoring, 442 variance, 360 censoring indicator, 443 better treatment trials,COPYRIGHTED 505 central MATERIAL limit theorem, 115, 125, 146, 153, BIC. see Bayesian Information Criterion 182, 198, 236 binary characteristic, 2 chance, 103, 116 binary data. see variable, binary change rate, 10 binomial distribution, 126, 132 chi‐square distribution, 125

Introductory , Second Edition. Chap T. Le and Lynn E. Eberly. © 2016 John Wiley & Sons, Inc. Published 2016 by John Wiley & Sons, Inc. Companion website: www.wiley.com/go/Le/Biostatistics

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chi‐square test, 212, 458, 470, 471 , 22, 197, 211 difference in proportions, 203 contingency table, ordered, 219 generalized Wilcoxon, 449 continuity correction, 210, 215 likelihood ratio, 366, 368, 370, 394, 399, continuous data, 318 405, 417, 458, 480, 482 correlation, 78, 299 log rank, 449 autoregressive (AR), 425 Mantel–Haenszel, 207 compound symmetry, 413, 425 McNemar’s, 200, 467 exchangeable (see correlation, compound Pearson’s, 212, 387 symmetry) score, 366, 448, 480 induced, 412 Wald, 480 inter-correlation, 300 Yates’ corrected, 215 intra‐class (ICC), 413 , 358, 494 intra-correlation, 300 phase I, 497 Kendall’s tau (τ), 84 phase II, 499 non‐parametric, 83 phases I‐IV, 495 Pearson’s r, 80, 83 clustered study, 409 Spearman’s rho (ρ), 83 coefficient of correlation, 300 unstructured, 425 coefficient of determination, 308, 310 working, 425, 428 coefficient of multiple determination, 321 correlation coefficient, 81, 307 , 76 covariate. see predictor variable cohort‐escalation study, 497 covariate, time dependent, 461 , 14, 130, 385, 439, 494 Cox model. see proportional hazards model common odds ratio, 26 cross‐classified table. see contingency table comparisonwise error, 258 crossing survival curves, 449 complete case analysis, 410 crude rate, 13 compound event, 126 cure model, 449 concordance, 22, 84, 112, 219 cut point, 183, 184, 187, 188 category‐specific, 112 overall, 112 death rate conditional independence, 206 adjusted, 13, 16 conditional logistic regression, 472 crude, 13 , 142, 146, 192 follow‐up, 14 for a correlation coefficient, 161 death set, 452, 462 for a difference of , 152 decision making rule. see cut point for a difference of proportions, 157 degrees of freedom, 75, 125, 212, 236, 242, effect of sample size on, 148 254, 275, 310, 321, 387 for a hazard ratio, 453, 457 density, 114 for a mean, 148 density curve, 115, 117, 124 for a odds ratio, 157, 356, 363, 426, 467, dependent variable. see response variable 475, 479 derived variable analysis, 410 for a paired mean difference, 152 deterministic relationship, 79 for a proportion, 154 deviation, 73 for a regression coefficient, 415 diagnostic procedure, 5 relation to p value, 191 diagnostics, 287, 302, 419 for a relative risk, 394 dichotomous characteristic. see variable, binary confidence level, 148 dichotomous data. see variable, binary confounder, 3, 15, 25, 131, 151, 165, 199, difference of means, 152 206, 238, 464 difference of proportions, 202

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direct method, 16 Fisher’s transformation, 503 discordance, 21, 23, 84, 219, 466, 518 fixed effect, 280 discrete data. see variable, discrete force of mortality. see hazard function disease registry, 5 frequency dispersion, 73–78, 360, 402, 403. see also cumulative, 64 variance cumulative relative, 64 distribution relative, 104 , 147, 157, 160 , 56, 114 skewed, 63, 71, 73, 76 frequency polygon, 60 symmetric, 63, 76 F , 255, 276–278, 284, 310, 322, unimodal, 61 414, 425, 428 DLT. see dose‐limiting toxicity full model, 276 dose‐limiting toxicity, 497 dose‐response, 314, 317 Gaussian distribution. see Normal dummy variable, 302, 318, 332, 351, 363, distribution 393, 397, 399, 412, 443, 456, 463, 472, GEE. see Generalized 477, 478 Generalized Estimating Equations, 425, 428 model‐based , 425 effect robust (empirical) standard error, , 274, 277 425, 428 main, 274, 277, 400 generalized odds, 22 modification, 4, 206–207, 274, 276–278, general linear F test, 276 281, 312, 319, 364, 368, 399, 457, gold standard, 112 459, 479 , 360, 402, 416, 462 simple, 274, 277 goodness of fit statistic. see chi‐square test, estimate, 141 Pearson’s interval, 146 point, 145 hazard function, 441 estimator, unbiased, 143 hazard ratio, 441, 442, 453, 514 event time, 443 hazard ratio, constant, 442 exact statistic, 249, 250 , 60, 114 exclusion criteria, 496 hypothesis, 181 expected deaths, 16, 29, 447 alternative, 181, 198 expected frequencies, 212 composite, 193 expected value, 303, 320 global null, 277, 322, 366, 394, 458, 479 experimental study. see randomized study null, 181, 197, 235 experimental unit, 280 omnibus (see hypothesis, global null) wise error, 258 simple, 193 explanatory variable. see predictor variable hypothesis test, 181 exponential growth (decay), 315, 316 exponentiation, 158, 161 incidence, 13 exposure, 2 inclusion criteria, 496 independence null hypothesis, 212 factorial, 273, 274 independent events, 108, 126 factors. see factorial independent trials, 126 false negative, 6, 186 independent variable. see predictor variable false positive, 6, 107, 186 indicator variable. see dummy variable F distribution, 125 infant mortality rate, 129 Fisher’s exact statistic, 217 interaction. see effect modification

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intercept, 301, 302 McNemar’s chi‐square test, 200, 476 inter‐correlation, 300, 313 mean, 67, 69 inter‐quartile , 89 geometric, 71 interval density, 60 square, 254, 275 interval midpoint, 70 measurement scale, effect of, 454 intra‐correlation, 300 , 65, 72, 76 IQR. see inter‐quartile range median effective dose, 314 median test. see Wilcoxon rank sum test Kaplan–Meier curve, 444 midrange, 89 kappa, 113 misclassification, 5 category‐specific, 114 , 364, 394, 410 overall, 114 , 73 problem with, 114 morbidity, 13 k samples, binary, 215 mortality, 13 MTD. see maximum tolerated dose least squares estimation, 303, 320 multi‐level model, 421 , 164, 354, 363, 391, 393, multiple comparisons adjustment, 469, 473, 476, 478 258, 283 likelihood ratio test. see chi‐square test, multiple testing, 369, 399 likelihood ratio multiplication rule, 108, 126, 212 linear association, 81 linearity, 302, 318, 364, 393, 416, 454, 457, 479 negative predictive value, 110 linear , 411 nested models, 417 conditional mean, 424 normal curve, 114 marginal mean, 424 , 124, 290 population‐average intercept, 411 mean, 116 random intercept, 411 variance, 116 random slope, 415 subject‐specific intercept, 411 , 281 line graph, 9 observed size. see p value log hazard, 442 odds, 19, 157 logistic regression, 352, 424 odds, generalized, 21, 219 logistic regression, conditional, 472 odds ratio, 18, 108, 131, 158, 355, 363, 426, lognormal distribution, 125 466, 516, 518, 520 log odds, 357, 424 as approximation to relative risk, 19, log rank test, 448 131, 359 log rank test, stratified, 460 Mantel–Haenszel, 26, 207, 469 longitudinal study, 409 matched pairs, 132, 165, 469, 475 omnibus hypothesis. see hypothesis, Mantel–Haenszel odds ratio, 26, 206 global null margin of error, 499, 501 one‐sample matching, 131, 199, 472 binary, 197 advantages and disadvantages, 464 continuous, 235 , 468 one‐sided test, 133, 188, 198, 202, multiple‐to‐one, 468 236, 242 one‐to‐one, 466 one‐tailed. see one‐sided test maximum likelihood estimation, 164, 355, ordered contingency table, 21 391, 393, 414 outlier, 76 maximum tolerated dose, 495 overdispersion, 359, 387, 402

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paired‐sample, non‐parametric, 250 prospective study, 2, 130, 358, 439, 494 pair‐matched p value, 189, 194, 199 binary, 130, 199 p value, relation to confidence interval, 191 case‐control study, 130 continuous, 237, 250 QIC. see quasi‐likelihood information pairwise comparisons, 258 criterion parallel lines assumption, 460 quasi‐likelihood information criterion, parameter, 116, 141, 143, 198, 236 425–426, 428 partial likelihood function, 452, 456, 462 Pearson’s chi‐square test, 387 random effect, 280, 410, 414, 421 , 64, 76 randomization, 496 percentile score, 64 randomized complete block design, 419 person‐years method, 14, 385 randomized study, 281, 283 , 8 random sampling, 493 placebo, 496 random selection, 103 Poisson distribution, 128, 384 range, 56, 73 mean, 129, 384 rate, 10 offset (see Poisson distribution, size) ratio, 18 relation to binomial, 384, 391 receiver operating characteristic (ROC) size, 389, 391, 427, 431 curve, 373, 374 variance, 129, 384 reduced model, 276 , 383, 427 reference group, 21, 28, 364, 399, 442 polytomous data, 318 regression, 297, 299 pooled variance, 242 coefficient, 302, 318, 356, 363, 391, 393, population, 116, 145, 182 410, 425, 428, 453, 458 average coefficient, 424 logistic, 353, 363 target, 104, 305 multiple, 318, 351, 362, 393, 410, 423, positive predictive value, 110 456, 478 power, 193, 509 Poisson, 389, 393 predicted value, 287, 303, 320 polynomial, 319, 365, 396 prediction, 297, 299, 303 simple, 351, 389 predictor variable, 274, 297, 351, 383, 450 simple linear, 298, 301 prevalence, 5, 103, 111 stepwise, 331, 332, 334, 351, 365, 369, primary endpoint. see primary outcome 404, 459, 483 primary outcome, 99 rejection region, 187–189, 198, 236, 242 probability, 103, 104, 117 relative frequency, 58, 114 conditional, 108 relative hazard. see hazard ratio joint, 106 relative risk, 18, 29, 359, 391, 466, marginal, 106, 212 516, 518 unconditional, 109 repeated measures, 409 univariate, 107 , 281, 283, 418 probability density function, 124, 129, 164 reproducibility, 112, 145 product‐limit estimation, 444 residual, 287, 416 proportion, 1, 77, 103, 104, 153, 198 residual, studentized, 287 proportional hazard assumption, 459, 462 response variable, 273, 297, 352, 383, proportional hazards, 514 409, 473 proportional hazards model, 442, 451, 456 retrospective study, 2, 130, 358, 439, 494 proportional hazards model, for matched risk, 391 pairs data, 475 risk factor, 2, 298

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risk function. see hazard function small sample test, 217 risk ratio, 18 spaghetti plot, 411 risk set, 452, 462 specificity, 5, 110, 186, 373 R‐square, 310, 321 specific rate, 13 staggered entry, 440 sample, 104, 116, 145, 182 , 74, 78, 146 paired, 151 standard error, 146, 298 pair matched, 151, 165 of a difference of means, 152 small, 148, 149 of a difference of proportions, 157 two independent, 152 of a mean, 148 sample mean, 115 of a proportion, 153 sample proportion, 115 standardize, 122, 147, 198, 219, 236, 247, sample size, 499, 501, 502, 505–507, 509, 250, 308, 366, 396, 448 512, 514, 516, 518, 521 standardized mortality ratio, 28 sampling standardized rate, 13, 15 for a block design, 281 standard normal distribution, 116, 124, 198 random, 105 standard normal score. see z statistic repeated, 104, 116, 143, 147, 182, 187, standard population, 16 198, 236 statistic, 1, 116, 143, 198, 236, 298 without replacement, 143 statistical association, 22, 78, 79, 106, 108, , 182, 198, 236 113, 297, 299 sampling frame, 105 negative, 79, 81 sandwich estimator. see Generalized positive, 79, 81 Estimating Equations, robust , 141, 145 standard error statistical relationship. see statistical scaled deviance, 360, 402 association scaled Pearson chi‐square, 360, 402 stem‐and‐leaf plot, 68 scatter diagram. see stratification, 459 scatter plot, 55, 79, 302 stratification, for matched pairs, 475 score equation, 425, 428 subject specific coefficient, 424 . see chi‐square test, score sum of squares screening test, 5, 106, 186, 314, 372 between (SSB), 254, 275 seasonality, 333 within (SSW), 253, 275 sensitivity, 5, 107, 110, 186, 373 error, 275, 310, 321 separation power, 373, 374 model, 275 separator variable, 372, 374 regression, 310, 321 sequential probability ratio test, 507 total (SST), 253, 275, 309, 321 significance survey study, 493, 499 level, 188, 198 survival curve, 441 practical, 190 survival data, 440 statistical, 180, 188, 190 , 441 test, 179 survival rate. see survival function significant difference, minimum clinical, survival time, 440 505, 510 Simon two‐stage phase II study, 504 target population, 493 size of test. see type I error t distribution, 125, 149, 236, 242 , 290 mean, 125 slope, 301, 302 variance, 125

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test, 141 variable, 55, 124 test for independence, 212, 307 Bernoulli, 124 test statistic, 182, 187 binary, 2, 77, 126, 318, 352 treatment factor, 280 binomial, 352 t statistic, 308, 310, 323, 324, 326, 352, 414 categorical, 197 one‐sample, 236 continuous, 55, 124, 297 paired sample, 238, 476 dichotomous (see variable, binary) two‐sample, 242, 255 discrete, 55, 77, 125 t test. see t statistic point binomial (see variable, Bernoulli) Tukey’s type I error adjustment, 259 polytomous, 2, 298, 311, 318, 363, two‐sample 393, 456 binary, 202 variance, 73, 77 non‐parametric, 246 two‐sided test, 133, 188, 198, 202, 236, Wilcoxon generalized test, 448 242, 307 Wilcoxon rank sum test, 246, 260 two‐tailed. see two‐sided test Wilcoxon signed rank test, 250, 476 two‐way or 2x2 table. see contingency table type 1 analysis, 401 Yates’ corrected chi‐square test, 215 type 3 analysis, 400 type I error, 180, 182, 185, 188, 252, 258, z score. see z statistic 369, 399, 404, 459, 509 z statistic, 116, 122, 128, 129, 198, 200, 202, type II error, 180, 182, 185, 187, 509 207, 219, 247, 250, 367, 396, 425, 428, 448, 449, 458, 467, 480 unit of observation, 389 z test. see z statistic

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