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Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
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Searching... | 30000010062154 | QA278.8 D47 2004 | Open Access Book | Book | Searching... |
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Summary
Summary
Balancing the "cookbook" approach of some texts with the more mathematical approach of others, Nonparametric Statistical Methods for Complete and Censored Data introduces commonly used non-parametric methods for complete data and extends those methods to right censored data analysis. Whenever possible, the authors derive their methodology from the general theory of statistical inference and introduce the concepts intuitively for students with minimal backgrounds. Derivations and mathematical details are relegated to appendices at the end of each chapter, which allows students to easily proceed through each chapter without becoming bogged down in a lot of mathematics.
In addition to the nonparametric methods for analyzing complete and censored data, the book covers optimal linear rank statistics, clinical equivalence, analysis of block designs, and precedence tests. To make the material more accessible and practical, the authors use SAS programs to illustrate the various methods included.
Exercises in each chapter, SAS code, and a clear, accessible presentation make this an outstanding text for a one-semester senior or graduate-level course in nonparametric statistics for students in a variety of disciplines, from statistics and biostatistics to business, psychology, and the social scientists.
Prerequisites: Students will need a solid background in calculus and a two-semester course in mathematical statistics.
Author Notes
M. M. Desu is Emeritus Professor in the Department of Biostatistics, School of Public Health and Health Professions, University at Buffalo, State University of New York, Buffalo, USA.
Table of Contents
1 Procedures for a single sample | p. 1 |
1.1 Introduction | p. 1 |
1.2 Binary response | p. 1 |
1.2.1 Estimation of success probability | p. 2 |
1.2.2 Testing one-sided hypotheses about [theta] | p. 4 |
1.2.3 P-values for one-sided tests | p. 6 |
1.2.4 Power function of one-sided tests | p. 7 |
1.2.5 Sample size | p. 8 |
1.2.6 Testing a two-sided hypothesis about [theta] | p. 10 |
1.2.7 Confidence intervals for [theta] | p. 10 |
1.3 Complete data on continuous responses | p. 14 |
1.3.1 Point estimation of the median | p. 14 |
1.3.2 Sign test for testing a simple null hypothesis about the median | p. 15 |
1.3.3 Estimation of the cdf | p. 17 |
1.3.4 Estimation of survival function | p. 19 |
1.3.5 Point estimation of population percentiles | p. 20 |
1.3.6 Confidence intervals for percentiles | p. 21 |
1.3.7 Kolmogorov's goodness-of-fit test | p. 22 |
1.3.8 Confidence band for the population distribution function | p. 27 |
1.3.9 A plotting procedure | p. 28 |
1.4 Procedures for censored data | p. 30 |
1.4.1 Kaplan-Meier estimate of the survival function | p. 31 |
1.4.2 Estimation of the quartiles | p. 34 |
1.5 Appendix A1: Mathematical supplement | p. 35 |
A1.1 Binomial cdf expressed as a beta integral | p. 35 |
A1.2 Union intersection principle | p. 36 |
A1.3 Distribution of the rth order statistic | p. 37 |
A1.4 Confidence intervals for percentiles | p. 38 |
A1.5 Delta method | p. 39 |
A1.6 Relation between percentiles of Kolmogorov tests | p. 41 |
1.6 Appendix B1: Computer programs | p. 41 |
B1.1 (1 - [alpha]) quantile and [alpha] quantile of Bin(n, [theta]) distribution | p. 41 |
B1.2 Sample size calculation | p. 43 |
B1.3 Confidence limits for [theta] using beta percentiles | p. 45 |
B1.4 Large sample confidence limits for [theta] (Ghosh's method) | p. 46 |
B1.5 Critical values for a two-sided test for the median | p. 47 |
B1.6 Critical values for a two-sided test for a quantile | p. 49 |
B1.7 K-S goodness of fit | p. 51 |
B1.8 Kaplan-Meier estimation | p. 55 |
1.7 Problems | p. 57 |
1.8 References | p. 60 |
2 Procedures for two independent samples | p. 63 |
2.1 Introduction | p. 63 |
2.2 Two-sample problem with binary responses | p. 63 |
2.2.1 Testing the homogeneity hypothesis | p. 64 |
2.2.2 Fisher's exact test | p. 66 |
2.2.3 Establishing clinical equivalence | p. 69 |
2.2.4 Confidence interval for the risk difference [Delta] = [theta subscript 1] - [theta subscript 2] | p. 70 |
2.2.5 Confidence interval for the risk ratio [psi] = ([theta subscript 1]/[theta subscript 2]) | p. 71 |
2.2.6 Designing a parallel study | p. 73 |
2.3 Studies with categorical responses | p. 74 |
2.4 Methods for continuous responses | p. 76 |
2.4.1 Precedence tests--control median test (Mathisen's test) | p. 77 |
2.4.2 Combined sample percentile tests: Mood's median test | p. 82 |
2.4.3 Wilcoxon-Mann-Whitney procedure | p. 86 |
2.4.4 Analysis of proportional hazards model | p. 97 |
2.4.5 Smirnov test | p. 100 |
2.4.6 P-P plot for the two-sample problem | p. 104 |
2.4.7 Confidence interval for the difference between medians without shift assumption | p. 105 |
2.5 Linear rank statistics for the two-sample problem | p. 107 |
2.5.1 Location model (shift model) | p. 109 |
2.5.2 Proportional hazards model | p. 112 |
2.5.3 Scale model | p. 112 |
2.6 Analysis of censored data | p. 114 |
2.6.1 Gehan's Wilcoxon test | p. 114 |
2.6.2 Logrank test | p. 116 |
2.6.3 Tarone and Ware test | p. 118 |
2.6.4 Testing for equivalence with censored data | p. 120 |
2.7 Asymptotic relative efficiency (Pitman efficiency) | p. 122 |
2.8 Appendix A2: Mathematical supplement | p. 128 |
A2.1 Derivation of the conditional distribution of A given T = t | p. 128 |
A2.2 Maximum likelihood estimation in the case of clinical equivalence | p. 129 |
A2.3 Koopman's interval for the ratio of two binomial [theta]'s | p. 130 |
A2.4 Calculation of exact P-values for the problem of Section 2.3: Extension of Fisher's exact test | p. 132 |
A2.5 Some models that induce stochastic ordering | p. 133 |
A2.6 The null distribution of T[subscript a] | p. 137 |
A2.7 Confidence interval for [Delta] from Mathisen's test | p. 139 |
A2.8 A class of distribution-free statistics | p. 139 |
A2.9 The null distribution of V | p. 141 |
A2.10 Confidence interval for [Delta] from Mood's median test | p. 141 |
A2.11 Null distribution of the rank vector | p. 142 |
A2.12 Mean and variance of linear rank statistics | p. 146 |
A2.13 Motivation for the definition of U*[subscript XY] as in (2.78) | p. 147 |
A2.14 Two properties of midranks | p. 147 |
A2.15 Confidence interval for [Delta] from the WMW test | p. 149 |
A2.16 Score test statistic for the PH model | p. 150 |
A2.17 Expectation of V[subscript (i,N)], of Section 2.5 | p. 151 |
A2.18 Asymptotic distribution of X[subscript (k)] the kth order statistic of a random sample of size n | p. 152 |
A2.19 Proof of (2.101) | p. 153 |
2.9 Appendix B2: Computer programs | p. 154 |
B2.1 Fisher's test for a 2 X 2 table | p. 154 |
B2.2 Testing for clinical equivalence | p. 155 |
B2.3 Sample size for one-sided test | p. 157 |
B2.4 Analysis of a 2 X 3 table | p. 158 |
B2.5 Wilcoxon procedure for complete data | p. 159 |
B2.6 Wilcoxon test for ordered categorical data | p. 160 |
B2.7 Confidence interval for [Delta] from the WMW test | p. 162 |
B2.8 Savage test | p. 164 |
B2.9 The Smirnov test | p. 165 |
B2.10 Wilcoxon and logrank tests for censored data | p. 168 |
2.10 Problems | p. 170 |
2.11 References | p. 172 |
3 Procedures for paired samples | p. 177 |
3.1 Introduction | p. 177 |
3.2 Analysis of paired binary responses | p. 177 |
3.2.1 McNemar's large sample test for the equality of marginal distributions | p. 178 |
3.2.2 Exact test for equality of marginal distributions | p. 180 |
3.2.3 Testing for clinical equivalence | p. 181 |
3.2.4 Confidence interval for the difference [Delta] | p. 182 |
3.2.5 Sample size for equivalence trials | p. 183 |
3.2.6 Estimation of the ratio of marginal probabilities | p. 184 |
3.3 Complete data on continuous responses | p. 186 |
3.3.1 Sign test for complete paired data | p. 187 |
3.3.2 Wilcoxon signed rank test | p. 188 |
3.3.3 Rank transformed t-test | p. 192 |
3.3.4 Confidence interval for [Delta] corresponding to Wilcoxon signed rank test | p. 192 |
3.3.5 Analysis of cross-over designs | p. 193 |
3.4 Asymptotic relative efficiency | p. 194 |
3.5 Analysis of censored data | p. 195 |
3.5.1 A sign test for censored data | p. 195 |
3.5.2 A generalized signed rank test | p. 196 |
3.5.3 Paired Prentice-Wilcoxon test | p. 199 |
3.6 Appendix A3: Mathematical supplement | p. 200 |
A3.1 Maximum likelihood estimation of [theta subscript 10] | p. 200 |
A3.2 Approximate variance of [phi] | p. 200 |
A3.3 Symmetric property of the distribution of W | p. 201 |
A3.4 Mean and variance of V[subscript +], under the null hypothesis | p. 201 |
A3.5 Statistic V[subscript +] expressed in terms of Walsh averages | p. 203 |
A3.6 Some general results about E(V[subscript +]) | p. 203 |
A3.7 Confidence interval for [Delta], using Wilcoxon signed rank test | p. 204 |
3.7 Appendix B3: Computer programs | p. 205 |
B3.1 McNemar test | p. 205 |
B3.2 Confidence interval for the ratio [psi] | p. 206 |
B3.3 Confidence interval for risk difference [Delta] | p. 208 |
B3.4 Sign and signed rank procedures | p. 209 |
B3.5 Rank transformed t-test | p. 212 |
B3.6 Confidence interval for [Delta] difference in means | p. 214 |
3.8 Problems | p. 216 |
3.9 References | p. 219 |
4 Procedures for several independent samples | p. 221 |
4.1 Introduction | p. 221 |
4.2 Discrete responses | p. 222 |
4.2.1 Binary response studies | p. 222 |
4.2.2 Categorical data with c categories | p. 224 |
4.3 Continuous responses with complete data | p. 226 |
4.3.1 Kruskal-Wallis test | p. 226 |
4.3.2 Savage test | p. 228 |
4.3.3 Mood's median test | p. 229 |
4.3.4 Extension of Mathisen's test | p. 230 |
4.4 Multiple comparison procedures | p. 232 |
4.4.1 Steel-Dwass procedure based on pairwise rankings | p. 233 |
4.5 Jonckheere's test for completely ordered alternatives | p. 235 |
4.6 Comparison of several treatments with a control | p. 237 |
4.6.1 Steel's multiple comparison test | p. 238 |
4.6.2 Spurrier's procedure | p. 238 |
4.6.3 Slivka's control quantile test | p. 239 |
4.6.4 Fligner and Wolfe test | p. 239 |
4.6.5 Chakraborti and Desu test | p. 240 |
4.7 Censored data | p. 242 |
4.8 Appendix A4: Mathematical supplement | p. 245 |
A4.1 Pearson's x[superscript 2] statistic | p. 245 |
A4.2 Derivation of the variance of W[subscript J] | p. 247 |
A4.3 Tukey's studentized range statistic | p. 250 |
A4.4 Null variance of T[subscript FW] | p. 251 |
A4.5 Reformulation of the sum of censored data scores | p. 251 |
4.9 Appendix B4: Computer programs | p. 252 |
B4.1 Homogeneity of three samples | p. 252 |
B4.2 Analysis of several independent samples | p. 253 |
B4.3 Computation of Jonckheere's test | p. 256 |
B4.4 Comparison of survival in three groups | p. 258 |
4.10 Problems | p. 260 |
4.11 References | p. 263 |
5 Analysis of block designs | p. 267 |
5.1 Introduction | p. 267 |
5.2 RCB designs with binary responses | p. 267 |
5.3 RCB designs with continuous uncensored data | p. 270 |
5.3.1 Friedman's test | p. 270 |
5.4 Rank tests for RCB designs | p. 273 |
5.4.1 Median procedures | p. 275 |
5.4.2 Downton's procedure | p. 276 |
5.5 General block designs with continuous uncensored data | p. 278 |
5.5.1 Proportional cell frequencies | p. 280 |
5.5.2 Equal block sizes | p. 281 |
5.5.3 Unequal block sizes | p. 282 |
5.5.4 GRCB designs | p. 284 |
5.5.5 Wilcoxon scores procedure | p. 285 |
5.5.6 Blocked comparison of two treatments | p. 286 |
5.5.7 Balanced incomplete block (BIB) designs | p. 287 |
5.6 A multiple comparison procedure using Friedman's ranks | p. 289 |
5.7 Page test for ordered alternatives in RCB designs | p. 289 |
5.8 RCB designs with censored data | p. 292 |
5.8.1 Woolson-Lachenbruch rank tests | p. 292 |
5.8.2 Comparing two treatments in blocks (or strata) | p. 295 |
5.9 Appendix A5: Mathematical supplement | p. 297 |
A5.1 Covariance matrix of T of Section 5.3 | p. 297 |
A5.2 Derivation of (5.47) | p. 297 |
5.10 Appendix B5: Computer programs | p. 298 |
B5.1 Computation of Friedman's statistic | p. 298 |
B5.2 Analysis of within block ranks for a design with unequal block sizes | p. 300 |
B5.3 Computation of page statistic | p. 302 |
B5.4 Within strata statistics | p. 304 |
5.11 Problems | p. 307 |
5.12 References | p. 309 |
6 Independence, correlation, and regression | p. 311 |
6.1 Introduction | p. 311 |
6.2 Analysis of a bivariate sample | p. 311 |
6.2.1 Test for independence between categorical responses | p. 312 |
6.2.2 A measure of agreement-[kappa] | p. 314 |
6.3 Testing for correlation between continuous variables | p. 315 |
6.3.1 Spearman's rank correlation test | p. 317 |
6.3.2 Kendall's tau | p. 319 |
6.4 Linear regression | p. 322 |
6.4.1 Testing a hypothesis about the slope (Theil's test) | p. 322 |
6.4.2 Estimation of the slope | p. 323 |
6.5 Logistic regression | p. 324 |
6.5.1 Interpretation of [alpha] and [beta] | p. 325 |
6.5.2 Estimation of [alpha] and [beta] | p. 325 |
6.5.3 Logistic regression with several explanatory variables | p. 327 |
6.6 Procedures for censored data | p. 329 |
6.6.1 Test for independence | p. 329 |
6.6.2 Proportional hazards (PH) model | p. 332 |
6.7 Appendix A6: Mathematical supplement | p. 335 |
A6.1 Confidence interval for the slope | p. 335 |
A6.2 Maximum likelihood equations for logistic regression | p. 336 |
6.8 Appendix B6: Computer programs | p. 337 |
B6.1 Test for independence | p. 337 |
B6.2 Spearman's correlation and Kendall's tau | p. 339 |
B6.3 Fitting logistic model for Example 6.4 data | p. 340 |
B6.4 Fitting logistic model with several X-variables | p. 342 |
B6.5 PH regression model | p. 345 |
6.9 Problems | p. 347 |
6.10 References | p. 349 |
7 Computer-intensive methods | p. 351 |
7.1 Introduction | p. 351 |
7.2 Permutation tests and randomization tests | p. 351 |
7.3 Bootstrap methods | p. 354 |
7.4 References | p. 357 |
Answers to selected problems | p. 359 |
Subject Index | p. 361 |
Author Index | p. 365 |