Details

Applied Medical Statistics


Applied Medical Statistics


1. Aufl.

von: Jingmei Jiang

103,99 €

Verlag: Wiley
Format: PDF
Veröffentl.: 01.04.2022
ISBN/EAN: 9781119716778
Sprache: englisch
Anzahl Seiten: 592

DRM-geschütztes eBook, Sie benötigen z.B. Adobe Digital Editions und eine Adobe ID zum Lesen.

Beschreibungen

<b>APPLIED MEDICAL STATISTICS</b> <p><b>An up-to-date exploration of foundational concepts in statistics and probability for medical students and researchers</B> <p>Medical journals and researchers are increasingly recognizing the need for improved statistical rigor in medical science. In <i>Applied Medical Statistics</i>, renowned statistician and researcher Dr. Jingmei Jiang delivers a clear, coherent, and accessible introduction to basic statistical concepts, ideal for medical students and medical research practitioners. The book will help readers master foundational concepts in statistical analysis and assist in the development of a critical understanding of the basic rationale of statistical analysis techniques. <p>The distinguished author presents information without assuming the reader has a background in specialized mathematics, statistics, or probability. All of the described methods are illustrated with up-to-date examples based on real-world medical research, supplemented by exercises and case discussions to help solidify the concepts and give readers an opportunity to critically evaluate different research scenarios. <p>Readers will also benefit from the inclusion of: <ul><li>A thorough introduction to basic concepts in statistics, including foundational terms and definitions, location and spread of data distributions, population parameters estimation, and statistical hypothesis tests</li> <li>Explorations of commonly used statistical methods, including t-tests,analysis of variance, and linear regression</li> <li>Discussions of advanced analysis topics, including multiple linear regression and correlation, logistic regression, and survival analysis</li> <li>Substantive exercises and case discussions at the end of each chapter</li></ul> <p>Perfect for postgraduate medical students, clinicians, and medical and biomedical researchers, <i>Applied Medical Statistics</i> will also earn a place on the shelf of any researcher with an interest in biostatistics or applying statistical methods to their own field of research.
<p>Preface xiii</p> <p>Acknowledgments xv</p> <p>About the Companion Website xvii</p> <p><b>1 What is Biostatistics </b><b>1</b></p> <p>1.1 Overview 1</p> <p>1.2 Some Statistical Terminology 2</p> <p>1.2.1 Population and Sample 2</p> <p>1.2.2 Homogeneity and Variation 3</p> <p>1.2.3 Parameter and Statistic 4</p> <p>1.2.4 Types of Data 4</p> <p>1.2.5 Error 5</p> <p>1.3 Workflow of Applied Statistics 6</p> <p>1.4 Statistics and Its Related Disciplines 6</p> <p>1.5 Statistical Thinking 7</p> <p>1.6 Summary 7</p> <p>1.7 Exercises 8</p> <p><b>2 Descriptive Statistics </b><b>11</b></p> <p>2.1 Frequency Tables and Graphs 12</p> <p>2.1.1 Frequency Distribution of Numerical Data 12</p> <p>2.1.2 Frequency Distribution of Categorical Data 16</p> <p>2.2 Descriptive Statistics of Numerical Data 17</p> <p>2.2.1 Measures of Central Tendency 17</p> <p>2.2.2 Measures of Dispersion 26</p> <p>2.3 Descriptive Statistics of Categorical Data 31</p> <p>2.3.1 Relative Numbers 31</p> <p>2.3.2 Standardization of Rates 34</p> <p>2.4 Constructing Statistical Tables and Graphs 38</p> <p>2.4.1 Statistical Tables 38</p> <p>2.4.2 Statistical Graphs 40</p> <p>2.5 Summary 47</p> <p>2.6 Exercises 48</p> <p><b>3 Fundamentals of Probability </b><b>53</b></p> <p>3.1 Sample Space and Random Events 54</p> <p>3.1.1 Definitions of Sample Space and Random Events 54</p> <p>3.1.2 Operation of Events 55</p> <p>3.2 Relative Frequency and Probability 58</p> <p>3.2.1 Definition of Probability 59</p> <p>3.2.2 Basic Properties of Probability 59</p> <p>3.3 Conditional Probability and Independence of Events 60</p> <p>3.3.1 Conditional Probability 60</p> <p>3.3.2 Independence of Events 60</p> <p>3.4 Multiplication Law of Probability 61</p> <p>3.5 Addition Law of Probability 62</p> <p>3.5.1 General Addition Law 62</p> <p>3.5.2 Addition Law of Mutually Exclusive Events 62</p> <p>3.6 Total Probability Formula and Bayes’ Rule 63</p> <p>3.6.1 Total Probability Formula 63</p> <p>3.6.2 Bayes’ Rule 64</p> <p>3.7 Summary 65</p> <p>3.8 Exercises 65</p> <p><b>4 Discrete Random Variable </b><b>69</b></p> <p>4.1 Concept of the Random Variable 69</p> <p>4.2 Probability Distribution of the Discrete Random Variable 70</p> <p>4.2.1 Probability Mass Function 70</p> <p>4.2.2 Cumulative Distribution Function 71</p> <p>4.2.3 Association Between the Probability Distribution and Relative Frequency Distribution 72</p> <p>4.3 Numerical Characteristics 73</p> <p>4.3.1 Expected Value 73</p> <p>4.3.2 Variance and Standard Deviation 74</p> <p>4.4 Commonly Used Discrete Probability Distributions 75</p> <p>4.4.1 Binomial Distribution 75</p> <p>4.4.2 Multinomial Distribution 80</p> <p>4.4.3 Poisson Distribution 82</p> <p>4.5 Summary 87</p> <p>4.6 Exercises 87</p> <p><b>5 Continuous Random Variable </b><b>91</b></p> <p>5.1 Concept of Continuous Random Variable 92</p> <p>5.2 Numerical Characteristics 93</p> <p>5.3 Normal Distribution 94</p> <p>5.3.1 Concept of the Normal Distribution 94</p> <p>5.3.2 Standard Normal Distribution 96</p> <p>5.3.3 Descriptive Methods for Assessing Normality 99</p> <p>5.4 Application of the Normal Distribution 102</p> <p>5.4.1 Normal Approximation to the Binomial Distribution 102</p> <p>5.4.2 Normal Approximation to the Poisson Distribution 105</p> <p>5.4.3 Determining the Medical Reference Interval 108</p> <p>5.5 Summary 109</p> <p>5.6 Exercises 110</p> <p><b>6 Sampling Distribution and Parameter Estimation </b><b>113</b></p> <p>6.1 Samples and Statistics 114</p> <p>6.2 Sampling Distribution of a Statistic 114</p> <p>6.2.1 Sampling Distribution of the Mean 115</p> <p>6.2.2 Sampling Distribution of the Variance 120</p> <p>6.2.3 Sampling Distribution of the Rate (Normal Approximation) 122</p> <p>6.3 Estimation of One Population Parameter 124</p> <p>6.3.1 Point Estimation and Its Quality Evaluation 124</p> <p>6.3.2 Interval Estimation for the Mean 126</p> <p>6.3.3 Interval Estimation for the Variance 130</p> <p>6.3.4 Interval Estimation for the Rate (Normal Approximation Method) 131</p> <p>6.4 Estimation of Two Population Parameters 132</p> <p>6.4.1 Estimation of the Difference in Means 132</p> <p>6.4.2 Estimation of the Ratio of Variances 136</p> <p>6.4.3 Estimation of the Difference Between Rates (Normal Approximation Method) 139</p> <p>6.5 Summary 141</p> <p>6.6 Exercises 141</p> <p><b>7 Hypothesis Testing for One Parameter </b><b>145</b></p> <p>7.1 Overview 145</p> <p>7.1.1 Concepts and Procedures 146</p> <p>7.1.2 Type I and Type II Errors 150</p> <p>7.1.3 One-sided and Two-sided Hypothesis 152</p> <p>7.1.4 Association Between Hypothesis Testing and Interval Estimation 153</p> <p>7.2 Hypothesis Testing for One Parameter 155</p> <p>7.2.1 Hypothesis Tests for the Mean 155</p> <p>7.2.1.1 Power of the Test 156</p> <p>7.2.1.2 Sample Size Determination 160</p> <p>7.2.2 Hypothesis Tests for the Rate (Normal Approximation Methods) 162</p> <p>7.2.2.1 Power of the Test 163</p> <p>7.2.2.2 Sample Size Determination 164</p> <p>7.3 Further Considerations on Hypothesis Testing 164</p> <p>7.3.1 About the Significance Level 164</p> <p>7.3.2 Statistical Significance and Clinical Significance 165</p> <p>7.4 Summary 165</p> <p>7.5 Exercises 166</p> <p><b>8 Hypothesis Testing for Two Population Parameters </b><b>169</b></p> <p>8.1 Testing the Difference Between Two Population Means: Paired Samples 170</p> <p>8.2 Testing the Difference Between Two Population Means: Independent Samples 173</p> <p>8.2.1 <i>t</i>-Test for Means with Equal Variances 173</p> <p>8.2.2 <i>F</i>-Test for the Equality of Two Variances 176</p> <p>8.2.3 Approximation <i>t</i>-Test for Means with Unequal Variances 178</p> <p>8.2.4 <i>Z</i>-Test for Means with Large-Sample Sizes 181</p> <p>8.2.5 Power for Comparing Two Means 182</p> <p>8.2.6 Sample Size Determination 183</p> <p>8.3 Testing the Difference Between Two Population Rates (Normal Approximation Method) 185</p> <p>8.3.1 Power for Comparing Two Rates 186</p> <p>8.3.2 Sample Size Determination 187</p> <p>8.4 Summary 188</p> <p>8.5 Exercises 189</p> <p><b>9 One-way Analysis of Variance </b><b>193</b></p> <p>9.1 Overview 193</p> <p>9.1.1 Concept of ANOVA 194</p> <p>9.1.2 Data Layout and Modeling Assumption 195</p> <p>9.2 Procedures of ANOVA 196</p> <p>9.3 Multiple Comparisons of Means 204</p> <p>9.3.1 Tukey’s Test 204</p> <p>9.3.2 Dunnett’s Test 206</p> <p>9.3.3 Least Significant Difference (LSD) Test 209</p> <p>9.4 Checking ANOVA Assumptions 211</p> <p>9.4.1 Check for Normality 211</p> <p>9.4.2 Test for Homogeneity of Variances 213</p> <p>9.4.2.1 Bartlett’s Test 213</p> <p>9.4.2.2 Levene’s Test 215</p> <p>9.5 Data Transformations 217</p> <p>9.6 Summary 218</p> <p>9.7 Exercises 218</p> <p><b>10 Analysis of Variance in Different Experimental Designs </b><b>221</b></p> <p>10.1 ANOVA for Randomized Block Design 221</p> <p>10.1.1 Data Layout and Model Assumptions 223</p> <p>10.1.2 Procedure of ANOVA 224</p> <p>10.2 ANOVA for Two-factor Factorial Design 229</p> <p>10.2.1 Concept of Factorial Design 230</p> <p>10.2.2 Data Layout and Model Assumptions 233</p> <p>10.2.3 Procedure of ANOVA 234</p> <p>10.3 ANOVA for Repeated Measures Design 240</p> <p>10.3.1 Characteristics of Repeated Measures Data 240</p> <p>10.3.2 Data Layout and Model Assumptions 242</p> <p>10.3.3 Procedure of ANOVA 243</p> <p>10.3.4 Sphericity Test of Covariance Matrix 245</p> <p>10.3.5 Multiple Comparisons of Means 248</p> <p>10.4 ANOVA for 2 × 2 Crossover Design 251</p> <p>10.4.1 Concept of a 2 × 2 Crossover Design 251</p> <p>10.4.2 Data Layout and Model Assumptions 252</p> <p>10.4.3 Procedure of ANOVA 254</p> <p>10.5 Summary 256</p> <p>10.6 Exercises 257</p> <p><b>11 χ<sup>2</sup> Test </b><b>261</b></p> <p>11.1 Contingency Table 262</p> <p>11.1.1 General Form of Contingency Table 263</p> <p>11.1.2 Independence of Two Categorical Variables 264</p> <p>11.1.3 Significance Testing Using the Contingency Table 265</p> <p>11.2 χ<sup>2</sup> Test for a 2 × 2 Contingency Table 266</p> <p>11.2.1 Test of Independence 266</p> <p>11.2.2 Yates’ Corrected χ<sup>2</sup> test for a 2 × 2 Contingency Table 269</p> <p>11.2.3 Paired Samples Design χ<sup>2</sup> Test 269</p> <p>11.2.4 Fisher’s Exact Tests for Completely Randomized Design 272</p> <p>11.2.5 Exact McNemar’s Test for Paired Samples Design 275</p> <p>11.3 χ<sup>2</sup> Test for <i>R </i>× <i>C </i>Contingency Tables 276</p> <p>11.3.1 Comparison of Multiple Independent Proportions 276</p> <p>11.3.2 Multiple Comparisons of Proportions 278</p> <p>11.4 χ<sup>2</sup> Goodness-of-Fit Test 280</p> <p>11.4.1 Normal Distribution Goodness-of-Fit Test 281</p> <p>11.4.2 Poisson Distribution Goodness-of-Fit Test 283</p> <p>11.5 Summary 284</p> <p>11.6 Exercises 285</p> <p><b>12 Nonparametric Tests Based on Rank </b><b>289</b></p> <p>12.1 Concept of Order Statistics 289</p> <p>12.2 Wilcoxon’s Signed-Rank Test for Paired Samples 290</p> <p>12.3 Wilcoxon’s Rank-Sum Test for Two Independent Samples 295</p> <p>12.4 Kruskal-Wallis Test for Multiple Independent Samples 299</p> <p>12.4.1 Kruskal-Wallis Test 299</p> <p>12.4.2 Multiple Comparisons 301</p> <p>12.5 Friedman’s Test for Randomized Block Design 303</p> <p>12.6 Further Considerations About Nonparametric Tests 306</p> <p>12.7 Summary 306</p> <p>12.8 Exercises 306</p> <p><b>13 Simple Linear Regression </b><b>311</b></p> <p>13.1 Concept of Simple Linear Regression 311</p> <p>13.2 Establishment of Regression Model 314</p> <p>13.2.1 Least Squares Estimation of a Regression Coefficient 314</p> <p>13.2.2 Basic Properties of the Regression Model 316</p> <p>13.2.3 Hypothesis Testing of Regression Model 317</p> <p>13.3 Application of Regression Model 321</p> <p>13.3.1 Confidence Interval Estimation of a Regression Coefficient 321</p> <p>13.3.2 Confidence Band Estimation of Regression Model 322</p> <p>13.3.3 Prediction Band Estimation of Individual Response Values 323</p> <p>13.4 Evaluation of Model Fitting 325</p> <p>13.4.1 Coefficient of Determination 325</p> <p>13.4.2 Residual Analysis 326</p> <p>13.5 Summary 327</p> <p>13.6 Exercises 328</p> <p><b>14 Simple Linear Correlation </b>331</p> <p><b>14.1 Concept of Simple Linear Correlation 331</b></p> <p>14.1.1 Definition of Correlation Coefficient 331</p> <p>14.1.2 Interpretation of Correlation Coefficient 334</p> <p>14.2 Hypothesis Testing of Correlation Coefficient 336</p> <p>14.3 Confidence Interval Estimation for Correlation Coefficient 338</p> <p>14.4 Spearman’s Rank Correlation 340</p> <p>14.4.1 Concept of Spearman’s Rank Correlation Coefficient 340</p> <p>14.4.2 Hypothesis Testing of Spearman’s Rank Correlation Coefficient 342</p> <p>14.5 Summary 342</p> <p>14.6 Exercises 343</p> <p><b>15 Multiple Linear Regression </b><b>345</b></p> <p>15.1 Multiple Linear Regression Model 346</p> <p>15.1.1 Concept of the Multiple Linear Regression 346</p> <p>15.1.2 Least Squares Estimation of Regression Coefficient 349</p> <p>15.1.3 Properties of the Least Squares Estimators 351</p> <p>15.1.4 Standardized Partial-Regression Coefficient 351</p> <p>15.2 Hypothesis Testing 352</p> <p>15.2.1 <i>F</i>-Test for Overall Regression Model 352</p> <p>15.2.2 <i>t</i>-Test for Partial-Regression Coefficients 354</p> <p>15.3 Evaluation of Model Fitting 356</p> <p>15.3.1 Coefficient of Determination and Adjusted Coefficient of Determination 356</p> <p>15.3.2 Residual Analysis and Outliers 357</p> <p>15.4 Other Aspects of Regression 359</p> <p>15.4.1 Multicollinearity 359</p> <p>15.4.2 Selection of Independent Variables 361</p> <p>15.4.3 Sample Size 364</p> <p>15.5 Summary 364</p> <p>15.6 Exercises 364</p> <p><b>16 Logistic Regression </b><b>369</b></p> <p>16.1 Logistic Regression Model 370</p> <p>16.1.1 Linear Probability Model 371</p> <p>16.1.2 Probability, Odds, and Logit Transformation 371</p> <p>16.1.3 Definition of Logistic Regression 373</p> <p>16.1.4 Inference for Logistic Regression 375</p> <p>16.1.4.1 Estimation of Model Coefficient 375</p> <p>16.1.4.2 Interpretation of Model Coefficient 378</p> <p>16.1.4.3 Hypothesis Testing of Model Coefficient 380</p> <p>16.1.4.4 Interval Estimation of Model Coefficient 382</p> <p>16.1.5 Evaluation of Model Fitting 385</p> <p>16.2 Conditional Logistic Regression Model 388</p> <p>16.2.1 Characteristics of Conditional Logistic Regression Model 390</p> <p>16.2.2 Estimation of Regression Coefficient 390</p> <p>16.2.3 Hypothesis Testing of Regression Coefficient 393</p> <p>16.3 Additional Remarks 394</p> <p>16.3.1 Sample Size 394</p> <p>16.3.2 Types of Independent Variables 394</p> <p>16.3.3 Selection of Independent Variables 395</p> <p>16.3.4 Missing Data 395</p> <p>16.4 Summary 395</p> <p>16.5 Exercises 396</p> <p><b>17 Survival Analysis </b><b>399</b></p> <p>17.1 Overview 400</p> <p>17.1.1 Concept of Survival Analysis 400</p> <p>17.1.2 Basic Functions of Survival Time 402</p> <p>17.2 Description of the Survival Process 405</p> <p>17.2.1 Product Limit Method 405</p> <p>17.2.2 Life Table Method 408</p> <p>17.3 Comparison of Survival Processes 410</p> <p>17.3.1 Log-Rank Test 410</p> <p>17.3.2 Other Methods for Comparing Survival Processes 413</p> <p>17.4 Cox’s Proportional Hazards Model 414</p> <p>17.4.1 Concept and Model Assumptions 415</p> <p>17.4.2 Estimation of Model Coefficient 417</p> <p>17.4.3 Hypothesis Testing of Model Coefficient 419</p> <p>17.4.4 Evaluation of Model Fitting 420</p> <p>17.5 Other Aspects of Cox’s Proportional Hazard Model 421</p> <p>17.5.1 Hazard Index 421</p> <p>17.5.2 Sample Size 421</p> <p>17.6 Summary 422</p> <p>17.7 Exercises 423</p> <p><b>18 Evaluation of Diagnostic Tests </b><b>431</b></p> <p>18.1 Basic Characteristics of Diagnostic Tests 431</p> <p>18.1.1 Sensitivity and Specificity 433</p> <p>18.1.2 Composite Measures of Sensitivity and Specificity 435</p> <p>18.1.3 Predictive Values 438</p> <p>18.1.4 Sensitivity and Specificity Comparison of Two Diagnostic Tests 440</p> <p>18.2 Agreement Between Diagnostic Tests 443</p> <p>18.2.1 Agreement of Categorical Data 444</p> <p>18.2.2 Agreement of Numerical Data 447</p> <p>18.3 Receiver Operating Characteristic Curve Analysis 448</p> <p>18.3.1 Concept of an ROC Curve 449</p> <p>18.3.2 Area Under the ROC Curve 450</p> <p>18.3.3 Comparison of Areas Under ROC Curves 453</p> <p>18.4 Summary 456</p> <p>18.5 Exercises 457</p> <p><b>19 Observational Study Design </b><b>461</b></p> <p>19.1 Cross-Sectional Studies 462</p> <p>19.1.1 Types of Cross-Sectional Studies 462</p> <p>19.1.2 Probability Sampling Methods 462</p> <p>19.1.3 Sample Size for Surveys 466</p> <p>19.1.4 Cross-Sectional Studies for Clues of Etiology 468</p> <p>19.2 Cohort Studies 469</p> <p>19.2.1 Measures of Association in Cohort Studies 469</p> <p>19.2.2 Sample Size for Cohort Studies 470</p> <p>19.3 Case-Control Studies 472</p> <p>19.3.1 Measures of Association in Case-Control Studies 472</p> <p>19.3.2 Sample Size for Case-Control Studies 473</p> <p>19.4 Summary 474</p> <p>19.5 Exercises 475</p> <p><b>20 Experimental Study Design </b><b>477</b></p> <p>20.1 Overview 478</p> <p>20.1.1 Basic Components of an Experimental Study 478</p> <p>20.1.2 Principles of Experimental Study Design 480</p> <p>20.1.3 Blinding Procedures in Clinical Trials 482</p> <p>20.2 Completely Randomized Design 483</p> <p>20.2.1 Concept of Completely Randomized Design 483</p> <p>20.2.2 Sample Size for Completely Randomized Design 485</p> <p>20.3 Randomized Block Design 486</p> <p>20.3.1 Concepts of Randomized Block Design 486</p> <p>20.3.2 Sample Size for Randomized Block Design 488</p> <p>20.4 Factorial Design 489</p> <p>20.5 Crossover Design 491</p> <p>20.5.1 Concepts of Crossover Design 491</p> <p>20.5.2 Sample Size for 2 × 2 Crossover Design 492</p> <p>20.6 Summary 493</p> <p>20.7 Exercises 493</p> <p>Appendix 495</p> <p>References 549</p> <p>Index 557</p>
<p><b>Jingmei Jiang, PhD,</b> is Professor of Biostatistics, as well as a Doctoral Tutor in the Institute of Basic Medical Sciences (IBMS) of the Chinese Academy of Medical Sciences (CAMS) and School of Basic Medicine of Peking Union Medical College (PUMC). She has edited or co-edited seven academic monographs on biostatistics, and is also an editorial board member of several international journals. She is undertaking several research projects at the National Natural Science Foundation of China and other agencies.</p>
<p><b>An up-to-date exploration of foundational concepts in statistics and probability for medical students and researchers</B></p> <p>Medical journals and researchers are increasingly recognizing the need for improved statistical rigor in medical science. In <i>Applied Medical Statistics</i>, renowned statistician and researcher Dr. Jingmei Jiang delivers a clear, coherent, and accessible introduction to basic statistical concepts, ideal for medical students and medical research practitioners. The book will help readers master foundational concepts in statistical analysis and assist in the development of a critical understanding of the basic rationale of statistical analysis techniques. <p>The distinguished author presents information without assuming the reader has a background in specialized mathematics, statistics, or probability. All of the described methods are illustrated with up-to-date examples based on real-world medical research, supplemented by exercises and case discussions to help solidify the concepts and give readers an opportunity to critically evaluate different research scenarios. <p>Readers will also benefit from the inclusion of: <ul><li>A thorough introduction to basic concepts in statistics, including foundational terms and definitions, location and spread of data distributions, population parameters estimation, and statistical hypothesis tests</li> <li>Explorations of commonly used statistical methods, including t-tests,analysis of variance, and linear regression</li> <li>Discussions of advanced analysis topics, including multiple linear regression and correlation, logistic regression, and survival analysis</li> <li>Substantive exercises and case discussions at the end of each chapter</li></ul> <p>Perfect for postgraduate medical students, clinicians, and medical and biomedical researchers, <i>Applied Medical Statistics</i> will also earn a place on the shelf of any researcher with an interest in biostatistics or applying statistical methods to their own field of research.