Preface |
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xiii | |
Foreword |
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xv | |
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Introduction to the Statistical Analysis of Clinical Trials, Continuous Data Analysis |
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1 | (1) |
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1 | (1) |
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2 | (1) |
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2 | (1) |
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Biology is full of variations |
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2 | (1) |
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3 | (1) |
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4 | (1) |
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4 | (1) |
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5 | (1) |
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6 | (1) |
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7 | (1) |
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Reject the null-hypothesis |
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8 | (1) |
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9 | (1) |
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9 | (1) |
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10 | (2) |
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12 | (2) |
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Unpaired testing of paired samples |
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14 | (1) |
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Positive and negative correlations |
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15 | (1) |
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Unpaired analysis of variance (ANOVA) |
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15 | (2) |
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Paired analysis of variance (ANOVA) |
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17 | (1) |
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Non-parametric testing for skewed data |
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18 | (1) |
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Paired non-parametric test (Mann-Whitney) |
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19 | (1) |
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Unpaired non-parametric test (Wilcoxon rank sum) |
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20 | (2) |
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22 | (1) |
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22 | (3) |
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A negative study ≠ equivalent study, why so? |
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25 | (1) |
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25 | (1) |
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26 | (1) |
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27 | (1) |
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28 | (1) |
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29 | (1) |
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Equivalent and at the same time significantly different |
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29 | (1) |
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Overview of all possibilities |
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30 | (1) |
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31 | (1) |
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Robustness of equivalence trials |
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31 | (1) |
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31 | (1) |
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Crossover equivalence studies with different levels of correlation |
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32 | (1) |
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33 | (1) |
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34 | (3) |
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Definition of statistical power |
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37 | (1) |
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Statistics gives no certainties |
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37 | (1) |
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38 | (1) |
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39 | (1) |
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39 | (1) |
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40 | (1) |
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41 | (1) |
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Power gets larger when the mean gets larger |
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41 | (1) |
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42 | (1) |
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43 | (1) |
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Use of T-table to find power |
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43 | (2) |
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Use of T-table to find power, one more example |
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45 | (2) |
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Use of T-table to find power, one more example |
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47 | (2) |
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49 | (1) |
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49 | (1) |
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A simple method to calculate required sample size |
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49 | (1) |
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A more accurate method to calculate required sample size, power index method |
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50 | (1) |
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Sample size computations for continuous variables, example |
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50 | (1) |
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Other formulas to calculate required sample size |
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51 | (1) |
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Type I, type II and Type III errors |
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52 | (1) |
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53 | (1) |
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54 | (3) |
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Proportional Data Analysis, Part I |
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Safety data are, generally, summaries of patients with side effects |
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57 | (1) |
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57 | (1) |
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Standard deviation of proportion |
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58 | (1) |
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Why is SD of proportion √[p (1-p)] |
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58 | (1) |
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Method-1 to test difference between two groups of proportional data |
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58 | (2) |
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Normal table rather than t-table must be used for proportional data |
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60 | (1) |
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More easy way to test proportions is the χ2 test |
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61 | (1) |
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How to use the squared curve |
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62 | (1) |
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How the χ2 test for proportions works in practice: 1x2 table |
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63 | (1) |
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How the χ2 test for proportions works in practice: 2x2 table |
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63 | (1) |
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Alternative way to find the adequate χ2 -value: 2x2 table |
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64 | (1) |
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One more way to find the adequate χ2 -value, Fisher-exact test: 2x2 table |
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64 | (1) |
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With χ2 welcome to the real world of statistics because it can be used for kx2 tables |
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65 | (1) |
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McNemar's test for paired yes/no observations |
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65 | (1) |
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Differences between proportions can also be assessed by calculating the odds ratios (or) and its 95% confidence intervals (cis) and checking whether the confidence intervals cross 1.0 |
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66 | (1) |
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How to calculate 95% confidence intervals of an odds ratio with paired observations |
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66 | (1) |
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Survival analysis (Kaplan-Meier method) |
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67 | (1) |
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Testing significance of difference between 2 Kaplan-Meier curves |
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67 | (1) |
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Conclusions: what you should know |
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68 | (1) |
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68 | (5) |
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Proportional Data Analysis, Part II |
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73 | (1) |
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Choice of statistical method: A |
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74 | (1) |
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Choice of statistical method: B |
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74 | (1) |
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Choice of statistical method: C |
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75 | (1) |
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Elements of statistical analysis |
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75 | (1) |
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Example 1: one group of patients measured once |
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76 | (1) |
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Example 1: quantification |
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76 | (1) |
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Example 1: confidence interval |
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77 | (1) |
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Example 1: hypothesis test |
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78 | (1) |
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Standard normal distribution |
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79 | (1) |
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Standard normal distribution: p-value |
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79 | (1) |
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Example 1: graphical illustration |
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80 | (1) |
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Example 2: comparing two groups of patients |
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80 | (1) |
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81 | (1) |
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Example 2: graphical illustration |
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81 | (1) |
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Example 2: risk difference |
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82 | (1) |
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Example 2: confidence interval |
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82 | (1) |
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Example 2: graphical illustration |
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83 | (1) |
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Example 2: hypothesis testing |
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83 | (2) |
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85 | (1) |
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Example 2: graphical illustration of risk ratio (RR) and odds ratio (OR) |
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85 | (1) |
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Example 2: hypothesis testing |
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86 | (1) |
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Example 2: chi-square (= χ2) test |
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87 | (1) |
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Example 2: Fisher exact test |
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87 | (1) |
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88 | (1) |
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88 | (1) |
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Example 3: 1 sample, two measurements |
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89 | (1) |
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90 | (1) |
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Example 3: McNemar's test |
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91 | (1) |
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Example 4: >2 repeated measurements |
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91 | (1) |
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Example 4: Cochran's test |
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92 | (1) |
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Other repeated measurements designs |
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92 | (1) |
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Other repeated measurements designs: special techniques |
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93 | (1) |
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93 | (1) |
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94 | (1) |
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Kaplan-Meier curve: definition |
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95 | (1) |
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Hazard, cumulative hazard, survival curve |
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96 | (1) |
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Cumulative hazard function: example |
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96 | (1) |
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97 | (1) |
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Comparing survival curves: logrank test |
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98 | (1) |
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Comparing survival curves: comments |
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98 | (1) |
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99 | (1) |
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100 | (3) |
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103 | (1) |
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A lot of misunderstanding |
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103 | (1) |
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104 | (1) |
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A summary of meta-analyses helpful to cardiologists for everyday decision-making |
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104 | (1) |
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Proportions, standard errors of proportions, odds, odds ratios |
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105 | (1) |
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How to calculate 95% confidence intervals of an odds ratio |
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106 | (1) |
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Another summary of meta-analyses helpful to cardiologists for everyday decision-making |
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107 | (1) |
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Example of an epidemiological meta-analysis |
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107 | (1) |
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Important matters need few words |
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108 | (1) |
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Clearly defined prior hypotheses |
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108 | (1) |
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Thorough search of trials |
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109 | (1) |
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Strict inclusion criteria |
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110 | (1) |
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Uniform guidelines for data analysis |
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110 | (1) |
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Data analysis: first pitfall, publication bias |
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110 | (1) |
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Data analysis:second pitfall, heterogeneity |
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111 | (1) |
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111 | (1) |
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How to test heterogeneity, calculate and pool odds ratios of various studies and to test whether pooled odds ratios are different from 1.0, example |
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112 | (1) |
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What to do in case of heterogeneity |
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113 | (2) |
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Data analysis: third pitfall, lack of robustness |
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115 | (1) |
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Criticizms of meta-analyses |
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116 | (1) |
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Example of published meta-analysis |
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117 | (4) |
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Additional exercises to chapter 6 |
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121 | (2) |
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Interim analysis: looking at the data before closure |
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123 | (1) |
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123 | (1) |
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Data consistency and availability |
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124 | (1) |
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124 | (1) |
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Changing inclusion criteria |
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125 | (1) |
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125 | (1) |
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126 | (1) |
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126 | (1) |
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Correction for increasing type-I error rate |
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127 | (1) |
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128 | (1) |
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128 | (1) |
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129 | (1) |
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130 | (1) |
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Difference of two means (V) |
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130 | (1) |
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131 | (1) |
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131 | (2) |
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133 | (1) |
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133 | (1) |
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134 | (1) |
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134 | (1) |
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Example 1: graphical display |
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135 | (1) |
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136 | (1) |
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136 | (1) |
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137 | (1) |
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137 | (1) |
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138 | (1) |
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Example 1: another graphical display |
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139 | (1) |
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Corrected confidence intervals |
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139 | (1) |
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139 | (1) |
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140 | (1) |
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140 | (1) |
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141 | (1) |
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141 | (1) |
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Example 2: graphical display |
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142 | (1) |
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142 | (1) |
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143 | (1) |
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Example 2: graphical display |
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143 | (1) |
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144 | (1) |
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144 | (3) |
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Principles of Linear Regression |
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Paired observations: regression analysis is for predicting one observations from another |
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147 | (1) |
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Paired data plotted first |
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148 | (1) |
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Regression line, the equation |
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148 | (1) |
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149 | (1) |
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SPSS Statistical software to analyze data from paragraph 1 (stool data) |
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150 | (1) |
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Three columns of paired observations instead of two |
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151 | (1) |
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SPSS Statistical software to analyze the above data |
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151 | (1) |
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Another example of multiple linear regression model |
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152 | (1) |
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Multicollinearity testing of the above example |
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153 | (1) |
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Results from the above example |
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153 | (1) |
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154 | (1) |
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154 | (5) |
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Subgroup Analysis Using Regression Modeling |
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159 | (1) |
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Different regression models |
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160 | (1) |
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General form of regression models |
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160 | (1) |
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161 | (1) |
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Assumptions of the linear regression model |
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162 | (1) |
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Logistic and Cox regression model |
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163 | (1) |
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An example where the Cox model fits |
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164 | (1) |
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An example where the Cox model does not fit |
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165 | (1) |
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Increasing precision: example |
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166 | (1) |
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Increasing precision using a regression model |
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166 | (1) |
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Increasing precision: example of a regression model |
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167 | (1) |
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Increasing precision: graphical illustration |
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168 | (1) |
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168 | (1) |
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169 | (1) |
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169 | (1) |
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170 | (1) |
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170 | (1) |
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Interaction/synergism: example |
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171 | (1) |
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Interaction/synergism: graphical illustration |
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171 | (1) |
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Interaction/synergism: graphical illustration |
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172 | (1) |
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Interaction/synergism: warnings |
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172 | (1) |
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172 | (1) |
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173 | (2) |
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Relationship Among Statistical Distributions |
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Variables to assess clinical data |
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175 | (1) |
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Central tendency and spread of data |
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175 | (1) |
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Creating a chi-square distribution |
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176 | (1) |
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176 | (1) |
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How χ2 works in practice: 1 x 2 table |
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177 | (1) |
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How χ2 works in practice: 2 x 2 table |
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178 | (1) |
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With χ2 welcome to the real world of statistics because it can be used for k x 2 tables |
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178 | (1) |
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Why not χ2 for continuous data |
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179 | (1) |
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What is the advantage of a χ2 -test compared to a z -test (normal test) or t-test |
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180 | (1) |
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With chi-square welcome to the real world of statistics, because variance can be simply added up |
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180 | (1) |
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181 | (1) |
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More examples, how to calculate 95% confidence intervals of an odds ratio with unpaired observations |
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181 | (1) |
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More examples, how to calculate 95% confidence intervals of an odds ratio with paired observations |
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182 | (1) |
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More examples, how to calculate and pool odds ratios of various studies (unpaired data) |
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182 | (2) |
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More examples: heterogeneity of trials in a meta-analysis |
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184 | (1) |
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More examples, extension of chi-square is the F-distribution |
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184 | (1) |
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Limitations of statistical tests as discussed and conclusions |
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185 | (1) |
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Questions and exercises to Chapter 11 |
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186 | (3) |
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Statistics Is Not Bloodless Algebra |
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Biological processes are full of variations |
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189 | (1) |
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Statistics is fun for clinical investigators |
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189 | (1) |
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189 | (1) |
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Statistical principles improve quality of trial |
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190 | (1) |
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Statistics provides extras |
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190 | (1) |
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Statistics provides extras, special designs can manage what parallel designs cannot |
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190 | (1) |
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For example, interim analyses |
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190 | (1) |
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Statistics is not like algebra and requires biological thinking and just a bit of maths |
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191 | (1) |
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Statistics turns art into science |
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191 | (1) |
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Statistics for support rather than illumination? |
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192 | (1) |
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Statistics helps the clinician to better understand the limitations of research |
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192 | (1) |
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Limitations of statistics |
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193 | (1) |
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193 | (1) |
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193 | (4) |
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Bias Due to Conflicts of Interests, Some Guidelines |
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197 | (1) |
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The randomized controlled clinical trial as the gold standard |
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197 | (1) |
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Need for circumspection recognized |
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198 | (1) |
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The expanding commend of the pharmaceutical industry over clinical trials |
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198 | (1) |
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Flawed procedures jeopardizing current clinical trials |
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199 | (1) |
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200 | (1) |
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Further solutions to the dilemma between sponsored research and the independence of science |
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200 | (2) |
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202 | (1) |
Statistical Tables |
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203 | (8) |
Answers to Questions and Exercises |
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211 | (10) |
Index |
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221 | |